Practice division

### 1.1. Solving exercises in the Practice Textbook Page 164, 165

**Lesson 1 Textbook page 164**

Calculate

a) \(\frac{{12}}{{17}}:6;\,\,\,16:\frac{8}{{11}};\,\,9:\frac{3}{ 5} \times \frac{4}{{15}}\)

b) 72:45 281.6:8 300.72:53.7

15:50 912.8:28 0.162:0.36

**Solution guide:**

a) \(\frac{{12}}{{17}}:6 = \frac{{12}}{{17}} \times \frac{1}{6} = \frac{{12}}{ {17 \times 6}} = \frac{{6 \times 2}}{{17 \times 6}} = \frac{2}{{17}}\)

\(\begin{array}{l}

16:\frac{8}{{11}} = 16 \times \frac{{11}}{8} = \frac{{16 \times 11}}{8}\\

= \frac{{8 \times 2 \times 11}}{8} = 22

\end{array}\)

\(\begin{array}{l}

9:\frac{3}{5} \times \frac{4}{{15}} = 9 \times \frac{5}{3} \times \frac{4}{{15}}\\

= \frac{{9 \times 5 \times 4}}{{3 \times 15}} = \frac{{3 \times 3 \times 5 \times 4}}{{3 \times 3 \times 5}} = 4

\end{array}\)

Lesson 2 Textbook page 164

Mental arithmetic:

a) 3.5:0.1 8.4:0.01 9.4:0.1

7.2:0.01 6.2:0.1 5.5:0.01

b) 12:0.5 20:0.25 \(\frac{3}{7}\):0.5

11:0.25 24:0.5 15:0.25

*Solution guide:*

\(\begin{array}{l}

a)3,5:0.1 = 3.5 \times 10 = 35\\

8.4:0.01 = 8.4 \times 100 = 840\\

9.4:0.1 = 9.4 \times 10 = 94\\

7.2:0.01 = 7.2 \times 100 = 720\\

6.2:0.1 = 6.2 \times 10 = 62\\

5.5:0.01 = 5.5 \times 100 = 550

\end{array}\)

\(\begin{array}{l}

b)12:0.5 = 12 \times 2 = 24\\

\frac{3}{7}:0.5 = \frac{3}{7} \times 2 = \frac{6}{7}\\

24:0.5 = 24 \times 2 = 48\\

11:0.25 = 11 \times 4 = 44\\

20:0.25 = 20 \times 4 = 80\\

15:0.25 = 15 \times 4 = 60.

\end{array}\)

Lesson 3 Textbook page 164

Write the result of the division as a fraction and a decimal (in the denominator):

a) 3:4; b) 7:5

c) 1:2; d) 7:4.

Pattern: \(3:4 = \frac{3}{4} = 0.75\)

*Solution guide:*

\(\begin{array}{l}

b)7:5 = \frac{7}{5} = 1,4;\\

c)1:2 = \frac{1}{2} = 0.5;\\

d)7:4 = \frac{7}{4} = 1.75.

\end{array}\)

Lesson 4 Textbook page 165

Choose a letter that has a right answer:

A class has 18 girls and 12 boys. What percentage of the total number of students are male students?

A. 150% B. 60% C. 66% D. 40%

*Solution guide:*

The total number of students in the class is:

18 + 12 = 30 (students)

The number of boys as a percentage of the total number of students in the class is:

12 : 30 = 0.4 = 40%

Choose answer D.

### 1.2. Solving exercises in the textbook Practice page 165

Lesson 1 Textbook page 165

Calculate the percentage of:

a) 2 and 5; b) 2 and 3 ;

c) 3.2 and 4 d) 7.2 and 3.2.

Note: If the percentage is a decimal, use only two digits in the decimal.

For example: 1 : 6 = 0.166666…

The percentages of 1 and 6 are: 16.66%.

*Solution guide:*

a) 2 : 5 = 0.4 = 40%

b) 2 : 3 = 0.6666 = 66.66%

c) 3.2 : 4 = 0.8 = 80%

d) 7.2 : 3.2 = 2.25 = 225%

Lesson 2 Textbook page 165

Calculate:

a) 2.5% + 10.34% ; b) 56.9% – 34.25% ; c) 100% – 23% – 47.5%.

*Solution guide:*

a) 2.5% + 10.34% = 12.84%;

b) 56.9% – 34.25% = 22.65% ;

c) 100% – 23% – 47.5% = 77% – 47.5% = 29.5%.

Lesson 3 Textbook page 165

One district has 320ha of land for coffee trees and 480ha of land for rubber trees. Ask:

a) What is the percentage of land planted with rubber trees?

b) What is the percentage of land planted with coffee trees?

*Solution guide:*

a) The ratio of the land area for rubber trees and the area for coffee trees is:

480 : 320 = 1.5

1.5 = 150%

b) The ratio of the percentage of the area planted with coffee trees and the area planted with rubber trees is:

320 : 480 = 0.6666…

0.6666… = 66.66%

Answer: a) 150% ;

b) 66.66%.

Lesson 4 Textbook page 165

Class 5A plans to plant 180 trees, so far 45% of them have been planted. According to the plan, how many more trees will class 5A have to plant?

*Solution guide:*

The number of trees class 5A has planted is:

180 x 45 : 100 = 81 (tree)

As planned, class 5A still has to plant as many trees as:

180 – 81 = 99 (tree)

Answer: 99 trees.

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