RATIO AND PROPORTION

Back to: Mathematics Primary 6

HELLO, WELCOME BACK TO CLASS

 

We use ratio to compare things. The ratio of two quantities ‘a’ and ‘b’ of the same kind and in the same units is a fraction a/b which shows that how many times one quantity is of the other and is written as a: b.

In the ratio a: b, the quantities a and b are called terms of the ratio. Here, ‘a’ is called the first term or the antecedent and `b’ is called the second term or consequent.

A ratio a: b is said to be in the simplest form if a and b have no common factor other than 1.

Example: Express 15: 10 in the simplest form.

Solution:  15/10

= (15 ÷ 5)/ (10 ÷ 5)

= 3/2 (In this we cancelled the common factor 5). Therefore, ratio is 3:2

ACTIVITY: Express the following ratios in the simplest form.

(a) 64 cm to 4.8 m

(b) 36 minutes to 36 seconds

(c) 30 dozen to 2 hundred

 

Proportion

We have already learnt that statement of equality of ratios is called proportion, if four quantities a, b, c, d are in proportion, then a : b = c : d

⇒ a/b = c/d

⇒ a × d = b × c(Cross multiplied)

⇒ ad = bc

 

Examples: Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers.

Solution:  Sum of the terms of the ratio = 3 + 4 = 7

Sum of numbers = 63

Therefore, first number = 3/7 × 63 = 27

Second number = 4/7 × 63 = 36

Therefore, the two numbers are 27 and 36.

 

ACTIVITIES

1. If x : y = 1 : 2, find the value of (2x + 3y) : (x + 4y)
2. A bag contains N510 in the form of 50k, 25k and 20k coins in the ratio 2 : 3 : 4. Find the number of coins of each type.
3. The length of the ribbon was originally 30 cm. It was reduced in the ratio 5 : 3. What is its length now?
4. Mother divided the money among Ron, Sam and Maria in the ratio 2 : 3 : 5. If Maria got N150, find the total amount and the money received by Ron and Sam.
5. Divide N370 into three parts such that the second part is 1/4 of the third part and the ratio between the first and the third part is 3 : 5. Find each part.
6. The ratio of number of boys and girls is 4 : 3. If there are 18 girls in a class, find the number of boys in the class and the total number of students in the class.

 

More Activities

School Owner? Looking for ready-made content and tools to save time and grow easily? Book a free demo session now

Get more class notes, videos, homework help, exam practice on Android [DOWNLOAD]

Get more class notes, videos, homework help, exam practice on iPhone [DOWNLOAD]