# Questions - Ratios & Proportion

**1)** What is a **Ratio** ?

A ratio compares the size of different parts of a whole.

A ratio is used to compare two numbers or quantities

When you **share** out an amount using a given ratio, then each share is a proportion of the total amount.

**2)** What does the word proportion mean ?

A share of a whole.

The relation in size or amount between one thing and another.

**3)** What is a **Proportion** ?

Proportions are statements that show two ratios as equivalent.

A proportion compares the size of one part with the whole.

**4)** What is Direct Proportion ?

Two quantities are said to be in direct proportion if they increase and decrease in the same ratio.

There is a direct proportion between two values when once is a multiple of the other.

**5)** What is Inverse Proportion ?

One value is inversely proportional to another if when one value increases, the other decreases.

**6)** A box contains 7 counters; 3 red counters and 4 blue counters.

The ratio of red to blue counters is 3:4

The proportion of red counters is 3/7

The proportion of blue counters is 4/7

**7)** What proportion of the employees are women ?

The ratio of men to women at a company is 3:5

ratio = 5/8

**8)** How long does it take 2 robots to build a wall that is 9m long ?

It takes 2 robots, 3 hours to build a wall that is 1.5m long.

1.5m : 3 hours

(1.5 x 6) = 9m

9m : (3 x 6) hours

Using Direct Proportion - 9m : 18 hours

**9)** How many robots does it take to build a 1.5m wall in 6 hours ?

It takes 2 robots, 3 hours to build a wall that is 1.5m long.

3 hours : 2 robots

(3 x 2) = 6 hours

(2 / 2) = 1 robot

Using Inverse Proportion - 6 hours : 1 robot

**10)** What is the ratio of blue to green ?

The ratio of blue to red is 4:5

The ratio of red to green is 7:10

We need to combine the ratios. Red appears in both so we can combine by making red the same.

b : r = 4 : 5

r : g = 7 : 10

Find a common multiple of 5 and 7.

b : r = (4 x 7) : (5 x 7) = 28 : 35

r : g = (7 x 5) : (10 x 5) = 35 : 50

So b : g = 28 : 50

**11)** Work out the size of each angle ?

The angles in a triangle are in the ratio 3:4:5

3 + 4 + 5 = 12

Angles in a triangle add up to 180.

(180 / 12) = 15

(3 x 15) , (4 x 15) , (5 x 15) = 45, 60, 75

**12)** How many sweets do they each eat ?

Richard has a bag of 30 sweets and he shares the sweets with a friend.

For every 3 sweets that Richard eats he gives his friend 2.

(30 / (3 + 2) ) = 30/5 = 6

Richard eats (6 x 3) = 18

Friend eats (6 x 2) = 12

**13)** What fraction of the shapes are red ?

Shapes are triangles or rectangles and are either red or blue.

The ratio of triangles to rectangles is 3:4.

For the triangles, the ratio of red to blue is 2:3

For the rectangles, the ratio of red to blue is 4:1

© 2022 Better Solutions Limited. All Rights Reserved. © 2022 Better Solutions Limited TopPrevNext