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### 1.1. Knowledge to remember

**Example 1:** A fleet of 5 trucks and 7 passenger cars.

I say :

– The ratio of the number of trucks to the number of passenger cars is 5 : 7 or \(\frac{5}{7}\).

This ratio indicates the number of trucks equal to \(\frac{5}{7}\) the number of passenger cars.

– The ratio of the number of passenger cars to the number of trucks is 7 : 5 or \(\frac{7}{5}\).

This ratio shows the number of passenger cars equal to \(\frac{7}{5}\) the number of trucks.

**Example 2: **

Number one | The second number | Ratio of first and second number số |

5 | 7 | 5 : 7 or \(\frac{5}{7}\) |

3 | 6 | 3 : 6 or \(\frac{3}{6}\) |

a | b (other than 0) | a : b or \(\frac{a}{b}\) |

We say that : The ratio of a and b is a : b or \(\frac{a}{b}\) (b is not zero).

### 1.2. Solving Textbook Exercises

**Lesson 1: **Write the ratio of a and b known

a) a = 2 ; b = 3 b) a = 7 ; b = 4

c) a = 6 ; b = 2 d) a = 4 ; b = 10

**Solution guide:**

- The ratio of a and b is a : b or \(\frac{a}{b}\) (b is not zero).

a) Is the ratio of 2 and 3 2 : 3 or \(\frac{2}{3}\).

b) The ratio of 7 and 4 is 7 : 4 or \(\frac{7}{4}\).

c) The ratio of 6 and 2 is 6 : 2 or \(\frac{6}{2}\).

d) Is the ratio of 4 and 10 4 : 10 or \(\frac{4}{{10}}\).

**Lesson 2: **In the box there are 2 red pens and 8 blue pens.

a) Write down the ratio of the number of red pens and the number of blue pens;

b) Write the ratio of the number of green pens to the number of red pens.

__Solution guide:__

The ratio of a and b is a : b or \(\frac{a}{b}\) (b is not zero).

Solution:

a) The ratio of the red pen to the blue pen is 2 : 8 or \(\frac{2}{8}\).

b) The ratio of the blue pen to the red pen is 8 : 2 or \(\frac{8}{2}\).

**Lesson 3: **In a nest there are 5 boys and 6 girls.

a) Write the ratio of the number of boyfriends to the number of friends in the group.

b) Write the ratio of the number of girls to the number of friends in the group.

__Solution guide:__

The ratio of a and b is a : b or \(\frac{a}{b}\) (b is not zero).

*Solution :*

The total number of friends in the group is:

5 + 6 = 11 (you)

a) The ratio of the number of boyfriends to the number of friends in the group is: 5 : 11 or \(\frac{5}{{11}}\).

b) The ratio of the number of girlfriends to the number of friends in the group is: 6 : 11 or \(\frac{6}{{11}}\).

**Lesson 4: **There are 20 cows on the lawn and there are as many buffaloes as \(\frac{1}{4}\) as many cows. How many buffaloes are there on that beach?

__Solution guide:__

- To find the number of buffaloes we look for \(\frac{1}{4}\) of 20 cows. To find the \(\frac{1}{4}\) of 20 children, multiply 20 by \(\frac{1}{4}\), then add units to the result.

*Solution*

The number of buffaloes on the lawn is:

\(20 \times \frac{1}{4} = 5\) (con)

Answer: 5 children

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