Free worksheets for ratio word problems - Free Printable

Of course! Let's solve each problem on the "Ratio Problems Worksheet" step by step and provide clear explanations. Remember, we need to simplify all ratios to their lowest terms.

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Problem 1a:
> 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
Black horses = 52 - 12 = 40

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

Step 3: Simplify the ratio.
Find the greatest common divisor (GCD) of 12 and 40.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
→ GCD = 4

Divide both numbers by 4:
12 ÷ 4 = 3
40 ÷ 4 = 10

✔ Answer: 3 : 10

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Problem 2a:
> A pattern has 5 blue triangles to every 80 yellow triangles. What is the ratio of blue triangles to all triangles?

Step 1: Find the total number of triangles.
Blue = 5
Yellow = 80
Total triangles = 5 + 80 = 85

Step 2: Write the ratio of blue to all triangles.
Blue : All = 5 : 85

Step 3: Simplify the ratio.
GCD of 5 and 85 is 5.

Divide both by 5:
5 ÷ 5 = 1
85 ÷ 5 = 17

✔ Answer: 1 : 17

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Problem 3a:
> Noah drew 22 hearts and 76 circles. What is the ratio of circles to all shapes?

Step 1: Find the total number of shapes.
Hearts = 22
Circles = 76
Total shapes = 22 + 76 = 98

Step 2: Write the ratio of circles to all shapes.
Circles : All = 76 : 98

Step 3: Simplify the ratio.
GCD of 76 and 98.
Factors of 76: 1, 2, 4, 19, 38, 76
Factors of 98: 1, 2, 7, 14, 49, 98
→ GCD = 2

Divide both by 2:
76 ÷ 2 = 38
98 ÷ 2 = 49

✔ Answer: 38 : 49

*(Note: 38 and 49 have no common factors other than 1, so this is simplified.)*

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Problem 4a:
> A pattern has 14 blue triangles to every 18 yellow triangles. What is the ratio of yellow triangles to blue triangles?

Step 1: Write the ratio as given, but switch to yellow to blue.
Yellow : Blue = 18 : 14

Step 2: Simplify the ratio.
GCD of 18 and 14 is 2.

Divide both by 2:
18 ÷ 2 = 9
14 ÷ 2 = 7

✔ Answer: 9 : 7

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Problem 5a:
> A pattern has 6 blue triangles to every 42 yellow triangles. What is the ratio of yellow triangles to blue triangles?

Step 1: Write the ratio of yellow to blue.
Yellow : Blue = 42 : 6

Step 2: Simplify the ratio.
GCD of 42 and 6 is 6.

Divide both by 6:
42 ÷ 6 = 7
6 ÷ 6 = 1

✔ Answer: 7 : 1

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Problem 6a:
> A group of preschoolers has 63 boys and 27 girls. What is the ratio of boys to all children?

Step 1: Find the total number of children.
Boys = 63
Girls = 27
Total children = 63 + 27 = 90

Step 2: Write the ratio of boys to all children.
Boys : All = 63 : 90

Step 3: Simplify the ratio.
GCD of 63 and 90.
Factors of 63: 1, 3, 7, 9, 21, 63
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
→ GCD = 9

Divide both by 9:
63 ÷ 9 = 7
90 ÷ 9 = 10

✔ Answer: 7 : 10

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## ✔ Final Answers:

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

Let me know if you’d like to see these explained with diagrams or real-world analogies!