Let’s solve each problem one by one, step by step.
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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: Total horses = 52
White horses = 12
So, black horses = 52 - 12 = 40
Step 2: Ratio of white to black = 12 : 40
Step 3: Simplify the ratio. Both numbers can be divided by 4.
12 ÷ 4 = 3
40 ÷ 4 = 10
→ Simplified ratio:
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: Blue = 5, Yellow = 80
Total triangles = 5 + 80 = 85
Step 2: Ratio of blue to all = 5 : 85
Step 3: Simplify. Divide both by 5.
5 ÷ 5 = 1
85 ÷ 5 = 17
→ Simplified ratio:
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: Hearts = 22, Circles = 76
Total shapes = 22 + 76 = 98
Step 2: Ratio of circles to all = 76 : 98
Step 3: Simplify. Find greatest common factor. Both divisible by 2.
76 ÷ 2 = 38
98 ÷ 2 = 49
Check if 38 and 49 have any common factors — no (38=2×19, 49=7×7)
→ Simplified ratio:
38 : 49
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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: Yellow = 18, Blue = 14
Ratio of yellow to blue = 18 : 14
Step 2: Simplify. Divide both by 2.
18 ÷ 2 = 9
14 ÷ 2 = 7
→ Simplified ratio:
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: Yellow = 42, Blue = 6
Ratio of yellow to blue = 42 : 6
Step 2: Simplify. Divide both by 6.
42 ÷ 6 = 7
6 ÷ 6 = 1
→ Simplified ratio:
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: Boys = 63, Girls = 27
Total children = 63 + 27 = 90
Step 2: Ratio of boys to all = 63 : 90
Step 3: Simplify. Both divisible by 9.
63 ÷ 9 = 7
90 ÷ 9 = 10
→ Simplified ratio:
7 : 10
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Final Answer:
1a. 3 : 10
2a. 1 : 17
3a. 38 : 49
4a. 9 : 7
5a. 7 : 1
6a. 7 : 10
Parent Tip: Review the logic above to help your child master the concept of math ratio worksheet.
