# Free Mathematics Tutorials # 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.