Toán 7 Bài 1: Tập hợp Q các số hữu tỉ Giải Toán lớp 7 trang 10

Mathematics 7 Lesson 1: Gathering q Friendship numbers Kite books help 7th grade students have more reference suggestions to solve questions and exercises faster and easier.

Solving math 7 pages 10, 11 kites Help students understand what is a rational number, how to represent the rational number on the digital axis. Solving Math 7 Lesson 1 Kite Book is clearly, carefully, easy to understand to help students quickly know how to do the test, and are a useful document to help teachers conveniently guide students to study . So the following is the detailed content of Grade 7 Math Lesson 1: Gather Q rational numbers, invite you to download here.

The theory of collection q Friendship numbers

1.

The rational number is the number that can be written in the form Math 7 Lesson 1: Gathering q The rational numbers of Mathematics Grade 7 Page 10 - Episode 1 Kite Book with a, b ∈ Mathbb z, b ne 0 and gather the rational numbers are denoted by MathBB Q

Example: numbers 5; dFrac {{ - 1}} {2}; dfrac {2} {3}; ... are rational numbers

2.

Each rational number is represented by a point on the digital axis and does not depend on how to select the specified fraction.

For example: rational number dfrac {2} 3 Represented by point M on the following number axis:

3. Compare rational numbers

To compare two rational numbers x, y we do the following:

- Write x, y in the form of fractions with the same positive sample.

x = dfrac {a} {m}; y = dfrac {b} {m} (m> 0)

- Compare the quartet is integer A and B

If a> b then x> y

If a = b then x = y

If A

Example: Compare two numbers x = Frac {2} {{{ - 5}} and y = Frac {{ - 3}} {{{13}}

We have x = Frac {2} {{{ - 5}} = Frac {{2.LEFT ({ - 13} Right)}}} {{LEFT ({ - 5} Right) .LEFT ({ - 13} Right)}} = frac{{ - 26}}{{65}} và y = frac{{ - 3}}{{13}} = frac{{ - 3.5}}{{13.5}} = frac{{ - 15}}{{ 65}}

But - 26!

Solving math 7 pages 10, 11 kites - volume 1

Lesson 1

Number 13, -29; -2,1; 2.28;Frac {{ - 12}} {{ - 18}} Is there a rational number? Why?

Suggestions for answers

Numbers 13, -29; -2,1; 2.28; Frac {{ - 12}} {{ - 18}} There is a rational number because:

13 = Frac {{13}} {1}; - 29 = Frac {{ - 29}} {1}; - 2.1 = Frac {{21}} {{10}}; 2.28 = Frac {{228}}} {{{100}} = Frac {{54}}} {{25}}; FrAC {{ - 12 12 }} {{ - 18}} = Frac {2} {3}

Attention: A integer is also a rational number.

Lesson 2

Suggestions for answers

Lesson 3

In the following statements, which statement is correct, which statement is wrong?

Suggestions for answers

a) Any natural number m is represented in the form of fractions Frac {m} {1}

=> If M is a natural number, M is also a rational number.

=> Statement A correct.

b) Any M integer is represented in the form of fractions Frac {m} {1}

=> If m is an integer, M is also a rational number.

=> Statement B correctly

c) If m is a rational number, m may be a natural number.

For example: -3 is both a rational number and a natural number.

If M is a rational number, M may not be a natural number.

For example: Frac {5} {6} Is a rational number but not a natural number.

=> If m is a rational number, m is not necessarily a natural number.

=> Wrong statement.

d) If m is a rational number, m may be integer.

For example: −2 is both a rational number and an integer.

If M is a rational number, M may not be an integer.

For example: Frac {1} {3} The rational number but not the integer.

=> If m is a rational number, m is not necessarily an integer.

=> Statement d wrong

e) Any natural number m is represented in the form of fractions Frac {m} {1}

=> If M is a natural number, M is also a rational number.

=> Speaking e wrong.

g) Any m integer m can be represented in the form of fractions Frac {m} {1}

=> If m is an integer, M is also a rational number.

=> Wrong statement.

Lesson 4

Observe the following number axis and indicate what points A, B, C, D represent the numbers:

Suggestions for answers

- The unit line is divided into 7 equal segments, new units equal Frac {1} {7} old unit.

Observe the drawing part on the right of point O:

+ Point C is located at O ​​in the segment equal to 2 new units.

=> Point C representing rational numbers: Frac {2} {7}

+ Point D is located a paragraph equal to 6 new units

=> Point D represented rational numbers: Frac {6} {7}

Observe the drawing on the left side of the point O (rational numbers are negative numbers)

+ Point B is located a paragraph equal to 3 new units.

=> Point B represents rational numbers: - Frac {3} {7}

+ Point A is located a paragraph equal to 9 new units

=> Point A represents a rational number: - Frac {9} {7}

Lesson 5

Find the number of each number:

FrAC {9} {{25}}; {text {}} frac {{ - 8}}} {7}; {5} {{ - 6}}; {text {}} 3.9; {text { -}} 12.5

Suggestions for answers

- The number of rational numbers Frac {9} {{25}} is the number - Frac {9} {{25}}

- The number of rational numbers Frac {{ - 8}} {7} is the number Frac {{8}} {7}

- The number of rational numbers - Frac {{15}} {{31}} is the number Frac {{15}} {{31}}

- The number of rational numbers Frac {5} {{ - 6}} is the number Frac {5} {{6}}

-The number of rational numbers 3.9 is -3.9

-The number of the rational number -12.5 is 12.5

Lesson 6

Representing the opposite number of each given number on the following shaft:

Suggestions for answers

- The number of rational numbers -frac {5} {6} is the number Frac {5} {6}

- The number of rational numbers - Frac {1} {3} is the number Frac {1} {3}

- The number of rational numbers Frac {7} {6} is the number -frac {7} {6}

Representing the numbers on the number as follows:

Lesson 7

Compare:

a) 2.4 and 2frac {3} {5}

b) -0,12 and - Frac {2} {5}

c) - Frac {2} {7} and -0.3

Suggestions for answers

a) 2.4 and 2frac {3} {5}

We have:

begin {Matrix} 2.4 = dfrac {{24}} {{{10}} = dfrac {{12}} {5} HFILL 2DFRAC {3}}} = DFRAC {{13}}}}} HFILL End { Matrix}

Do 12 <13 => Frac {{12}} {5} <Frac {{13}} {5}

=> 2.4 <2frac {3} {5}

So 2.4 <2frac {3} {5}

b) -0,12 and - Frac {2} {5}

We have:

begin{matrix} - 0,12 = - dfrac{{12}}{{100}} = - dfrac{3}{{25}} hfill - dfrac{2}{5} = dfrac{{ - 2.5}} {{{5.5}} = - dfrac {{10}} {{25}} hfill end {Matrix}

Do 3 <10 => -3> -10

=> - Frac {3} {{25}}> - Frac {{10}} {{25}}

=> - 0.12> - Frac {2} {5}

So - 0.12> - Frac {2} {5}

c) - Frac {2} {7} and -0.3

We have: - 0.3 = Frac {{ - 3}} {{10}}

begin {matrix} dfrac {{ - 3}} {{{10}} = dfrac {{{ - 3.7}}} {{7.10}} = - DFRAC {{21} {{70}} HFILL - DFRAC {2} {} {{{ 7} = dfrac {{{ - 2.10}} {{{7.10}} = - dfrac {{20}} {{70}} HFILL End {Matrix}

Do 21> 20 => -21 <-20

=> - Frac {{21}} {{{70}} < - Frac {{20}} {{{70}}

=> - 0.3 < - Frac {2} {7}

So - 0.3 < - Frac {2} {7}

Lesson 8

a) Arrange the following numbers in the order of increasing - Frac {3} {7}; 0.4; - 0.5; Frac {2} {7}.

b) Arrange the following numbers in the order of decreasing Frac {{ - 5}} {6}; - 0.75; - 4,5; - 1.

Suggestions for answers

a) We have: 0.4 = Frac {4} {{10}} = Frac {2} {5}, - 0.5 = - Frac {1} {2}

begin {Matrix} - dfrac {3} {7} = dfrac {{{ - 30}} {{{70}} hfill dfrac {2}}} = dfrac {{2.14}}} {{5.14}}}}}}} = dfrac {{{{{{{{{{{ 28}} {{{70}} hfill - dfrac {1} {2} = dfrac {{{ - 1.35}} {{{2.35}} = DFRAC {{{ - 35}} {{70}} HFILL DFRAC {2} {7} = dfrac {{2.10}} {{{7.10}} = dfrac {{20}} {{70}} HFILL End {Matrix}

That -35 <-30 <30 <28

Deduce Frac {{ - 35}} {{70}} <Frac {{ - 30}}} {{70}} <Frac {{20}} {{70}}

Deduce - 0.5 < - Frac {3} {7} <Frac {2} {7} <0.4

So arrange the following numbers in the order of increasing - 0.5; - Frac {3} {7}; Frac {2} {7}; 0.44

b) We have: - 0.75 = - Frac {{75}} {{{100}} = Frac {{ - 3}} {4}; - 4.5 = - Frac {{45}} {{10}} = Frac {{ - 9}}} {2}

begin {matrix} dfrac {{ - 5}} {6} = dfrac {{ - 5.2}} {{{6.2}} = dfrac {{ - 10}}} {{12}} HFILL DFRAC {{ - 3}}}}} {{{{ 4} = dfrac {{{ - 3.3}} {{{4.3}} = dfrac {{ - 9}} {{12}} HFILL DFRAC {{ - 9}}}} = DFRAC {{{ - 9.6}}} {{{{{{{{{{{{{{{{{{{{ 2.6}} = DFRAC {{ - 54}} {{12}} HFILL - 1 = DFRAC {{{ - 1.12}}} {{{1.12}}} = DFRAC {{ - 12}} {{12}} HFILL End { Matrix}

That -9> -12> -10> -54

Deduce Frac {{ - 9}} {{12}}> Frac {{ - 10}}} {{12}}> Frac {{ - 12}}} {{12}}> Frac {{ - 54}}} {12}}}}}}}}}}}} }

Inferred: - 0.75> - Frac {5} {6}> - 1> - 4,5

So the following numbers in order decreasing are: - 0.75; - Frac {5} {6}; - 1; - 4.5

Lesson 9

Linh is weighing their weight (Figure 4) where the lines recorded 46 and 48 encroaching on measurements of 46kg and 48kg, when looking at the position where the needle pointed, you read the measurement of 47.15kg , Yang read the measurement of 47.3kg, Quan read the measurement of 47.65kg. Who has read the correct measurement? Why?

Suggestions for answers

Observe the drawing we see:

The distance from 46 to 48 is divided into equal parts.

Each line corresponds to 2: 20 = 0.1 (g)

The bold bar between 46 and 48 is 47kg

On the picture of the weighing needle pointing to the line 3 from the bold line

The number of needles weighing is pointed to

47 + 0.1. 3 = 47.3 (kg)

So Duong is the right reader of Linh's weight.

Lesson 10

Hanh intends to build a basement for the family's house. A construction consultancy company has provided Hanh to choose one of the six height measurements of the basement as follows: 2.3 m; 2.35 m; 2.4 m; 2.55 m; 2.5 m; 2.75 m. Ms. Hanh intends to choose the height of the larger basement Frac {{13}} {5}M to ensure light, airy, balanced architecture and convenient in use. Please help Ms. Hanh choose the correct height measurement of the basement.

Suggestions for answers

We have:

begin {matrix} dfrac {{13}} {5} = dfrac {{{13.20}} {{{5.20}}} = dfrac {{260}} {{{100}} hfill 2.3 = DFRAC {{23}}} { {10}} = dfrac{{230}}{{100}} hfill 2,35 = dfrac{{235}}{{100}} hfill 2,4 = dfrac{{24}}{{10}} = DFRAC {{240}} {{{100}} HFILL 2.55 = DFRAC {{255}} {{{100}} HFILL 2.5 = DFRAC {{25}} {{10}}} = DFRAC {{{{ 250}} {{100}} hfill 2.75 = dfrac {{275}}} {{{100}} hfill end {Matrix}

We have: 230 <235 <240 <250 <255 <260 <275

Deduce dfrac {{230}} {{{100}} <Frac {{235}}} {{{100}} <Frac {{240}} {{{100}} <Frac {{250}}} {100}}} <Frac { {255}} {{{100}} <frac {{260}} {{{100}} <Frac {{275}} {{{{100}}}

=> 2.3 <2.35 <2,4 <2.5 <2.55 <Frac {{13}} {5} <2.75

That Hanh intends to choose the height of the larger basement Frac {{13}} {5}m

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