Divide a natural number by a decimal

### 1.1. Knowledge to remember

**a)** Calculate and compare the results:

25 : 4 and (25 x 5) : (4 x 5)

4.2 : 7 and ( 4.2 x 10) : (7 x 10)

37.8 : 9 and (37.8 x 100) : (9 x 10)

*When multiplying the divisor and the divisor with a non-zero number, the quotient does not change.*

**b)** __Example 1__: A rectangular garden has an area of 57m2, length 9.5m. How many meters wide is the garden?

We have to do the division: 57 : 9.5 = ? square meter

We have: 57 : 9.5 = (57 x 10 ) : (9.5 x 10)

57 : 9.5 = 570 : 95

Usually we set the calculation and then do the following:

- The decimal part of the number 9.5 has one digit.
- Add a zero to the right of 57 to get 570; remove the comma at 9.5 to get 95.
- Perform division 570 : 95

So 5.7 : 9.5 = 6 (m)

**c)** __Example 2__: 99 : 8.25 = ?

We calculate and then do the following:

- The decimal part of 8.25 has two digits.
- Add two zeros to the right of 99 to get 9900, remove the comma at 8.25 and get 825
- Do the division 9900: 825

******* To divide a natural number by a decimal, do the following:

- Count how many decimal places there are in the decimal part of the divisor, then add 0’s to the right of the divisor.
- Remove the comma from the divisor and then perform the division as if it were a natural number.

### 1.2. Solution of textbook exercises page 70

**Lesson 1**

Calculate then calculate:

a) 7 : 3.5 b) 702 : 7.2

c) 9 : 4.5 d) 2 : 12.5.

*Solution guide:*

Lesson 2

Mental arithmetic:

a) 32 : 0.1 b) 168 : 0.1

32 : 10 168 : 10

c) 934 : 0.01

934 : 100

*Solution guide:*

a) 32:0,1=32 ; 32:10=3.2

b) 168:0.1=1680168:0.1=1680 ; 168:10=16.8

c) 934:0.01=93400 ; 934:100=9.34

Comment: a:0.1=a×10; a:0.01=a×100; a:0.001=a×1000;…

To divide a natural number by 0.1;0.01;0.001;… we just need to add to the right of that number one, two, three, … digit 0 respectively.

lesson 3

An iron rod 0.8m long weighs 16kg. How many kilograms does an iron bar of the same type 0.18m0.18m long and weigh?

*Solution guide:*

The weight of an iron rod 1m long and the weight of kilograms is:

16:0.8=20(kg)

The iron rod 0.18 m long and the weight in kilograms is:

20×0.18=3.6(kg)

Answer: 3.6kg.

### 1.3. Solving the exercises in the textbook Practice page 70

Lesson 1

Calculate and compare the results:

a) 5:0.5 and 5×2

52:0.5 and 52×2

b) 3:0.2 and 3×5

18:0.25 and 18×4

*Solution guide:*

a) 5:0.5=10;5×2=10.

So: 5:0.5=5×2.

+) 52:0.5=104;52×2=104.

So: 52:0.5=52×2.

b) 3:0.2=15;3×5=15.

So: 3:0.2=3×5.

+) 18:0.25=72;18×4=72.

So: 18:0.25=18×4.

Lesson 2

Find x:

a) x × 8.6 = 387 b) 9.5 × x = 399

*Solution guide:*

a) x × 8.6 = 387

x = 387:8.6

x = 45

b) 9.5 × x = 399

x = 399 : 9.5

x = 42

lesson 3

The big tank has 21 liters of oil, the small one has 15 liters of oil. That amount of oil is stored in the same bottles, each bottle has 0.75l. How many bottles of oil are there in all?

*Solution guide:*

The two tanks have all liters of oil:

21 + 15 = 36(l)

The total number of oil bottles is:

36 : 0.75 = 48 (bottle)

Answer: 48 bottles.

Lesson 4

A rectangular field has a width of 12.5m and an area equal to the area of a square with sides 25m. Calculate the perimeter of that rectangular field.

*Solution guide:*

The area of a square with side 25m is:

25×25=625 (m^{2} )

According to the problem, a rectangle has an area equal to a square with side 25m, so the area of the rectangle is 625m.^{2}

The length of the rectangular field is:

625 : 12.5 = 50(m)

The perimeter of that field is:

(50 + 12.5) × 2 = 125(m)

Answer: 125m.

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