Ratio Worksheets | Ratio Worksheets for Teachers - Free Printable

Let's solve each problem step by step and explain the reasoning.

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1 a.

Problem: A herd of 52 horses has 12 white and some black horses. What is the ratio of white to black horses?

Step 1: Find the number of black horses.
Total horses = 52
White horses = 12
So, black horses = 52 - 12 = 40

Step 2: Write the ratio of white to black horses:
White : Black = 12 : 40

Step 3: Simplify the ratio.
Divide both numbers by their greatest common divisor (GCD).
GCD of 12 and 40 is 4.
12 ÷ 4 = 3
40 ÷ 4 = 10

✔ Answer: 3:10

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2 a.

Problem: A pattern has 5 blue triangles to every 80 yellow triangles. What is the ratio of blue triangles to all triangles?

Step 1: Total triangles = blue + yellow = 5 + 80 = 85

Step 2: Ratio of blue to all triangles = 5 : 85

Step 3: Simplify.
GCD of 5 and 85 is 5.
5 ÷ 5 = 1
85 ÷ 5 = 17

✔ Answer: 1:17

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3 a.

Problem: Noah drew 22 hearts and 76 circles. What is the ratio of circles to all shapes?

Step 1: Total shapes = hearts + circles = 22 + 76 = 98

Step 2: Ratio of circles to all shapes = 76 : 98

Step 3: Simplify.
GCD of 76 and 98 is 2.
76 ÷ 2 = 38
98 ÷ 2 = 49

✔ Answer: 38:49

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4 a.

Problem: A pattern has 14 blue triangles to every 18 yellow triangles. What is the ratio of yellow triangles to blue triangles?

Step 1: Yellow : Blue = 18 : 14

Step 2: Simplify.
GCD of 18 and 14 is 2.
18 ÷ 2 = 9
14 ÷ 2 = 7

✔ Answer: 9:7

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5 a.

Problem: A pattern has 6 blue triangles to every 42 yellow triangles. What is the ratio of yellow triangles to blue triangles?

Step 1: Yellow : Blue = 42 : 6

Step 2: Simplify.
GCD of 42 and 6 is 6.
42 ÷ 6 = 7
6 ÷ 6 = 1

✔ Answer: 7:1

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6 a.

Problem: A group of preschoolers has 63 boys and 27 girls. What is the ratio of boys to all children?

Step 1: Total children = 63 + 27 = 90

Step 2: Ratio of boys to all children = 63 : 90

Step 3: Simplify.
GCD of 63 and 90 is 9.
63 ÷ 9 = 7
90 ÷ 9 = 10

✔ Answer: 7:10

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✔ Final Answers:

1. 3:10
2. 1:17
3. 38:49
4. 9:7
5. 7:1
6. 7:10

All ratios are in simplified form as requested.