Ratio and Proportion

Ratio

is the spoken language of arithmetic. It is a way of comparing two or more quantities having the same units.

A ratio can be written as a is tob or a : b or by giving the value of theirquotient𝑎𝑏

Terms of Ratio

Antecedent refers to the first term of the quantity of the ratio.

Consequent refers to the second quantity of the ratio.

Express the ratio of the two quantities (circles and triangles) in three different ways.

Word form →2is to3

Colon form →2:3

Fraction form →2/3

Proportion

is an equality between two ratiosor fractions. A proportion can be written in two ways: as two equal fractions 𝑎𝑏= 𝑐𝑑

or usinga colon a : b = c : d → read as a is to b as c is d

Terms in Proportion

Means itrefers to the inner numbers of the proportion.

Extremes it refers to the outside numbers of the proportion.

 2 out of 3 is equal to 4 out of 6 

 Therefore, the two ratios are equal, so they are in proportion.

𝟐𝟑=𝟒𝟔

 hence, in a proportion the product of the means is equal to the     product of the extremes. 

3 x 4 = 2 x6.                                                   

 12 =  12

Solutions: Step by Sep

 𝟔/𝟐𝟒, 𝟐 /𝟖

Write a proportion → 𝟔 /𝟐𝟒=𝟐 𝟖

Form a cross product →  6 x 8 = 2 x 24     

   Multiply       → 48 = 48    

Answer: The two ratios form a proportion.

Multiple Choice

Find the value of N in each of the following proportions.

12/n=28/24

• 6

• 5

• 7

• 4