Find Ratios in Maths - Grade 7 Maths Questions With Detailed Solutions

How to find a ratio in maths? Grade 7 questions are presented along with detailed solutions. Detailed Solutions and explanations are included.

What is a ratio in maths and where are they needed?

In maths, a ratio is used to compare quantities.

Example 1:

There are 8 boys and 6 girls in a classroom. Find the ratio of:

  1. boys to girls
  2. girls to boys
  3. boys to the total
  4. girls to the total

Solution

  1. The ratio of boys to girls is:
    As a fraction: \( \dfrac{\text{boys}}{\text{girls}} = \dfrac{8}{6} \)
    Simplify by dividing numerator and denominator by the greatest common factor (2):
    \( \dfrac{8}{6} = \dfrac{8 \div 2}{6 \div 2} = \dfrac{4}{3} \)
    Other forms:

  2. The ratio of girls to boys is:
    As a fraction: \( \dfrac{\text{girls}}{\text{boys}} = \dfrac{6}{8} = \dfrac{3}{4} \)
    Other forms:

  3. First, find the total number of students:
    \( \text{Total} = 8 + 6 = 14 \)
    The ratio of boys to the total is:
    \( \dfrac{\text{boys}}{\text{total}} = \dfrac{8}{14} = \dfrac{4}{7} \)
    Other forms:

  4. The ratio of girls to the total is:
    \( \dfrac{\text{girls}}{\text{total}} = \dfrac{6}{14} = \dfrac{3}{7} \)
    Other forms:

Answer the following questions

  1. There are 3 triangles and 6 squares. Find the ratios
    a) triangles to squares
    b) squares to total
    c) triangles to total
  2. 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
  3. There are 200 chairs and 150 tables. Find the ratios
    a) chairs to total
    b) total to tables
  4. 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
  5. 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?
    6. Detailed Solutions and explanations to the above questions.

Links and References