Detailed Solutions to Questions on Finding Ratios
Detailed solutions to the questions on finding ratio are presented.

There are 3 triangles and 6 squares. Find the ratios
a) triangles to squares
b) squares to total
c) triangles to total
Solution
a) Number of triangles = 3, number of squares = 6. Hence in fraction form the ratio is:
ratio: triangle to squares = 3 / 6
Divide both numerator 3 and denominator 6 by 3 to reduce the fraction:
ratio: 1 / 2 or 1 to 2 or 1:2
b) Totale (triangles + squares) = 3 + 6 = 9
ratio: squares to total = 6 / 9 , simplify : 2 / 3 or 2 to 3 or 2:3
c) Triangles to total
ratio: triangles to total = 3 / 9 , simplify : 1 / 3 or 1 to 3 or 1:3

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
Solution
Total of boys and girls:
Total = 300 + 500 = 800
a) Ratio boys to total:
ratio: 300 / 800
Divide numerator 300 and denominator 800 by 100 to simplify ratio.
ratio: 3 / 8 or 3 to 8 or 3:8
b) Ratio girls to total
ratio: girls to total = 500 / 800 , simplify : 5 / 8 or 5 to 8 or 5:8
c) Ratio boys to girls
ratio: boys to girls = 300 / 500 , simplify : 3 / 5 or 3 to 5 or 3:5

There are 200 chairs and 150 tables. Find the ratios
a) chairs to total
b) total to tables
Solution
Total of chairs and tables:
Total = 200 + 150 = 350
a) Ratio chairs to total:
ratio: 200 / 350
Divide numerator 200 and denominator 350 by 50 (because 50 is the GCF of 200 and 350) to simplify ratio.
ratio: 4 / 7 or 4 to 7 or 4:7
b) Ratio total to tables
ratio: total to tables = 350 / 150 , simplify : 7 / 3 or 7 to 3 or 7:3

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
Solution
a) Ratio of students to teachers
ratio: 500 / 25
Divide numerator 500 and denominator 25 by 25 (because 25 is the GCF of 500 and 25) to simplify ratio.
ratio: 20 / 1 or 20 to 1 or 20:1
b) Number of Boys.
number of boys = total  number of girls = 500  300 = 200
Ratio boys to teachers.
ratio: boys to teachers = 200 / 25 , simplify : 8 / 1 or 8 to 1 or 8:1

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?
Solution
Ratio of GPs to number of people in city A
ratio city A: 420,000 / 200
Divide numerator 420,000 and denominator 200 by 200.
ratio: 2100 / 1 or 2100 to 1 or 2100:1
Ratio of GPs to number of people in city B.
ratio city B: 460,000 / 230
Divide numerator 460,000 and denominator 230 by 230.
ratio city B: 2000 / 1 or 2000 to 1 or 2000:1
City A has a higher ratio of GPs to number of people.
Links and References
Middle School Math (Grades 6, 7, 8, 9)  Free Questions and Problems With AnswersHigh School Math (Grades 10, 11 and 12)  Free Questions and Problems With Answers
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