Divide a number by a product

### 1.1. Knowledge to remember

Calculate and compare the values of the expressions:

24 : (3 × 2) 24 : 3 : 2 24 : 2 : 3

We have: 24 : (3×2) = 24 : 6 = 4

24 : 3 : 2 = 8 : 2 = 4

24 : 2 : 3 = 12 : 3 = 4

So: 24 : (3 × 2) = 24 : 3 : 2 = 24 : 2 : 3

**When we divide a number by a product of two factors, we can divide that number by one factor, and then divide the result by the other factor.**

### 1.2. Solving Textbook Exercises

**Lesson 1:** Calculate expression value

a) 50 : (2 × 5) ; b) 72 : (9 × 8); c) 28 : (7 × 2).

__Solution guide:__

- When we divide a number by a product of two factors, we can divide that number by one factor, and then divide the result by the other factor.

a : (b × c) = (a : b) : c = (a : c) : b

a) 50 : (2 × 5) = 50 : 10 = 5

50 : (2 × 5) = 50 : 2 : 5 = 25 : 5 = 5

50 : (2 × 5) = 50 : 5 : 2 = 10 : 2 = 5

b) 72 : (9 × 8) = 72 : 72 = 1

72 : (9 × 8) = 72 : 9 : 8 = 8 :8 = 1

72 : (9 × 8) = 72 : 8 : 9 = 9 : 9 = 1

c) 28 : (7 × 2)= 28 : 14 = 2

28 : (7 × 2) = 28 : 7 : 2 = 4 : 2 = 2

28 : (7 × 2) = 28 : 2 : 7 = 14 : 7 = 2.

**Lesson 2: **Convert each of the following divisions into a division of a number divided by a product and calculate

a) 80 : 40 b) 150 : 50. c) 80 : 16

__Solution guide:__

- Write the divisor as the product of two suitable numbers and then divide the divisor by a product to calculate the given expression value.

a) 80 : 40 = 80 : (10 × 4) = 80 : 10 : 4 = 8 : 4 = 2

b) 150 : 50 = 150 : ( 10 × 5) = 150 : 10 : 5 = 15 : 5 = 3

c) 80 : 16 = 80 : (8 × 2) = 80 : 8 : 2 = 10 : 2 = 5

**Lesson 3:** There are 2 students, each of you buys 3 notebooks of the same type and all have to pay 7200 VND. Calculate the cost of each book.

__Solution guide:__

- Find the number of books you both bought.
- To find the price of 1 book, we divide the amount paid by the number of books both of you buy.

*Solution*

The number of books you bought is:

3 × 2 = 6 (book)

The price for each book is:

7200 : 6 = 1200 (VND)

Answer: 1200 VND.

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