Ratios

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