Independent work Number 6. Topics: "dividers and multiple", "signs of divisibility", "Nod", "NOK", "Property of fractions", "Reduction of fractions", "action with fractions", "proportions", "scale", "Length and area of \u200b\u200bthe circle", "Coordinates", "opposite numbers", "Module Chi
Education is one of the most important components of human life. Its important should not be neglected even in the youngest years of the child. In order to achieve success, it is necessary to follow successfulness from an early age. So, the first class is perfect for this suitable.
Popularity is gaining an opinion that a two-way can build an excellent career, but it is not true. Of course, there are such cases in the form of Albert Einstein or Bill Gates, but it is rather an exception than the rules. If you turn to statistics, you can see that students with five and fours best of all surrenderThey easily occupy budget places.
Psychologists say about their superiority. They argue that such schoolchildren have collected and purposefulness. These are excellent leaders and managers. After the end of prestigious universities, they occupy leading places in companies, and sometimes they base their firms.
To achieve such success, you need to try. So, the student is obliged to visit movies, to do exercises. Everything examination and testsonly excellent assessments and points should be brought. At the same time, the working program will be learned.
What if difficulties arose?
The most problematic subject was and there will be mathematics. It is difficult to assimilate, but at the same time is a mandatory examination discipline. To assimilate it, you do not need to hire tutors or recorded on the circles. All that is needed is a notebook, a bit of free time and Reshebnik Yershova.
GDZ on the textbook for grade 6contains:
- right answers to any number. You can look after independent fulfillment of the task. This method will help test yourself and improve knowledge;
- if the topic remains notading, then you can analyze the provided task solutions;
- checking no longer represent labor, because the answer is on them.
Here everyone can find such a manual in online mode.
Topics: "Dividers and multiple", "signs of divisibility", "Nod", "NOK", "The property of fractions", "Reduction of fractions", "action with fractions", "proportions", "scale", "Length and area of \u200b\u200ba circle "," Coordinates "," opposite numbers "," module of the number "," Comparison of numbers "and others.
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Educational aids and simulators in the online store "Integral" for grade 6
Interactive simulator: "Rules and exercises in mathematics" for grade 6
Electronic workbook in mathematics for grade 6
Independent work №1 (I quarter) on the topics: "The divisibility of the number, dividers and multiple", "signs of divisibility"
Option I.1. Number 28 is specified. Find all its dividers.
2. Numbers are given: 3, 6, 18, 23, 56. Select the number of 4860 divisors.
3. Numbers are set: 234, 564, 642, 454, 535. Choose those that are divided by 3, 5, 7 without a residue.
4. Find such a number x so that 57x shall be divided without a balance at 5 and 7.
a) 900.
6. Find all dividers of the number 18, select the numbers that are multiple number 20.
Option II.
1. Number 39 is specified. Find all its dividers.
2. Numbers are given: 2, 7, 9, 21, 32. Choose the number of 3648 dividers from them.
3. Numbers are given: 485, 560, 326, 796, 442. Choose those that are divided by 2, 5, 8 without a residue.
4. Find such a number x so that 68x shall be divided without a residue to 4 and 9.
5. Find such a number Y that satisfies the conditions:
a) 820.
6. Write all dividers for the number 24, select the numbers that are multiple number 15.
Embodiment III.
1. Number 42 is specified. Find all its dividers.
2. Numbers are given: 5, 9, 15, 22, 30. Choose the number 4510 divisors from them.
3. Numbers are set: 392, 495, 695, 483, 196. Choose those that are divided by 4, 6 and 8 without a residue.
4. Find such a number x so that 78x shall be divided without a balance at 3 and 8.
5. Find such a number Y that satisfies the conditions:
a) 920.
6. Write all dividers for Numbers 32 and select the numbers that are multiple of the number 30.
Independent work number 2 (i quarter): "Simple and constituent numbers", "decomposition of simple factors", "Nod and Nok"
Option I.1. Explore numbers 28; 56 on simple factors.
2. Determine what numbers are simple, and which components: 25, 37, 111, 123, 238, 345?
3. Find all dividers for the number 42.
4. Find a node for numbers:
a) 315 and 420;
b) 16 and 104.
5. Find NOC for numbers:
a) 4, 5 and 12;
b) 18 and 32.
6. Decide the task.
The wizard has 2 wires with a length of 18 and 24 meters. He needs to cut both wires on pieces of equal length without residues. What length is slices?
Option II.
1. Explore numbers 36; 48 on simple factors.
2. Determine what numbers are simple, and which components: 13, 48, 96, 121, 237, 340?
3. Find all dividers for the number 38.
4. Find a node for numbers:
a) 386 and 464;
b) 24 and 112.
5. Find NOC for numbers:
a) 3, 6 and 8;
b) 15 and 22.
6. Decide the task.
In the mechanical workshop there are 2 pipes with a length of 56 and 42 meters. In the slices of what length should be cutting the pipes so that the length of all pieces is the same?
Embodiment III.
1. Explore the number 58; 32 on simple multipliers.
2. Determine what numbers are simple, and which components: 5, 17, 101, 133, 222, 314?
3. Find all dividers for the number 26.
4. Find a node for numbers:
a) 520 and 368;
b) 38 and 98.
5. Find NOC for numbers:
a) 4.7 and 9;
b) 16 and 24.
6. Decide the task.
Atelier needs to order a roll of fabrics for sewing costumes. What length should I order a roll so that it shall be shared without residues to pieces of 5 meters long and 7 meters?
Independent work number 3 (I quarter): "The main property of the fraction, a reduction of fractions", "bringing fractions to the general denominator", "Compare fractions"
Option I.1. Reduce the specified fractions. If the fraction is decimal, then imagine it in the form of an ordinary fraction: 12/20; 18/24; 0.55; 0.82.
2. A number of numbers are set: 12/20; 24/3; 0.70. Are there any number among them equal to the number 3/4?
a) 200 grams from tons;
b) 35 seconds from minute;
c) 5 cm from the meter.
4. Bring the shot 6/9 to the denominator 54.
a) 7/9 and 4/6;
b) 9/14 and 15/18.
6. Decide the task.
The length of the red pencil is equal to 5/8 of the decimeter, and the length of the blue pencil is 7/10 decimeter. What pencil is longer?
7. Compare the fraction.
a) 4/5 and 7/10;
b) 9/12 and 12/16.
Option II.
1. Reduce the specified fractions. If the fraction is decimal, then imagine it in the form of an ordinary fraction: 18/22; 9/15; 0.38; 0.85.
2. A number of numbers are set: 14/24; 2/4; 0.40. Are there any number among them equal to the number 2/5?
3. What part of the whole part is part?
a) 240 grams from tons;
b) 15 seconds from minute;
c) 45 cm from the meter.
4. Track 7/8 to the denominator 40.
5. Give a fraction to a common denominator.
a) 3/7 and 6/9;
b) 8/14 and 12/16.
6. Decide the task.
The bag with potatoes weighs 5/12 centners, and the bag with grain weighs 9/17 centner. What is easier: potatoes or grain?
7. Compare the fraction.
a) 7/8 and 3/4;
b) 7/15 and 23/25.
Embodiment III.
1. Reduce the specified fractions. If the fraction is decimal, then imagine it in the form of an ordinary fraction: 8/14; 16/20; 0.32; 0.15.
2. A number of numbers are set: 20/3; 10/18; 0.80; 6/20. Are there any number among them equal to the number 5/8?
3. What part of the whole part of the part:
a) 450 grams from ton;
b) 50 seconds from a minute;
c) 3 dm from meter.
4. Bring the fraction 4/5 to the denominator 30.
5. Give a fraction to a common denominator.
a) 2/5 and 6/7;
b) 3/12 and 12/18.
6. Decide the task.
One machine weighs 12/25 tons, and the second machine weighs 7/18 tons. What machine is easier?
7. Compare the fraction.
a) 7/9 and 4/6;
b) 5/7 and 8/10.
Independent work number 4 (II quarter): "Addition and subtraction of fractions with different denominators", "Addition and subtraction of mixed numbers"
Option I.1. Perform steps with fractions: a) 7/9 + 4; / 6; b) 5/7 - 8; / 10; c) 1/2 + (3; / 7 - 0.45).
2. Decide the task.
The length of the first board is equal to 4/7 meters, the length of the second board is 7/12 meters. What board is longer and how much?
3. Decide equations: a) 1/3 + x \u003d 5/4; b) z - 5/18 \u003d 1/7.
4. Decide examples with mixed numbers: a) 3 - 1 7/12 + 2; / 6; b) 1 2/5 + 2 3; / 8 - 0.6.
5. Decide equations with mixed numbers: a) 1 1/7 + x \u003d 4 5/9; b) y - 3/7 \u003d 1/8.
6. Decide the task.
Workers spent 3/8 parts of the working time on the preparation of the workplace and 2/16 parts - to clean the territory after work. The rest of the time they worked. How much time did they work if the working day lasted 8 hours?
Option II.
1. Perform actions with fractions: a) 7/12 + 8; / 15; b) 3/9 - 6; / 8; c) 4/5 + (5; / 8 - 0.54).
2. Decide the task.
A red piece of fabric is equal to 3/5 meters, the blue slicing length is 8/13 meters. Which of the pieces is longer and how much?
3. Decide equations: a) 2/5 + x \u003d 9/11; b) z - 8/14 \u003d 1/7.
4. Decide examples with mixed numbers: a) 5 - 2 8/9 + 4; / 7; b) 2 2/7 + 3 1; / 4 - 0.7.
5. Decide equations with mixed numbers: a) 2 5/9 + x \u003d 5 8/14; b) y - 6/9 \u003d 1/5.
6. Decide the task.
The secretary talked on the phone 3/12 hours, and compiled a letter for 2/6 hours longer than talked by phone. All the rest of the time he put in order a workplace. How long did the secretary put in order his workplace in order if at work he was 1 hour?
Embodiment III.
1. Perform steps with fractions: a) 8/9 + 3; / 11; b) 4/5 - 3; / 10; c) 2/9 + (2; / 5 - 0.70).
2. Decide the task.
If I have 2 notebooks. The first notebook thickness 3/5 centimeters, the second notebook with a thickness of 8/12 centimeter. Which of the notebooks is thicker and what is the total thickness of the notebooks?
3. Decide equations: a) 5/8 + x \u003d 12/15; b) z - 7/8 \u003d 1/16.
4. Decide examples with mixed numbers: a) 7 - 3 8/11 + 3; / 15; b) 1 2/7 + 4 2; / 7 - 1.7.
5. Decide equations with mixed numbers: a) 1 5/7 + x \u003d 4 8/2; b) y - 8/10 \u003d 2/7.
6. Decide the task.
Having come home after school, Kolya 1/15 hours soap hands, then 2/6 hours he warmed food. After that, he dined. How much time he ate, if dinner passed twicest longer than in order to wash his hands and warm dinner?
Independent work number 5 (II quarter): "Multiplication of the number", "Finding a fraction from the whole"
Option I.1. Perform actions with fractions: a) 2/7 * 4/5; b) (5/8) 2.
2. Find the value of the expression: 3/7 * (5/6 + 1/3).
3. Decide the task.
The cyclist was driving at a speed of 15 km / h for 2/4 hours and at a speed of 20 km / h - 2 3/4 hours. What distance drove a cyclist?
4. Find 2/9 from 18.
5. In the circle, 15 students are engaged. Of these - 3/5 boys. How many girls do in the mathematical circle?
Option II.
1. Perform steps with fractions: a) 5/6 * 4/7; b) (2/3) 3.
2. Find the value of the expression: 5/7 * (12/15 - 4/12).
3. Decide the task.
The traveler walked at a speed of 5 km / h for 2/5 hours and at a speed of 6 km / h - 1 2/6 hours. What distance passed a traveler?
4. Find 3/7 from 21.
5. The sections are engaged in 24 athletes. Of these - 3/8 girls. How many young men do in the section?
Embodiment III.
1. Perform steps with fractions: a) 4/11 * 2/3; b) (4/5) 3.
2. Find the value of the expression: 8/9 * (10/16 - 1/7).
3. Decide the task.
The bus drove at a speed of 40 km / h within 1 2/4 hours and at a speed of 60 km an hour for 4/6 hours. What distance drove the bus?
4. Find 5/6 from 30.
5. In the village of 28 houses. Of these - 2/7 two-story. The rest are one-story. How many single-storey houses in the village?
Independent work number 6 (III quarter): "The distribution property of multiplication", "mutually reverse numbers"
Option I.1. Perform actions with fractions: a) 3 * (2/7 + 1/6); b) (5/8 - 1/4) * 6.
2. Find numbers inversely specified: a) 5/13; b) 7 2/4.
3. Decide the task.
Master and his assistant must make 80 details. Master made 1/4 part of the details. His assistant did 1/5 of what Master did. How many details do they need to do to execute the plan?
Option II.
1. Perform steps with fractions: a) 6 * (2/9 + 3/8); b) (7/8 - 4/13) * 8.
2. Find numbers inversely specified. a) 7/13; b) 7 3/8.
3. Decide the task.
On the first day, Pope planted 1/5 part of the trees. Mom planted 75% of what the dad was planted. How many trees need to be planted if 20 trees should grow in the garden?
Embodiment III.
1. Perform steps with fractions: a) 7 * (3/5 + 2/8); b) (6/10 - 1/4) * 8.
2. Find numbers inversely specified. a) 8/11; b) 9 3/12.
3. Decide the task.
On the first day, tourists passed 1/5 part of the route. On the second day - another 3/2 part of the route, which passed in the first day. How many kilometers should they still pass if the length of the route is 60 km?
Independent work number 7 (III quarter): "Decision", "Finding a number on his fraction"
Option I.1. Perform actions with fractions: a) 2/7: 5/9; b) 5 5/12: 7 1/2.
2. Find the value of the expression: (2/8 + (1/2) 2 + 1 5/8): 17/6.
3. Decide the task.
The bus drove 12 km. This was 2/6 ways. How many kilometers should the bus go?
Option II.
1. Perform steps with fractions: a) 8/9: 5/7; b) 4 1/1 11: 2 1/5.
2. Find the value of the expression: (2/3 + (1/3) 2 + 1 5/9): 7/21.
3. Decide the task.
Traveler passed 9 km. This was 3/8 tracks. How many kilometers should the traveler go?
Embodiment III.
1. Perform steps with fractions: a) 5/6: 7/10; b) 3 1/6: 2 2/3.
2. Find the value of the expression: (3/4 + (1/2) 2 + 4 2/8): 21/24.
3. Decide the task.
The athlete ran 9 km. This was 2/3 distances. What distance should the athlete be overcome?
Independent work number 8 (III quarter): "Relations and proportions", "Direct and reverse proportional dependence"
Option I.1. Find numbers ratio: a) 146 to 8; b) 5.4 K 2/5.
2. Decide the task.
Sasha has 40 brands, and Petit - 60. Which time Petit is more brands than Sasha? Express the answer in relationships and in percent.
3. Decide equations: a) 6/3 \u003d y / 4; b) 2.4 / 5 \u003d 7 / z.
4. Decide the task.
It was planned to collect 500 kg of apples, but the brigade exceeded the plan by 120%. How many kg of apples collected a brigade?
Option II.
1. Find numbers ratio: a) 133 K 4; b) 3.4 K 2/7.
2. Decide the task.
Paul has 20 icons, and Sasha - 50. How many times did Paul have fewer icons than Sasha? Express the answer in relationships and in percent.
3. Decide equations: a) 7/5 \u003d y / 3; b) 5.8 / 7 \u003d 8 / z.
4. Decide the task.
Workers were to put 320 meters of asphalt, but exceeded the plan by 140%. How many meters asphalt laid the workers?
Embodiment III.
1. Find the number of numbers: a) 156 to 8; b) 6.2 K 2/5.
2. Decide the task.
Oli has 32 flags, Lena - 48. How many times the Olya flags are less than the Lena? Express the answer in relationships and in percent.
3. Decide equations: a) 8/9 \u003d y / 4; b) 1.8 / 12 \u003d 7 / z.
4. Decide the task.
Grade 6 guys planned to assemble 420 kg of waste paper. But they collected 120% more. How many waste paper gathered guys?
Independent work number 9 (III quarter): "Scale", "Circle Length and Circle Square"
Option I.1. Card scale 1: 200. What are the length and width of the rectangular platform, if they are equal to 2 and 3 cm on the map?
2. Two points are distant from each other by 40 km. On the map this distance is 2 cm. What is the scale of the card?
3. Locate the circumference length if its diameter is 15 cm. The number pi \u003d 3.14.
4. Find the circle area if its diameter is 32 cm. The number pi \u003d 3.14.
Option II.
1. Map scale 1: 300. What are the length and width of the rectangular platform, if on the map they are equal to 4 and 5 cm?
2. Two points are distant from each other by 80 km. On the map this distance is 4 cm. What is the scale of the card?
3. Locate the circumference length if its diameter is 24 cm. The number pi \u003d 3.14.
4. Find the area of \u200b\u200bthe circle if its diameter is 45 cm. The number pi \u003d 3.14.
Embodiment III.
1. Map scale 1: 400. What are the length and width of the rectangular platform, if on the map they are equal to 2 and 6 cm?
2. Two points are distant from each other by 30 km. On the map this distance is 6 cm. What is the scale of the card?
3. Locate the circumference length if its diameter is 45 cm. The number pi \u003d 3.14.
4. Find the area of \u200b\u200bthe circle if its diameter is 30 cm. The number pi \u003d 3.14.
Independent work number 10 (IV quarter): "Coordinates on a straight", "opposite numbers", "module of the number", "Comparison of numbers"
Option I.1. Indicate on the coordinate direct number: A (4); & nbsp b (8,2); & NBSP C (-3.1); & nbsp d (0.5); & NBSP E (- 4/9).
2. Find numbers opposite to specified: -21; & NBSP 0.34; & NBSP -1 4/7; & NBSP 5.7; & NBSP 8 4/19.
3. Find the numbers module: 27; & nbsp -4; & NBSP 8; & nbsp -3 2/9.
4. Perform: | 2.5 | * | -7 | - | 3 1/3 | * | - 3/5 |.
a) 3/4 and 5/6,
b) -6 4/7 and -6 5/7.
Option II.
1. Indicate on the coordinate direct number: A (2); & nbsp b (11,1); & NBSP C (0.3); & nbsp d (-1); & NBSP E (-4 1/3).
2. Find numbers opposite to the specified: -30; & nbsp 0.45; & NBSP -4 3/8; & NBSP 2.9; & nbsp -3 3/14.
3. Find the numbers module: 12; & nbsp -6; & NBSP 9; & nbsp -5 2/7.
4. Perform: | 3.6 | * | - 8 | - | 2 5/7 | * | -7 / 5 |.
5. Compare numbers and write down the result in the form of inequality:
a) 2/3 and 5/7;
b) -3 4/9 and -3 5/9.
Embodiment III.
1. Indicate on the coordinate direct number: A (3); & nbsp b (7); & nbsp c (-4,5); & nbsp d (0); & NBSP E (-3 1/7).
2. Find numbers opposite to the specified: -10; & NBSP 12.4; & NBSP -12 3/11; & NBSP 3.9; & nbsp -5 7/11.
3. Find the numbers module: 4; & nbsp -6.8; & NBSP 19; & nbsp -4 3/5.
4. Perform: | 1.6 | * | -2 | - | 3 8/9 | * | - 3/7 |.
5. Compare numbers and write down the result in the form of inequality:
a) 1/4 and 2/9;
b) -5 12/17 and -5 14/17.
Independent work №11 (IV quarter): "Multiplication and division of positive and negative numbers"
Option I.a) 5 * (-4);
b) -7 * (-0,5).
2. Perform:
a) 12 * (-4) + 5 * (-6) + (-4) * (-3).
b) (4 6/3 - 7) * (- 6/3) - (-4) * 3.
a) -4: (-9);
b) -2.7: 6/14.
4. Decide the following equation: 2/5 Z \u003d 1 8/10.
Option II.
1. Perform multiplication of the following numbers:
a) 3 * (-14);
b) -2,6 * (-4).
2. Perform:
a) (-3) * (-2) - 3 * (-4) - 5 * (-8);
b) (-2 3/6 - 8) * (-2 7/9) - (-2) * 4.
3. Perform the division of the following numbers:
a) -5: (-7);
b) 3.4: (- 6/10).
4. Decide the following equation: 6/10 y \u003d 3/4.
Embodiment III.
1. Perform multiplication of the following numbers:
a) 2 * (-12);
b) -3.5 * (-6).
2. Perform:
a) (-6) * 2 + (-5) * (-8) + 5 * (-12);
b) (-3 4/5 + 7) * (2 4/8) + (-6) * 7.
3. Perform the division of the following numbers:
a) -8: 5;
b) -5.4: (- 3/8).
4. Decide the following equation: 4 1/6 Z \u003d - 5/4.
Independent work number 12 (IV quarter): "Action with rational numbers", "brackets"
Option I.1. Prepare the following numbers in the form of x / y: 2 5/6; & NBSP 7.8; & NBSP - 12 3/8.
2. Perform the steps: (- 5/7) * 7 + 2 2/7 * (-2 1/1 14).
a) 4.5 + (2.3 - 5,6);
b) (44.76 - 3.45) - (12.5 - 3.56).
4. Simplify the expression: 5a - (2a - 3b) - (3a + 5b) - a.
Option II.
1. Prepare the following numbers in the form of x / y: 3 2/3; & nbsp -2.9; & NBSP -3 4/9.
2. Perform: 2 3/9 * 4 - 1 2/9 * (- 1/3).
3. Perform the action correctly opening brackets:
a) 5.1 - (2,1 + 4.6);
b) (12.7 - 2.6) - (5.3 + 3,1).
4. Simplify the expression: z + (3z - 3Y) - (2z - 4y) - z.
Embodiment III.
1. Prepare the following numbers in the form of x / y: -1 5/7; & NBSP 5.8; & NBSP -1 3/5.
2. Perform: (- 2/5) * (8 - 2 3/5) * 3 2/15.
3. Perform the action correctly opening brackets:
a) 0.5 - (2.8 + 2.6);
b) (10.2 - 5,6) - (2.7 + 6,1).
4. Simplify the expression: C + (6D - 2C) - (D - 4C) - C.
Independent work №13 (IV quarter): "coefficients", "similar terms"
Option I.1. Simplify the expression: 5x + (3x + 3 4/2) + (2x - 4/4).
2. What are the coefficients at x?
a) 5x * (-3);
b) (-4.3) * (s).
3. Decide equations:
a) 4x + 5 \u003d 3x + 7;
b) (A - 2) / 3 \u003d 2.4 / 1.2.
Option II.
1. Simplify the expression: y - (2y + 1 2/3) - (y - 4/6).
2. What are the coefficients at y?
a) 3ow * (-2);
b) (-1,5) * (-Y).
3. Decide equations:
a) 4y - 3 \u003d 2y + 7;
b) (A - 3) / 4 \u003d 4.8 / 8.
Embodiment III.
1. Simplify the expression: (3z - 1 3/5) + (Z - 2/10).
2. What are the coefficients at a?
a) -3,4a * 3;
b) 2.1 * (-a).
3. Decide equations:
a) 3z - 5 \u003d z + 7;
b) (B - 3) / 8 \u003d 5.6 / 4.
Option I.
1. 1,2,4,7,14,28.
2. 3, 6, 18.
3. 3 is divided into 234, 564, 642; 7 is not divided into one number; 535 divides 535.
4. 35.
5. 940.
6. 1,2.
Option II.
1. 1,3,13,39.
2. 2,32.
3. 2 is divided by 560, 326, 796, 442; 5 is divided by 485, 560; 8 is divided by 560.
4. 36.
5. 840.
6. 1,3.
Embodiment III.
1. 1,2,3,6,7,14,21,42.
2. 5,22.
3. 4 for 392, 196; 6 is not divided into one number; 8 is divided into 392.
4. 24.
5. 990.
6. 1,2.
Option I.
1. $28=2^2*7$; $56=2^3*7$.
2. Simple: 37, 111. Composite: 25, 123, 238, 345.
3. 1,2,36,7,14,21,42.
4. a) node (315, 420) \u003d 105; b) Node (16, 104) \u003d 8.
5. a) NOC (4,5,12) \u003d 60; b) NOC (18.32) \u003d 288.
6. 6 m.
Option II.
1. $36=2^2*3^2$; $48=2^4*3$.
2. Simple: 13, 237. Composite: 48, 96, 121, 340.
3. 1,2, 19, 38.
4. a) node (386, 464) \u003d 2; b) Node (24, 112) \u003d 8.
5. a) NOC (3,6,8) \u003d 24; b) NOC (15.22) \u003d 330.
6. 14 m.
Embodiment III.
1. $58=2*29$; $32=2^5$.
2. Simple: 5, 17, 101, 133. Composite: 222, 314.
3. 1,2,13,26.
4. a) node (520, 368) \u003d 8; b) Node (38, 98) \u003d 2.
5. a) NOC (4,7,9) \u003d 252; b) NOC (16.24) \u003d 48.
6. 35 m.
Option I.
1. $ \\ FRAC (3) (5) $; $ \\ FRAC (3) (4) $; $ \\ FRAC (11) (20) $; $ \\ FRAC (41) (50) $.
2. $ \\ FRAC (24) (32) $.
3. a) $ \\ FRAC (1) (5000) $; b) $ \\ FRAC (7) (12) $; c) $ \\ FRAC (1) (20) $.
4. $ \\ FRAC (36) (54) $.
5. a) $ \\ FRAC (14) (18) $ and $ \\ FRAC (12) (18) $; b) $ \\ FRAC (81) (126) $ and $ \\ FRAC (105) (126) $.
6. Blue.
7. a) 4/5\u003e 7/10; & NBSP b) 9/12 \u003d 12/16.
Option II.
1. $ \\ FRAC (9) (11) $; $ \\ FRAC (3) (5) $; $ \\ FRAC (19) (50) $; $ \\ FRAC (17) (20) $.
2. 0,40.
3. a) $ \\ FRAC (3) (12500) $; b) $ \\ FRAC (1) (4) $; c) $ \\ FRAC (9) (20) $.
4. $ \\ FRAC (35) (40) $.
5. a) $ \\ FRAC (27) (63) $ and $ \\ FRAC (42) (63) $; b) $ \\ FRAC (64) (112) $ and $ \\ FRAC (84) (112) $.
6. Potato bag.
7. a) 4/5\u003e 7/10; & NBSP b) 9/12 Embodiment III.
1. $ \\ FRAC (4) (7) $; $ \\ FRAC (4) (5) $; $ \\ FRAC (8) (25) $; $ \\ FRAC (3) (20) $.
2. $ \\ FRAC (20) (32) $.
3. a) $ \\ FRAC (9) (20,000) $; b) $ \\ FRAC (5) (6) $; c) $ \\ FRAC (3) (10) $.
4. $ \\ FRAC (24) (30) $.
5. a) $ \\ FRAC (14) (35) $ and $ \\ FRAC (30) (35) $; b) $ \\ FRAC (9) (36) $ and $ \\ FRAC (24) (36) $.
6. Second machine.
7. a) 7/9\u003e 4/6; & NBSP b) 5/7
Option I.
1. a) $ \\ FRAC (13) (9) $; b) $ - \\ FRAC (3) (35) $; c) $ \\ FRAC (67) (140) $.
2. The second board is longer than $ \\ FRAC (1) (84) $ m.
3. a) $ x \u003d \\ FRAC (11) (12) $; b) $ \\ FRAC (53) (126) $.
4. a) $ \\ FRAC (21) (12) $; b) $ \\ FRAC (127) (40) $.
5. a) $ x \u003d \\ FRAC (215) (63) $; b) $ Y \u003d \\ FRAC (31) (56) $.
6. 4 hours.
Option II.
1. a) $ 1 \\ FRAC (7) (60) $; b) $ \\ FRAC (15) (36) $; c) $ \\ FRAC (177) (200) $.
2. Blue piece of fabric is longer than $ \\ FRAC (1) (65) $ m.
3. a) $ x \u003d \\ FRAC (23) (55) $; b) $ z \u003d \\ FRAC (5) (7) $.
4. a) $ \\ FRAC (169) (63) $; b) $ \\ FRAC (306) (70) $.
5. a) $ \\ FRAC (190) (63) $; b) $ \\ FRAC (13) (15) $.
6. $ \\ FRAC (1) (6) $ an hour (10 minutes).
Embodiment III.
1. a) $ \\ FRAC (115) (99) $; b) $ \\ FRAC (1) (2) $; c) $ - \\ FRAC (11) (90) $.
2. Second notebook thicker. The total thickness is $ 1 \\ FRAC (4) (15) $.
3. a) $ x \u003d \\ FRAC (7) (40) $; b) $ z \u003d - \\ FRAC (13) (16) $.
4. a) $ \\ FRAC (191) (55) $; b) $ \\ FRAC (1) (70) $.
5. A) $ 2 \\ FRAC (14) (21) $ b) $ \\ FRAC (38) (35) $.
6. $ \\ FRAC (12) (15) $ an hour (48 minutes).
Option I.
1. a) $ \\ FRAC (8) (35) $; b) $ \\ FRAC (25) (64) $.
2. $ \\ FRAC (1) (2) $.
3. 62.5 km.
4. 4.
5. 6 girls.
Option II.
1. a) $ \\ FRAC (10) (21) $; b) $ - \\ FRAC (4) (9) $.
2. $ \\ FRAC (1) (3) $.
3. 10 km.
4. 9.
5. 15 boys.
Embodiment III.
1. a) $ \\ FRAC (8) (33) $; b) $ - \\ FRAC (32) (125) $.
2. $ \\ FRAC (3) (7) $.
3. 100 km.
4. 25.
5. 20.
Option I.
1. a) $ 2 \\ FRAC (6) (7) $; b) $ \\ FRAC (21) (4) $.
2. a) $ - \\ FRAC (5) (13) $; b) $ -7 \\ FRAC (1) (2) $.
3. 56 details.
Option II.
1. a) $ \\ FRAC (43) (12) $; b) $ \\ FRAC (59) (13) $.
2. a) $ - \\ FRAC (7) (13) $; b) $ -7 \\ FRAC (3) (8) $.
3. 13 trees.
Embodiment III.
1. a) $ \\ FRAC (119) (20) $; b) $ 2 \\ FRAC (4) (5) $.
2. a) $ - \\ FRAC (8) (11) $; b) $ -9 \\ FRAC (3) (12) $.
3. 30 km.
Option I.
1. a) $ \\ FRAC (18) (35) $; b) $ \\ FRAC (13) (18) $.
2. $ \\ FRAC (3) (4) $.
3. 36 km.
Option II.
1. a) $ \\ FRAC (56) (45) $; b) $ \\ FRAC (225) (121) $.
2. $ \\ FRAC (441) (63) $.
3. 24 km.
Embodiment III.
1. a) $ \\ FRAC (25) (21) $; b) $ \\ FRAC (19) (16) $.
2. 6.
3. 13.5 km.
Option I.
1. a) $ \\ FRAC (146) (8) $; b) $ \\ FRAC (27) (2) $.
2. In $ \\ FRAC (3) (2) $ 3 times, by 50%.
3. a) y \u003d 8; b) $ z \u003d \\ FRAC (175) (12) $.
4. 60 kg.
Option II.
1. a) $ \\ FRAC (133) (4) $; b) 11.9.
2. In $ \\ FRAC (2) (5) $ 3 times, by 150%.
3. a) y \u003d 4.2; b) $ z \u003d \\ FRAC (280) (29) $.
4. 448 m.
Embodiment III.
1. a) $ \\ FRAC (39) (2) $; b) $ \\ FRAC (31) (2) $.
2. In $ \\ FRAC (2) (3) times; by 50% $.
3. a) $ y \u003d \\ FRAC (32) (9) $; b) $ z \u003d \\ FRAC (420) (9) $.
4. 504 kg.
Option I.
1. 4 m and 6 m.
2. 1:2000000.
3. 47.1 cm.
4. $ 803.84 cm ^ $ 2.
Option II.
1. 12 m and 15 m.
2. 1:2000000.
3. 75.36 cm.
4. $ 1589.63 cm ^ $ 2.
Embodiment III.
1. 8 m and 24 m.
2. 1:500000.
3. 141.3 cm.
4. $ 706.5 cm ^ $ 2.
Option I.
2. 21; & nbsp -0.34; & NBSP 1 4/7; & nbsp -5.7; & NBSP -8 4/19.
3. 27; & nbsp 4; & NBSP 8; & NBSP 3 2/9.
4. 15,5.
5. A) 3/4 -6 5/7.
Option II.
2. 30; & nbsp -0.45; & NBSP 4 3/8; & nbsp -2.9; & NBSP 3 3/14.
3. 12; & NBSP 6; & NBSP 9; & NBSP 5 2/7.
4. -9,2.
5. a) 2/3 -3 5/9.
Embodiment III.
2. 10; & nbsp -12.4; & NBSP 12 3/11; & nbsp -3.9; & NBSP 5 7/11.
3. 4; & NBSP 6.8; & NBSP 19; & NBSP 4 3/5.
4. $ \\ FRAC (23) (15) $.
5. a) 1/4\u003e 2/9; & NBSP b) -5 12/17\u003e -5 14/17.
Option I.
1. a) -20; b) 3.5.
2. a) -66; b) 10.
3. a) $ \\ FRAC (4) (9) $; b) -6.3.
4. Z \u003d 4.5.
Option II.
1. A) -42; b) 10.4.
2. a) 58; b) 45.5.
3. a) $ \\ FRAC (5) (7) $; b) $ - \\ FRAC (17) (3) $.
4. Y \u003d 1.25.
Embodiment III.
1. a) -24; b) 21.
2. a) -32; b) -34.
3. a) $ - \\ FRAC (8) (5) $; b) 14.4.
4. z \u003d -0.2.
Option I.
1. $ \\ FRAC (17) (6) $; $ \\ FRAC (78) (10) $; $ - \\ FRAC (99) (8) $.
2. $ - \\ FRAC (477) (49) $.
3. a) 1.2; b) 32.37.
4. -2B-a.
Option II.
1. $ \\ FRAC (11) (3) $; & NBSP $ - \\ FRAC (29) (10) $; & NBSP $ - \\ FRAC (31) (9) $.
2. $ \\ FRAC (263) (27) $.
3. a) -1.6; b) 1.7.
4. Z + Y.
Embodiment III.
1. $ - \\ FRAC (12) (7) $; & NBSP $ \\ FRAC (58) (10) $; & NBSP $ - \\ FRAC (8) (5) $.
2. $ \\ FRAC (752) (375) $.
3. a) -4.9; b) -4.2.
4. 2C + 5D.
Option I.
1. 10x + 5.
2. a) -15; b) 4.3.
3. a) x \u003d 2; b) a \u003d 8.
Option II.
1. -2Y-1.
2. a) -6; b) 1.5.
3. a) y \u003d 5; b) a \u003d 5.4.
Embodiment III.
1. $ 4Z-1 \\ FRAC (4) (5) $.
2. a) -10.2; b) -2.1.
3. a) z \u003d 6; b) b \u003d 14.2.
K.R 2, 6 CL. Option 1
# 1. Calculate:
d): 1.2; e):
№ 4. Calculated:
: 3,75 -
№ 5. Share Equation:
K.R 2, 6 CL. Option 2.
# 1. Calculate:
d): 0.11; e): 0.3
№ 4. Calculated:
· 2.3 - · 2.3
№ 5. Share Equation:
K.R 2, 6 CL. Option 1
# 1. Calculate:
a) 4.3 +; b) - 7,163; c) · 0.45;
d): 1.2; e):
# 2. Own yacht speed 31.3 km / h, and its speed for the river flow 34.2 km / h. What distance the yacht saves if 3 h against the river flow will move?
No. 3. Travelers on the first day of its path were 22.5 km, in the second - 18.6 km, in the third - 19.1 km. How many kilometers did they go on the fourth day, if on average they took place 20 km per day?
№ 4. Calculated:
: 3,75 -
№ 5. Share Equation:
K.R 2, 6 CL. Option 2.
# 1. Calculate:
a) 2.01 +; b) 9,5 -; in) ;
d): 0.11; e): 0.3
# 2. Own ship speed is 38.7 km / h, and its speed against the river current is 25.6 km / h. What distance saves the motor ship if 5.5 hours go to the river?
No. 3. In Monday, Misha made a homework for 37 minutes, on Tuesday - for 42 minutes, on Wednesday - for 47 min. How much time did he spend on the fulfillment of his homework on Thursday, if on average for these days he went to perform homework 40 minutes?
№ 4. Calculated:
· 2.3 - · 2.3
№ 5. Share Equation:
Preview:
KR No. 3, CL 6
Option 1
# 1. How much are:
# 2. Find a number if:
a) 40% of it is 6.4;
b) % it is 23;
c) 600% are t.
№ 6. Equation:
Option 2.
# 1. How much are:
# 2. Find a number if:
a) 70% is 9.8;
b) % is 18;
c) 400% are k.
№ 6. Equation:
KR No. 3, CL 6
Option 1
# 1. How much are:
a) 8% of 42; b) 136% of 55; c) 95% of A?
# 2. Find a number if:
a) 40% of it is 6.4;
b) % it is 23;
c) 600% are t.
# 3. How much percent is 14 less than 56?
How much percent is 56 more than 14?
No. 4. The price of strawberries was 75 rubles. At first it decreased by 20%, and then another 8 rubles. How many rubles began to cost strawberries?
№ 5. The bag was 50 kg of cereals. It took 30% of the cereals at first, and then another 40% residue. How many cereals remain in the bag?
№ 6. Equation:
Option 2.
# 1. How much are:
a) 6% of 54; b) 112% of 45; c) 75% of b?
# 2. Find a number if:
a) 70% is 9.8;
b) % is 18;
c) 400% are k.
# 3. How much percent is 19 less than 95?
How much percent is 95 more than 19?
№ 4. The estimmers decided to sing a barley of 45% of the field 80 gang. On the first day, 15 hectares were sown. What area of \u200b\u200bthe field remains to fall barley?
№ 5. The barrel was 200 liters of water. It took 60% of the water at first, and then another 35% residue. How much water remains in the barrel?
№ 6. Equation:
Preview:
Option 1
90 – 16,2: 9 + 0,08
Option 2.
# 1. Find the value of the expression:
40 – 23,2: 8 + 0,07
Option 1
# 1. Find the value of the expression:
90 – 16,2: 9 + 0,08
# 2. The width of the rectangular parallelepiped 1.25 cm, and its length is 2.75 cm more. Find the volume of parallelepiped if it is known that the height is 0.4 cm less than the length.
Option 2.
# 1. Find the value of the expression:
40 – 23,2: 8 + 0,07
# 2. The height of the rectangular parallelepiped 0.73 m, and its length is 4.21 m greater. Find the volume of the parallelepiped, if it is known that the width is 3.7 less than the length.
Preview:
C p 11, cl 6
Option 1
Option 2.
C p 11, cl 6
Option 1
No. 1. What was the initial amount if it was 6% at an annual decrease in its 6% after 4 years 5320 rubles.
# 2. The depositor put 9000 rubles on the bank account. Under 20% per annum. What amount will be at his account after 2 years, if the bank charges: a) simple interest; b) complex interest?
Number 3*. The straight angle was reduced 15 times, and then increased by 700%. How many degrees is the resulting angle? Draw it.
Option 2.
№1. What was the initial contribution if with an annual increase by 18% it increased to 7280 rubles for 6 months.
No. 2. The client put on the bank 12,000 rubles. The annual interest rate of the Bank is 10%. What amount will be on the client's account after 2 years, if the bank charges: a) simple interest; b) complex interest?
Number 3*. The detailed angle was reduced 20 times, and then increased by 500%. How many degrees is the resulting angle? Draw it.
Preview:
Option 1
a) Paris is the capital of England.
b) There are no seas on Venus.
c) the boil is longer than cobra.
a) number 3 less;
Option 2.
# 1. Build the denial of statements:
b) There are crater on the moon.
c) Birch below poplar.
d) in the year 11 or 12 months.
No. 2. Write the proposals on the mathematical language and the construction of their denial:
a) number 2 more than 1.9999;
c) Square of numbers 4 is 8.
Option 1
# 1. Build the denial of statements:
a) Paris is the capital of England.
b) There are no seas on Venus.
c) the boil is longer than cobra.
d) A handle and notebook lie on the table.
No. 2. Write the proposals on the mathematical language and the construction of their denial:
a) number 3 less;
b) Amount 5 + 2.007 more or equal to seven whole thousand thousands;
c) Square of the number 3 is not equal to 6.
Number 3*. Write in descending order all possible natural numbers made up of 3 seven and 2 zeros.
Option 2.
# 1. Build the denial of statements:
a) Volga flows into the Black Sea.
b) There are crater on the moon.
c) Birch below poplar.
d) in the year 11 or 12 months.
No. 2. Write the proposals on the mathematical language and the construction of their denial:
a) number 2 more than 1.9999;
b) the difference is 18 - 3.5 less or equal to fourteen to a total of fourteen thousands;
c) Square of numbers 4 is 8.
Number 3*. Write in ascending order all possible natural numbers made up of 3 nine and 2 zeros.
Preview:
S.R. 4, 6 cl.
Option 1
x -2.3 if x \u003d 72.
Square rectangleand cm 2 a \u003d 50)
№ 3. Solutions Equation:
Cube amount of doubledh. and the square of the number y. (x \u003d 5, y \u003d 3)
S.R. 4, 6 cl.
Option 2.
No. 1. Find the value of the expression with the variable:
y - 4.2 if y \u003d 84.
No. 2. Make an expression and find its value at this value of the variable:
№ 3. Solutions Equation:
(3,6Y - 8,1): + 9.3 \u003d 60.3
№ 4 *. Translate to Mathematical Language and find the value of the expression when these variable values \u200b\u200bare:
Number Cube Difference Squareh. and triple number y. (x \u003d 5, y \u003d 9)
S.R. 4, 6 cl.
Option 1
No. 1. Find the value of the expression with the variable:
x -2.3 if x \u003d 72.
No. 2. Make an expression and find its value at this value of the variable:
Square rectanglea cm 2. And the length is 40% of the number equal to its area. Find the perimeter of the rectangle. (a \u003d 50)
№ 3. Solutions Equation:
(4.8 x + 7.6): - 9.5 \u003d 34.5
№ 4 *. Translate to Mathematical Language and find the value of the expression when these variable values \u200b\u200bare:
Cube amount of doubledh. and the square of the number y. (x \u003d 5, y \u003d 3)
S.R. 4, 6 cl.
Option 2.
No. 1. Find the value of the expression with the variable:
y - 4.2 if y \u003d 84.
No. 2. Make an expression and find its value at this value of the variable:
The length of the rectangle M dm, which is 20% of the number equal to its area. Find the perimeter of the rectangle. (m \u003d 17)
№ 3. Solutions Equation:
(3,6Y - 8,1): + 9.3 \u003d 60.3
№ 4 *. Translate to Mathematical Language and find the value of the expression when these variable values \u200b\u200bare:
Number Cube Difference Squareh. and triple number y. (x \u003d 5, y \u003d 9)
Preview:
Wed 5, 6 CL
Option 1
№ 2. SOLUTION Equation: 4.5
m n α km / h? "
Wed 5, 6 CL
Option 2.
No. 1. The truth or falsity of statements. Build the denial of false statements: on the board
№ 3. Translate the condition of the task of mathematical language:
m n d details per hour? "
Wed 5, 6 CL
Option 1
No. 1. The truth or falsity of statements. Build the denial of false statements: on the board
№ 2. Equation:
4.5 x + 3.2 + 2.5 x + 8.8 \u003d 26.14
№ 3. Translate the condition of the task of mathematical language:
"The tourist was walking during the first 3 hours at speeds.m. km / h, and in the next 2 h - at speedn. km / h How much time drove the same way cyclist, moving uniformly at speedα km / h? "
No. 4. The sum of the figures of the three-digit number is 8, and the work is 12. What is this number? Find all possible options.
Wed 5, 6 CL
Option 2.
No. 1. The truth or falsity of statements. Build the denial of false statements: on the board
№ 2. Equation: 2,3Y + 5.1 + 3,7Y +9.9 \u003d 18.3
№ 3. Translate the condition of the task of mathematical language:
"The student did during the first 2 hoursm. parts per hour, and in the following 3 hours -n. parts per hour. How long can the master work, if its performanced details per hour? "
№ 4. The sum of the figures of the three-digit number is 7, and the work is 8. What is the number? Find all possible options.
Wed 5, 6 CL
Option 1
No. 1. The truth or falsity of statements. Build the denial of false statements: on the board
№ 2. SOLUTION Equation: 4.5x + 3.2 + 2.5 x + 8.8 \u003d 26.14
№ 3. Translate the condition of the task of mathematical language:
"The tourist was walking during the first 3 hours at speeds.m. km / h, and in the next 2 h - at speedn. km / h How much time drove the same way cyclist, moving uniformly at speedα km / h? "
No. 4. The sum of the figures of the three-digit number is 8, and the work is 12. What is this number? Find all possible options.
Wed 5, 6 CL
Option 2.
No. 1. The truth or falsity of statements. Build the denial of false statements: on the board
№ 2. Equation: 2,3Y + 5.1 + 3,7Y +9.9 \u003d 18.3
№ 3. Translate the condition of the task of mathematical language:
"The student did during the first 2 hoursm. parts per hour, and in the following 3 hours -n. parts per hour. How long can the master work, if its performanced details per hour? "
№ 4. The sum of the figures of the three-digit number is 7, and the work is 8. What is the number? Find all possible options.
Preview:
S.R. eight . 6 CL
Option 1
S.R. eight . 6 CL
Option 2.
№1 Find the average arithmetic numbers:
a) 1.2; ; 4.75 b) k; n; x; y.
S.R. eight . 6 CL
Option 1
№1 Find the average arithmetic numbers:
a) 3.25; one ; 7.5 b) a; b; d; k; N.
No. 2. Find the amount of the four numbers if their arithmetic average is 5.005.
№ 3. In the school football team 19 people. Their average age is 14 years old. After another player was taken to the team, the middle age of the team participants stood 13.9 years. How old is the new team player?
№ 4. The arithmetic average of three numbers is 30.9. The first number is 3 times more than the second, and the second is 2 times less than the third. Find these numbers.
S.R. eight . 6 CL
Option 2.
№1 Find the average arithmetic numbers:
a) 1.2; ; 4.75 b) k; n; x; y.
# 2. Find the amount of the five numbers if their arithmetic average is 2.31.
№ 3. In a hockey team 25 people. Their average age is 11 years old. How old is the coach if the middle age of the team together with the coach is 12 years old?
№ 4. The arithmetic average of three numbers is 22.4. The first number is 4 times more than the second, and the second is 2 times less than the third. Find these numbers.
S.R. eight . 6 CL
Option 1
№1 Find the average arithmetic numbers:
a) 3.25; one ; 7.5 b) a; b; d; k; N.
No. 2. Find the amount of the four numbers if their arithmetic average is 5.005.
№ 3. In the school football team 19 people. Their average age is 14 years old. After another player was taken to the team, the middle age of the team participants stood 13.9 years. How old is the new team player?
№ 4. The arithmetic average of three numbers is 30.9. The first number is 3 times more than the second, and the second is 2 times less than the third. Find these numbers.
S.R. eight . 6 CL
Option 2.
№1 Find the average arithmetic numbers:
a) 1.2; ; 4.75 b) k; n; x; y.
# 2. Find the amount of the five numbers if their arithmetic average is 2.31.
№ 3. In a hockey team 25 people. Their average age is 11 years old. How old is the coach if the middle age of the team together with the coach is 12 years old?
№ 4. The arithmetic average of three numbers is 22.4. The first number is 4 times more than the second, and the second is 2 times less than the third. Find these numbers.
S.R. eight . 6 CL
Option 1
№1 Find the average arithmetic numbers:
a) 3.25; one ; 7.5 b) a; b; d; k; N.
No. 2. Find the amount of the four numbers if their arithmetic average is 5.005.
№ 3. In the school football team 19 people. Their average age is 14 years old. After another player was taken to the team, the middle age of the team participants stood 13.9 years. How old is the new team player?
№ 4. The arithmetic average of three numbers is 30.9. The first number is 3 times more than the second, and the second is 2 times less than the third. Find these numbers.
a) decreased 5 times;
b) increased 6 times;
# 2. Find:
a) how much is 0.4% of 2.5 kg;
b) from which value of 12% from 36 cm;
c) how many percent are 1.2 from 15.
№ 3. Compare: a) 15% of 17 and 17% of 15; b) 1.2% of 48 and 12% of 480; c) 147% of 621 and 125% of 549.
# 4. How much percent is 24 less than 50.
2) Independent work
Option 1
№ 1
a) increased 3 times;
b) decreased 10 times;
№ 2
Find:
a) how much is 9% of 12.5 kg;
b) from which value of 23% is from 3.91 cm2 ;
c) How many percent are 4.5 from 25?
№ 3
Compare: a) 12% of 7.2 and 72% of 1.2
№ 4
For how many percent of 12 less than 30.
№ 5*
a) was 45 rubles, and became 112.5 rubles.
b) there was 50 rubles, and it became 12.5 rubles.
Option 2.
№ 1
How much percent changed the magnitude if she:
a) decreased by 4 times;
b) increased 8 times;
№ 2
Find:
a) from which value of 68% is from 12.24 m;
b) how much is 7% of 25.3 hectares;
c) How many percent are 3.8 from 20?
№ 3
Compare: a) 28% of 3.5 and 32% of 3.7
№ 4
For how many percent of 36 less than 45.
№ 5*
For how many percent, the price of the goods changed if she:
a) there was 118.5 rubles, and it became 23.7 rubles.
b) Was 70 rubles, and became 245 rubles.
13th ed., Pererab. and add. - M.: 2016 - 96c. 7th ed., Pererab. and add. - M.: 2011 - 96c.
This manual fully complies with the new educational standard (second generation).
The manual is a necessary addition to the school textbook by N.Ya. Vilenkin and others. "Mathematics. Grade 6 "recommended by the Ministry of Education and Science of the Russian Federation and included in the federal list of textbooks.
The manual contains various materials to control and evaluate the quality of training of students in grades of grades, provided for by the Grade 6 program at the "Mathematics" course.
36 independent work are presented, each in two versions, so if necessary, you can check the completeness of students' knowledge after each topic passed; 10 test works presented in four versions make it possible to accurately appreciate the knowledge of each student as accurately as possible.
The manual is addressed to teachers will be useful in student in preparation for lessons, control and independent work.
Format: PDF. (2016 , 13th ed. per. and add., 96c.)
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CONTENT
Independent work 8.
To § 1. The divisibility of numbers 8
Independent work number 1. Dividers and multiple 8
Independent work number 2. Signs of divisibility by 10, 5 and at 2. Signs of divisibility by 9 and 3 9
Independent work number 3. Simple and constituent numbers. Decomposition for simple multipliers 10
Independent work number 4. The greatest common divisor. Mutually simple numbers 11
Independent work number 5. The smallest total multiple 12
To § 2. Addition and subtraction of fractions with different denominators 13
Independent work number 6, the main property of the fraction. Reducing fractions 13.
Independent work number 7, bringing fractions to the general denominator 14
Independent work number 8. Comparison, addition and subtraction of fractions with different denominators 16
Independent work number 9. Comparison, addition and subtraction of fractions with different denominators 17
Independent work number 10. Addition and subtraction of mixed numbers 18
Independent work №11. Addition and subtraction of mixed numbers 19
To § 3. Multiplication and division of ordinary fractions 20
Independent work number 12. Multiplication of fractions 20.
Independent work №13. Multiplication of fractions 21.
Independent work number 14. Finding a shot from the number 22
Independent work number 15. Apply the distribution properties of multiplication.
Constrate numbers 23.
Independent work number 16. Division 25
Independent work number 17. Finding a number by its fraction 26
Independent work number 18. Fractional expressions 27
To § 4. Relations and proportions 28
Independent work №19.
Relationship 28.
Independent work l £ 20. Proportions, direct and inverse proportional
Dependencies 29.
Independent work number 21. Scale 30
Independent work number 22. Circle length and Circle Area. Bowl 31.
To § 5. Positive and negative numbers 32
Independent work l £ 23. Coordinates on a straight line. Opposite
Numbers 32.
Independent work number 24. Module
Numbers 33.
Independent work number 25. Comparison
numbers. Change values \u200b\u200b34.
To § 6. Addition and subtraction of positive
and negative numbers 35
Independent work number 26. The addition of numbers with the help of the coordinate direct.
Addition of negative numbers 35
Independent work number 27, addition
Numbers with different signs 36
Independent work number 28. Subtraction 37
To § 7. Multiplication and division of positive
and negative numbers 38
Independent work number 29.
Multiplication 38.
Independent work number 30. Decision 39
Independent work number 31.
Rational numbers. Properties of action
with rational numbers 40
K § 8. Solution of equations 41
Independent work number 32. Disclosure
brackets 41.
Independent work number 33.
Coefficient. Similar terms 42.
Independent work number 34. Decision
equations. 43.
To § 9. Coordinates on the plane 44
Independent work number 35. Perpendicular direct. Parallel
straight. Coordinate plane 44.
Independent work number 36. Study
Charts. Charts 45.
Examination 46.
To § 1 46
Examination number 1. Dividers
and multiple. Signs of divisibility by 10, on 5
And on 2. Signs of divisibility by 9 and 3.
Simple and constituent numbers. Decomposition
on simple factors. The greatest common
divider. Mutually simple numbers.
The smallest total multiple 46
To § 2 50
Examination number 2. Main
Property fractions. Reducing fractions.
Bringing fractions to a common denominator.
Comparison, addition and subtraction of fractions
with different denominator. Addition
and subtraction of mixed numbers 50
To § 3 54
Examination number 3. Multiplication
frains. Finding the fraction from the number.
Application of distribution properties
Multiplication. Mutually reverse numbers 54
Examination No. 4. Decision.
Finding a number by its fraction. Fractional
expressions 58.
To § 4 62
Examination number 5. Relationship.
Proportions. Direct and inverse
Proportional dependencies. Scale.
Circle Length and Circle Square 62
To § 5 64
Examination number 6. Coordinates on a straight line. Opposite numbers.
The absolute value of a number. Comparison of numbers. The change
Values \u200b\u200b64.
To § 6 68
Examination number 7. Addition of numbers
Using the coordinate direct. Addition
Negative numbers. Addition of numbers
With different signs. Subtraction 68.
To § 7 70
Examination number 8, multiplication.
Division. Rational numbers. Properties
actions with rational numbers 70
To § 8 74
Examination number 9. Disclosure of brackets.
Coefficient. Similar terms. Decision
Equations 74.
To § 9 78
Examination number 10. Perpendicular straight lines. Parallel straight. Coordinate plane. Column
Charts. Graphs 78.
Answers 80.
Presented multi-level independent work on the topics of grade 6. The level of the student can choose himself!
Download:
Preview:
C-1. Dividers and multiples
Option A1 Option A2
1. Check that:
a) Number 14 is a divider of Number 518; a) number 17 is a divider of the number 714;
b) Number 1024 more than 32. b) Number 729 multiple number27.
2. Among these numbers 4, 6, 24, 30, 40, 120, select:
a) those that are divided into 4; a) those who are divided by 6;
b) those that are divided by the number 72; b) those that are divided by the number 60;
c) dividers 90; c) dividers 80;
d) multiple 24. g) multiple 40.
3. Find all valuesx, which
past 15 and satisfy are divisors 100 and
inequality x. 75. satisfy inequalityx\u003e 10.
Option B1 Option B2
- Name:
a) all dividers of the number 16; a) all dividers of the number 27;
b) three numbers, multiple 16. b) three numbers, multiple 27.
2. Among these numbers 5, 7, 35, 105, 150, 175, select:
a) dividers 300; a) dividers 210;
b) multiple 7; b) multiple 5;
c) numbers that are not divisors 175; c) numbers that are not divisors 105;
d) numbers, not multiple 5. g) numbers, not multiple 7.
3. Find
all numbers, multiple 20 and constituting all dividers of the number 90, not
less than 345% of this number. Superior 30% of this number.
Preview:
C-2. Signs of divisibility
Option A1 Option A2
- From data numbers 7385, 4301, 2880, 9164, 6025, 3976
select numbers that
2. Of all the numbers x satisfying inequality
1240 h. 1250, 1420 h. 1432,
Select numbers that
a) are divided into 3;
b) are divided into 9;
c) are divided by 3 and 5. c) divided by 9 and 2.
3. For the number 1147, find the nearest natural
Number that
a) more than 3; a) multiple 9;
b) multiple 10. b) more than 5.
Option B1 Option B2
- Dana numbers
4, 0 and 5. 5, 8 and 0.
Using each of the numbers one time in the record of one
Numbers, make up all three digits that
a) are divided into 2; a) divided by 5;
b) are not divided into 5; b) are not divided into 2;
c) divided by 10. B) are not divided by 10.
2. Specify all the figures that you can replace the asterisk.
So that
a) the number 5 * 8 was divided into 3; a) the number 7 * 1 was divided into 3;
b) the number * 54 was divided into 9; b) the number * 18 was divided into 9;
c) the number 13 * was divided by 3 and by 5. c) the number 27 * was divided by 3 and 10.
3. Find the valuex, if
a) H. - the greatest two-digit number is that a)h. - the smallest three-digit number
production 173 · x divided by 5; such that work 47X is divided
On 5;
b) H. - the smallest four-digit number b)h. - the largest three-digit number
such that differenceh. - 13 divided by 9. Such a sumx + 22 is divided into 3.
Preview:
C-3. Simple and constituent numbers.
Decomposition of simple factors
Option A1 Option A2
- Prove that numbers
695 and 2907 832 and 7053
Are composite.
- Spread the number of numbers for simple factors:
a) 84; a) 90;
b) 312; b) 392;
c) 2500. c) 1600.
3. Record all dividers
numbers 66. numbers 70.
4. Can the difference between the two simple 4. Can the sum of two simple
Numbers be a simple number? Numbers be a simple number?
Respond confirm by an example. Respond confirm by an example.
Option B1 Option B2
- Replace the asterisk digit so that
this number was
a) simple: 5 *; a) simple: 8 *;
b) Composite: 1 * 7. b) Composite: 2 * 3.
2. Explore the number of numbers:
a) 120; a) 160;
b) 5940; b) 2520;
c) 1204. c) 1804.
3. Record all dividers
numbers 156. Numbers 220.
Emphasize those of them that are simple numbers.
4. Can the difference between the two components 4. Can the sum of two components
Be a simple number? Explain the answer. Numbers be a simple number? Answer
Explain.
Preview:
C-4. The greatest common divider.
The smallest common pain
Option A1 Option A2
a) 14 and 49; a) 12 and 27;
b) 64 and 96. b) 81 and 108.
a) 18 and 27; a) 12 and 28;
b) 13 and 65. b) 17 and 68.
3 . Aluminum pipe is necessary3 . Takes brought to school
without waste cut to equal it is necessary to equal
parts. Distribute between students.
a) what the smallest length a) what is the largest number
must have a pipe to her students, between which
it was possible to cut out how to distribute 112 notebooks in a cage
parts 6 m long and parts and 140 notebooks in a ruler?
8 m long? b) what the smallest number
b) on some of which largest notebooks can be distributed as
lengths you can cut two between 25 students and between
pipes 35 m and 42 m? 30 students?
4 . Find out whether mutually simple numbers are
1008 and 1225. 1584 and 2695.
Option B1 Option B2
- Find the greatest common divisor:
a) 144 and 300; a) 108 and 360;
b) 161 and 350. b) 203 and 560.
2 . Find the smallest common multiple numbers:
a) 32 and 484 a) 27 and 36;
b) 100 and 189. b) 50 and 297.
3 . The video channel is necessary3. Agrofirma produces vegetable
pack and send oil to shops and distinguishes it into the bidones for
for sale. Sending for sale.
a) how many cassettes can be without residue a) how many liters can be without
pack as in the boxes of 60 pieces, the remainder is poured as in 10 liters
both in the boxes of 45 pieces, if the entire bidones and 12-liter beedons,
cassettes less than 200? If there is less than 100 b) what is the largest number of liters?
stores that can be equally b) what is the greatest number
distribute 24 comedies and 20 outlets in which you can
melodram How many films of each equal to distribute 60 liters of genre at the same time will receive one sunflower and 48 liters of corn
score? oil? How many liters of oil
Like this will get one trading
Point?
four . From numbers
33, 105 and 128 40, 175 and 243
Choose all pairs of mutually prime numbers.
Preview:
C-6. The main property of the fraction.
Reducing fractions
Option A1 Option A2
- Cut the fraction (decimal fraction in the form
ordinary fraction)
but) ; b); c) 0.35. but) ; b); c) 0.65.
2. Among these frains, find equal:
; ; ; 0,8; . ; 0,9; ; ; .
3. Determine what part
a) kilogram make up 150 g; a) tons make up 250 kg;
b) An hour is 12 minutes. b) Minutes make up 25 seconds.
- Find X if
= + . = - .
Option B1 Option B2
- Reduce fractions:
but) ; b) 0,625; in) . but) ; b) 0.375; in) .
2. Write three fractions,
equal, with a denominator less than 12. Equal, with a denominator less than 18.
3. Determine what part
a) the year amount to 8 months; a) day constitute 16 hours;
b) the meter is 20 cm. b) kilometer make up 200 m.
Record the answer in the form of an unstable fraction.
- Find X if
1 + 2. = 1 + 2.
Preview:
C-7. Bringing fractions to a common denominator.
Compare fractions
Option A1 Option A2
- Bring:
a) fraction to the denominator 20; a) fraction to the denominator 15;
b) fractions and to a common denominator; b) fractions and to a common denominator;
2. Compare:
a) and; b) and 0.4. a) and; b) and 0.7.
3. Mass of one package is kg, 3. The length of one board is M,
and the mass of the second - kg. Which of the length is the second - m. Which of the boards
packages are harder? In short?
- Find all natural valuesx, in which
true inequality
Option B1 Option B2
- Bring:
a) fraction to the denominator 65; a) fraction to the denominator 68;
b) fractions and 0.48 to a common denominator; b) fractions and 0.6 to a common denominator;
c) fractions and to a common denominator. c) fractions and to a common denominator.
2. Place the fraction in order
ascending: ,. descending: ,.
3. A tube with a length of 11 m was sawed by 15 3. 8 kg of sugar packaged in 12
equal parts, and a pipe 6 m long - identical packets, and 11 kg of cereals -
on 9 parts. In which case part in 15 packages. Which package is harder -
turned out shorter? With sugar or with a cereal?
4. Determine which of fractions, and 0.9
Are solutions of inequality
X1. .
Preview:
C-8. Addition and subtraction of fractions
With different denominator
Option A1 Option A2
- Calculate:
a) +; b) -; c) +. but) ; b); in) .
2. Decide equations:
but) ; b). but) ; b).
3. The length of the segment Av is equal to M, and the length 3. The mass of the caramel package is equal to kg, and
cutting CD - m. Which segments mass of the package of nuts - kg. Which one of
long? How much? Packages are easier? How much?
reduced to increase on? Subdued to reduce on?
Option B1 Option B2
- Calculate:
but) ; b); in) . a); b) 0.9 -; in) .
2. Decide equations:
but) ; b). but) ; b).
3. On the path from Utkin into a chaktally 3. Read article from two chapter
Voronino one tourist spent an hour. spent an hour. As what time
How much time overcame this path read the same article professor if
the second tourist, if the path from Utkino before the first chapter he spent on an hour
Voronino he passed on an hour more faster, and on the second - an hour less,
first, and the path from Voronino to Chaykino - how does the associate professor?
for hours slower first?
4. How will the difference value change if
reduced to reduce on, and reduced to increase by, and
survected to increase on? Subdued to reduce on?
Preview:
C-9. Addition and subtraction
Mixed numbers
Option A1 Option A2
- Calculate:
- Decide equations:
but) ; b). but) ; b).
3. In the lesson of mathematics, part of the time 3. Of the money allocated by parents, Kostya
was spent on checking the home spent on purchases for home - on
tasks, part - to explain the new passage, and I bought the rest
topics, and the remaining time - for the solution of ice cream. What part of the allocated money
tasks. What part of the time of the lesson Kostya spent on ice cream?
was the problem of tasks?
- Guess the root of the equation:
Option B1 Option B2
- Calculate:
but) ; b); in) . but) ; b); in) .
- Decide equations:
but) ; b). but) ; b).
3. The perimeter of the triangle is 30 cm. One 3. The wire 20 m long was cut into three
it is 8 cm from its sides, which is 2 cm parts. The first part has a length of 8 m,
less second side. Find the third that 1 m is larger than the length of the second part.
the side of the triangle. Find the length of the third part.
- Compare fractions:
I. and.
Preview:
C-10. Multiplication of fractions
Option A1 Option A2
- Calculate:
but) ; b); in) . but) ; b); in) .
2. For the purchase of 2 kg of rice by r. For 2. Distance between points A and Equal
kilogram Kolya paid 10 p. 12 km. Tourist came from point A to point in
How much should it get 2 hours at the speed of the KM / h. how many
for delivery? kilometers left to go?
- Find the value of the expression:
- Imagine
fraction fraction
In the form of a work:
A) an integer and fraction;
B) two fractions.
Option B1 Option B2
- Calculate:
but) ; b); in) . but) ; b); in) .
2. Tourist was an hour at the speed of the KM / h. 2. Bought a kg of cookies by r. per
and hour at the speed of the KM / h. What kilogram and kg of sweets on p. per
distance he passed during this time? kilogram. What amount paid for
All purchase?
3. Find the value of the expression:
4. It is known that a 0. Compare:
a) a and a; a) a and a;
b) a and a. b) a and a.
Preview:
C-11. Application of multiplication of fractions
Option A1 Option A2
- Find:
a) from 45; b) 32% of 50. a) from 36; b) 28% of 200.
- Using the distribution law
multiplication, calculate:
but) ; b). but) ; b).
3. Olga Petrovna bought rice kg. 3. Of the paint highlighted on
Bought rice she spent repairs class, spent
on cooking kulebsaki. How much to paint the party. How many liters
rice kilograms remained from Olga Paints left to continue
Petrovna? repair?
- Simplify the expression:
- The coordinate beam has a point
A (M. ). Mark on this ray
point to point in
And find the length of the segment AV.
Option B1 Option B2
1. Find:
a) from 63; b) 30% of 85. a) from 81; b) 70% of 55.
2. Using the distribution law
multiplication, calculate:
but) ; b). but) ; b).
3. One side of the triangle is 15 cm, 3. The perimeter of the triangle is 35 cm.
the second is 0.6 first, and the third - one of his sides is
second. Find the perimeter of the triangle. perimeter, and the other is the first.
Find the length of the third party.
4. Prove that the value of the expression
does not depend on x:
5. The coordinate beam is noted point
A (M. ). Mark on this ray
points in and from point in and with
And compare the lengths of the segments of AB and Sun.
Preview:
Option B1 Option B2
- Draw the coordinate straight
Taking two cells for a single segment
Notebooks and mark points on it
A (3.5), in (-2,5) and C (-0.75). A (-1.5), in (2.5) and C (0.25).
Note Points A.1, in 1 and 1, coordinates
Which are opposite to Coordinates
Points A, B and C.
- Find the opposite
a) number; a) number;
b) the value of expression. b) the value of expression.
- Find valuewhat if
a) - a \u003d; a) - a \u003d;
b) - A \u003d. b) - A \u003d.
- Determine:
A) what numbers on the coordinate direct
Removed
from among 3 per 5 units; from among -1 by 3 units;
B) how many integers on the coordinate
Straight locally between numbers
8 and 14. -12 and 5.
Preview:
The greatest common divisel
Find nodes numbers (1-5).
Option 1 1) 12 and 16; | Option 2. 1) 16 and 24; | Option 3. 1) 15 and 25; | Option 4. 1) 27 and 15; |
Table of responses for students
Table of answers for teacher
Preview:
The smallest common pain
Find the smallest general multiple numbers (1-5).
Option 1 1) 9 and 36; | Option 2. 1) 9 and 4; | Option 3. 1) 7 and 28; | Option 4. 1) 7 and 4; |
Table of responses for students
Table of answers for teacher
