What is a ratio in math and where are they needed?
In math, a ratio is used to compare quantities.
Example 1:There are 8 boys and 6 girls in a classroom. What is the ratio of
a) boys to girls?
b) girls to boys?
c) boys to the total?
d) girls to the total?
Solution
a) The ratio of boys to girls is
As a fraction: boys / girls = 8/6
which may be simplified by dividing both numearator and denominator by the same greatest common factor (to 8 and 6) which here is 2.
8 / 6 = (8÷2) / (6÷2) = 4/3
Other ways to write a ratio:
fraction: 4/3 , using colon 4:3 or as "4 to 3".
b) The ratio of girls to boys is
As a fraction: girls / boys = 6/8 = 3/4 , 3:4 , "3 to 4".
c) The total of students
total = boys + girls = 8 + 6 = 14
The ratio of boys to the total
Ratio as a fraction: boys / total = 8/14 = 4/7 , 4:7 , "4 to 7".
d)The ratio of girls to the total
Ratio as a fraction: girls / total = 6/14 = 3/7 , 3:7 , "3 to 7".
Answer the following questions about ratios.

There are 3 triangles and 6 squares. Find the ratios
a) triangles to squares
b) squares to total
c) triangles to total

There are 300 boys and 500 girls in a school. find the ratios
a) boys to total
b) girls to total
c) boys to girls

There are 200 chairs and 150 tables. Find the ratios
a) chairs to total
b) total to tables

There are 25 teachers, and 500 students of which 300 are girls. Find the ratios
a) total of students to teachers
b) boys to teachers

City A has a population of 420,000 people and 200 general practitioners (GP). City B has has a population of 460,000 people and 230 general practitioners. Which city has a higher ratio GP to number of people?
Detailed Solutions and explanations to the above questions.