Find Ratios in Math - Grade 7 Practice & Solutions

Understanding how to find a ratio is an essential math skill used to compare different quantities and understand proportions in real-world situations.

This page features a clear lesson on ratios and Grade 7 practice questions. Each question comes with a detailed, step-by-step solution to help students, teachers, and parents confidently master the concept.

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

In math, a ratio is used to compare quantities. Ratios can be expressed in three common ways: as a fraction, using a colon (:), or using the word "to".

Example 1: Boys and Girls in a Classroom

Scenario: 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

Step-by-Step Solutions:

a) The ratio of boys to girls is:

First, write it as a fraction: \( \dfrac{\text{boys}}{\text{girls}} = \dfrac{8}{6} \)

Simplify by dividing the numerator and denominator by the greatest common factor (which is 2):
\( \dfrac{8 \div 2}{6 \div 2} = \dfrac{4}{3} \)

Forms: Fraction: \( \dfrac{4}{3} \) | Colon: \( 4:3 \) | Words: "4 to 3"


b) The ratio of girls to boys is:

As a fraction: \( \dfrac{\text{girls}}{\text{boys}} = \dfrac{6}{8} = \dfrac{3}{4} \)

Forms: Fraction: \( \dfrac{3}{4} \) | Colon: \( 3:4 \) | Words: "3 to 4"


c) The ratio of boys to the total is:

First, find the total number of students: \( \text{Total} = 8 + 6 = 14 \)

As a fraction: \( \dfrac{\text{boys}}{\text{total}} = \dfrac{8}{14} = \dfrac{4}{7} \)

Forms: Fraction: \( \dfrac{4}{7} \) | Colon: \( 4:7 \) | Words: "4 to 7"


d) The ratio of girls to the total is:

As a fraction: \( \dfrac{\text{girls}}{\text{total}} = \dfrac{6}{14} = \dfrac{3}{7} \)

Forms: Fraction: \( \dfrac{3}{7} \) | Colon: \( 3:7 \) | Words: "3 to 7"

Practice Questions & Step-by-Step Solutions

Answer the following questions. Expand the solution blocks to check your work and reasoning.

Question 1

There are 3 triangles and 6 squares. Find the ratios of:

  1. triangles to squares
  2. squares to total
  3. triangles to total
View Solution

Number of triangles = 3, Number of squares = 6. The total is \( 3 + 6 = 9 \).

  1. Triangles to squares:
    \( \dfrac{\text{triangles}}{\text{squares}} = \dfrac{3}{6} \). Simplify by dividing by 3 to get \( \mathbf{\dfrac{1}{2}} \) or \( \mathbf{1:2} \).
  2. Squares to total:
    \( \dfrac{\text{squares}}{\text{total}} = \dfrac{6}{9} \). Simplify by dividing by 3 to get \( \mathbf{\dfrac{2}{3}} \) or \( \mathbf{2:3} \).
  3. Triangles to total:
    \( \dfrac{\text{triangles}}{\text{total}} = \dfrac{3}{9} \). Simplify by dividing by 3 to get \( \mathbf{\dfrac{1}{3}} \) or \( \mathbf{1:3} \).

Question 2

There are 300 boys and 500 girls in a school. Find the ratios of:

  1. boys to total
  2. girls to total
  3. boys to girls
View Solution

Total students = \( 300 + 500 = 800 \).

  1. Boys to total:
    \( \dfrac{\text{boys}}{\text{total}} = \dfrac{300}{800} \). Divide the numerator and denominator by 100 to get \( \mathbf{\dfrac{3}{8}} \) or \( \mathbf{3:8} \).
  2. Girls to total:
    \( \dfrac{\text{girls}}{\text{total}} = \dfrac{500}{800} \). Divide by 100 to get \( \mathbf{\dfrac{5}{8}} \) or \( \mathbf{5:8} \).
  3. Boys to girls:
    \( \dfrac{\text{boys}}{\text{girls}} = \dfrac{300}{500} \). Divide by 100 to get \( \mathbf{\dfrac{3}{5}} \) or \( \mathbf{3:5} \).

Question 3

There are 200 chairs and 150 tables. Find the ratios of:

  1. chairs to total
  2. total to tables
View Solution

Total pieces of furniture = \( 200 + 150 = 350 \).

  1. Chairs to total:
    \( \dfrac{\text{chairs}}{\text{total}} = \dfrac{200}{350} \). Divide the numerator and denominator by their greatest common factor, 50: \( \dfrac{200 \div 50}{350 \div 50} = \mathbf{\dfrac{4}{7}} \) or \( \mathbf{4:7} \).
  2. Total to tables:
    \( \dfrac{\text{total}}{\text{tables}} = \dfrac{350}{150} \). Divide by 50 to get \( \mathbf{\dfrac{7}{3}} \) or \( \mathbf{7:3} \).

Question 4

There are 25 teachers, and 500 students of which 300 are girls. Find the ratios of:

  1. total students to teachers
  2. boys to teachers
View Solution
  1. Total students to teachers:
    \( \dfrac{\text{students}}{\text{teachers}} = \dfrac{500}{25} \). Divide by 25 to get \( \mathbf{\dfrac{20}{1}} \) or \( \mathbf{20:1} \).
  2. Boys to teachers:
    First, find the number of boys: \( 500 \text{ students} - 300 \text{ girls} = 200 \text{ boys} \).
    \( \dfrac{\text{boys}}{\text{teachers}} = \dfrac{200}{25} \). Divide by 25 to get \( \mathbf{\dfrac{8}{1}} \) or \( \mathbf{8:1} \).

Question 5

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

View Solution

To find which city has the higher ratio of GPs to people, set up the ratio fraction for each city: \( \dfrac{\text{GPs}}{\text{People}} \).

City A:
\( \dfrac{200}{420,000} \). Simplify by dividing the numerator and denominator by 200:
\( \dfrac{1}{2100} \) (This means there is 1 GP for every 2100 people).

City B:
\( \dfrac{230}{460,000} \). Simplify by dividing the numerator and denominator by 230:
\( \dfrac{1}{2000} \) (This means there is 1 GP for every 2000 people).

Now compare the fractions: \( \dfrac{1}{2000} \) is larger than \( \dfrac{1}{2100} \). Because there are fewer people sharing one GP in City B, the proportion of GPs to the population is greater.

Therefore, City B has a higher ratio of GPs to people.

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