Ratio compares two or more quantities.
Symbol of ratio is :
Ratio of quantity A to quantity B s written as
A : B
** Ratio has no unit of measure
Example
Write the ratio 200: 250 in its simplest form
200 : 250
20÷5 : 25 ÷ 5
4 : 5
a : b: c => a: b , b : c
Equivalent Ratios
Example
4 : 10
= 4 ÷2 : 10÷2
= 2 : 5
4 : 10 and 2 : 5 are equivalent ratios.
Ratio in its simplest form
Example
Write 8 : 12: 36 in its simplest form
Step: Find the common factors for the given numbers and reduce
8 ÷4 : 12÷4 : 36÷4
2 : 3 : 9
Example: Write the ratio 200: 250 in its simplest form
200 : 250
20÷5 : 25 ÷ 5
4 : 5
Example
The ratio of the number of tables to the number of chairs is 1 : 4 in the restaurant. There are 6 tables, how many chairs are there?
Step 1 : Write the ratio and number of tables
T C
1 : 4
Step 2 : Write the number of tables on both side of the ratio and multiply
T C
1 : 4
x 4 x4
= 4 : 16
Step3 : Answer
There are 16 chairs
Ratio with different Unit of Measure (UOM)
The UOM must be the same when comparing two of more quantities
Example:
John has $1 and Sally has 80cts as their daily allowance. What is the ratio of their allowance?
Step 1 : Convert the amount to the same unit (of the 'smaller' UOM)
$1 = 100cts
Step 2 : Write the ratio and reduce the the lowest term
100 : 80
5 10 : 8 4
5 : 4
Step 3 : Write the Answer
The ration is 5 : 4
Ratio involving Fractions and Decimals
Example
Express the following ratios in its simplest form.
1.2 : 3
Step 1 : Multiply 10 to both side (to remove the decimal)
x10. 1.2. : 3 x 10
12 : 30
Step 2 : Reduce the simplest term
<< divide by 6 for both side >>
2 12 : 30 5
The ratio is 2 : 5
Example
Express the following ratios in its simplest form.
b. 1 ¾. : 2 ½
Step 1: Change both to improper fractions
7 : 5
4 2
Step 2 : Make both side to have the same denominator
<< multiply 2 , by 2 >>
7 : 5 x 2
4 2 x 2
7 : 10
4 4
Step 3 : Write the numerators as the ratio
7 : 10
Connecting Ratio with Fraction
For a ratio A : B, the 'total number of parts' = A + B
Thus in fraction form, A's part is A / A+B
B's part is B / A+B
Example
There are 10 girls and 15 boys.
The ratio of the number of girls to the number of boys =
10 : 15 or 2 : 3
The total part = 2 + 3 = 5
=> Number of girls = 2/3 of number of boys
=> Number of girls = 2/5 of the total
=> Number of boys = 3/2 of number of girls
=> Number of boys = 3/5 of the total.
Example
Abby and Bobby have 10 oranges altogether.
The oranges are to be divided in the ratio of 3 : 2
How many oranges will each of them get?
Step 1: Find the total parts
Total = 3 + 2 = 5
Step 2 : Compute their fraction's
Abby = 3/5 , Bobby = 2/5
Step 3 : Compute by multiplying total quantity with the fractions
Abby has 3/5 x 10 = 6 oranges
Bobby has 2/5 x 10 = 4 oranges
Practice
1. Express the following ratios in its simplest form.
(a) 4 : 20 [1 : 5]
(b) 35 : 14 [7 : 2]
(c). 64 : 56 : 16 [8 : 7 : 2]
2. Express the following ratios in its simplest form.
a. ⅚ kg : 2 kg [5 : 12 ]
b. 1.6 cm : 4 mm [4 : 1 ]
c. 1 ½ hr : 20 mins [9 : 2 ]
d. 250 ml : 1 litre [1 : 4 ]
3. Mary and Andy share a pizza in the ratio of 1 : 2. Andy gets 4 slices of the pizza. How many slices does Mary get? [2]
4. Alice, Betty and Coby share their marbles in the ratio of 2 : 3 : 5. Find the amount each gets for each of the marbles.
a. 420 (b) 70 [a. 84, 126, 210 b. 14, 21, 35]
