Solved Examples and Worksheet for Understanding and Exploring Ratios

Q1A standard Tennis court has length-to-width ratio of 7 : 3. A Tennis court at a local club measures 170 ft by 70 ft. Verify whether the two ratios are equal.

A. Yes
B. No

Solutions
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Step: 1
The length-to-width ratio of the Tennis court at the local club = 17070
Step: 2
= 170÷1070÷10
  [Divide 170 and 70 by their GCF 10.]
Step: 3
= 177 = 17 : 7
  [Express as a ratio.]
Step: 4
Since 7 : 3 ≠ 17 : 7, the length-to-width ratio of the Tennis court at the club is not equal to that of the standard .
Correct Answer is :   No
Q2Write the ratio of 21 to 4 in decimal form.
A. 6.25
B. 4.25
C. 7.25
D. 5.25

Solutions
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Step: 1
21 to 4 = 214
  [Express ratio as a fraction.]
Step: 2
214 = 21×254×25
  [Multiply the numerator and the denominator by 25 to make denominator 100.]
Step: 3
= 525100 = 5.25
  [Move the decimal point 2 places to the left.]
Step: 4
The decimal form of 21 to 4 is 5.25.
Correct Answer is :   5.25
Q3A carnival game has 2 winners for every 5 losers. Find two ratios equal to the ratio of winners to losers.

A. 104, 156
B. 410, 715
C. 510, 615
D. 410, 615

Solutions
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Step: 1
The ratio of winners to losers = 25
Step: 2
25 = 2 × 25 × 2 = 410
  [Multiply both the numerator and the denominator by 2.]
Step: 3
25 = 2 × 35 × 3 = 615
  [Multiply both the numerator and the denominator by 3.]
Step: 4
The two ratios equal to the ratio of winners to the losers are 410 and 615.
Correct Answer is :   410, 615
Q4Write an equivalent decimal number for the ratio 36 : 5.

A. 72
B. 9.2
C. 7.2
D. 6.2

Solutions
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Step: 1
36 : 5 = 365
  [Express the ratio as a fraction.]
Step: 2
365 = (36×20)(5×20)
  [Multiply both numerator and denominator by 20 to make denominator 100.]
Step: 3
= 720100 = 7.20
  [Move the decimal point 2 places towards left.]
Step: 4
The equivalent decimal number for the ratio 36 : 5 is 7.2
Correct Answer is :   7.2
Q5Which of the two ratios are equal to 24?
A. 58 and 12
B. 84 and 12
C. 38 and 12
D. 48 and 12

Solutions
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Step: 1
24 = 2×24×2 = 48
  [Multiply both the numerator and denominator by 2.]
Step: 2
24 = 2÷24÷2 = 12
  [Divide both the numerator and denominator by 2.]
Step: 3
The two ratios are 48 and 12.
Correct Answer is :   48 and 12
Q6The weight of one tiger is about 300 lb and the weight of another tiger is 500 lb. Express the ratio of their weights in its simplest form.

A. 3 : 5
B. 2 : 5
C. 2 : 3
D. 3 : 4

Solutions
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Step: 1
The ratio of the weight of small tiger to that of big tiger = 300500
Step: 2
= 300 ÷ 100500 ÷ 100 = 35
  [Divide both the numerator and the denominator by 100.]
Step: 3
= 3 : 5
  [Write the fraction as ratio.]
Step: 4
The simplest form of the ratio is 3 : 5.
Correct Answer is :   3 : 5
Q7A volleyball team won 4 out of 8 games. What is the ratio of number of wins to total games?

A. 1 : 1
B. 2 : 3
C. 2 : 1
D. 1 : 2

Solutions
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Step: 1
The ratio of the number of wins to total number of games = number of winstotal number of games
Step: 2
= 48
  [Substitute the values.]
Step: 3
= 4 ÷ 48 ÷ 4 = 12
  [Divide both the numerator and the denominator by their G.C.F, 4.]
Step: 4
The ratio of number of wins to total number of games is 1 : 2.
Correct Answer is :   1 : 2
Q8A volleyball team won 6 out of 10 games. Write a ratio of wins to losses.

A. 3 : 2
B. 4 : 5
C. 3 : 5
D. None of the above

Solutions
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Step: 1
The number of losses = total number of games - number of wins
= 10 - 6 = 4
  [Substitute the values and subtract.]
Step: 2
The ratio of the number of wins to the number of losses
= 64
  
Step: 3
= 6 ÷ 24 ÷ 2 = 32
  [Divide both the numerator and the denominator by the G.C.F, 2.]
Step: 4
The ratio of wins to losses is 3 : 2.
Correct Answer is :   3 : 2
Q9A car can travel 160 miles in 4 hours and a truck can travel 360 miles in 5 hours. What is the ratio of the speed of the car to that of the truck?
A. 9 : 5
B. 72 : 41
C. 41 : 72
D. 5 : 9

Solutions
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Step: 1
Speed = distancetime
Step: 2
The speed of the car = 160 miles4 hours = 40 miles/hour
  [Substitute 160 for distance and 4 for time and divide.]
Step: 3
The speed of the truck = 360 miles5 hours= 72 miles/hour
  [Substitute 360 for distance and 5 for time and divide.]
Step: 4
The ratio of the speed of the car to that of the truck = 40 miles/hour72 miles/hour
Step: 5
4072 = 40 ÷ 872 ÷ 8 = 5 : 9
  [Divide both the numerator and the denominator by the GCF, 8.]
Step: 6
The ratio of the speed of the car to the speed of the truck is 5 : 9.
Correct Answer is :   5 : 9
Q10Are the two ratios 12 : 20 and 3 : 5 equal?
A. Yes
B. No

Solutions
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Step: 1
12 : 20 = 1220
  [Rewrite as a fraction.]
Step: 2
= 12÷420÷4
  [Divide both numerator and denominator by the G.C.F, 4.]
Step: 3
= 35 = 3 : 5
  
Step: 4
So, both ratios are equal.
Correct Answer is :   Yes
Q11Write the ratio 10 : 6 in its simplest form.
A. 2 : 1
B. 5 : 3
C. 1 : 2
D. 3 : 5

Solutions
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Step: 1
10 : 6 = 106
  [Write the ratio as a fraction.]
Step: 2
= 10÷26÷2 = 53
  [Divide both the numerator and the denominator by the GCF, 2.]
Step: 3
= 5 : 3
  [Rewrite the fraction as ratio.]
Step: 4
The simplest form of the ratio is 5 : 3.
Correct Answer is :   5 : 3
Q12In a school of 630 students, 360 students are boys and the remaining students are girls. What is the ratio of boys to girls?

A. 3 : 4
B. 4 : 3
C. 360 : 271
D. 271 : 360

Solutions
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Step: 1
Number of girls in the school = total number of students - number of boys = 630 - 360 = 270
Step: 2
The ratio of boys to girls = number of boysnumber of girls
= 360270
  [Substitute the values.]
Step: 3
= 360 ÷ 90270 ÷ 90 = 4 : 3
  [Divide both the numerator and the denominator by G.C.F, 90.]
Step: 4
The ratio of boys to girls is 4 : 3.
Correct Answer is :   4 : 3
Q13Find the ratio of 15 Jazz CDs to 20 Rock CDs.
A. 3 : 4
B. 2 : 3
C. 3 : 2
D. 4 : 3

Solutions
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Step: 1
The ratio of the Jazz CDs to the Rock CDs = number of jazz CDsnumber of Rock CDs = 1520
= 15 ÷ 520 ÷ 5
  [Divide both the numerator and the denominator by the GCF, 5.]
Step: 2
= 34
  
Step: 3
The ratio of the Jazz CDs to the Rock CDs is 3 : 4.
Correct Answer is :   3 : 4
Q14The table shows the school enrollment in the U.S. in two different years. Find the ratio of the number enrolled in Elementary School to the number enrolled in Middle School during the year 1990.

A. 17 : 6
B. 6 : 7
C. 6 : 17
D. 7 : 6

Solutions
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Step: 1
The Enrollment of the Elementary in 1990 was 34 million and in the Secondary was 12 million.
Step: 2
The ratio of the number enrolled in Elementary to that of Secondary School = 3412
Step: 3
= 342122 = 176 = 17:6
  [Divide the numerator and the denominator by the G.C.F, 2.]
Step: 4
The ratio of the Enrollment of the Elementary to the Secondary was 17 : 6.
Correct Answer is :   17 : 6
Q15The table shows the details of the population of the U.S. in different areas in two different years. What is the ratio of the population in the Northeast to that in the West in 1990?

A. 20 : 9
B. 5 : 7
C. 25 : 26
D. 26 : 25

Solutions
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Step: 1
The ratio of the population in the Northeast to the West = Population in the Northeastpopulation in the West = 5052
  [Substitute.]
Step: 2
= 50÷252÷2 = 2526
  [Divide the numerator and the denominator by the G.C.F, 2.]
Step: 3
= 25 : 26
  [Write the fraction as ratio.]
Step: 4
The ratio of the population in the Northeast to the West in 1990 was 25 : 26.
Correct Answer is :   25 : 26

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