Let’s solve each problem step by step. We’re dividing whole numbers by fractions. The key idea is:
dividing by a fraction is the same as multiplying by its reciprocal (flip the fraction). But since this worksheet asks us to use models, we’ll think about how many times the fraction fits into the whole number — like cutting up strips.
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Problem 1:
4 ÷ ½ = ?
Think: How many halves are in 4 wholes?
Each whole has 2 halves → 4 × 2 = 8
✔ Answer:
8
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Problem 2:
2 ÷ ⅖ = ?
We want to know how many groups of ⅖ fit into 2.
First, flip ⅖ → becomes 5/2
Now multiply: 2 × 5/2 = (2×5)/2 = 10/2 = 5
✔ Answer:
5
*(Model way: Each whole can be split into 5 parts of size ⅕. So 2 wholes = 10 fifths. Since we’re grouping them into chunks of 2 fifths (⅖), then 10 ÷ 2 = 5 groups.)*
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Problem 3:
6 ÷ ¾ = ?
Flip ¾ → becomes 4/3
Multiply: 6 × 4/3 = (6×4)/3 = 24/3 = 8
✔ Answer:
8
*(Model: Each whole has 4 quarters. 6 wholes = 24 quarters. Group them into sets of 3 quarters (¾) → 24 ÷ 3 = 8 groups.)*
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Problem 4:
3 ÷ ³⁄₇ = ?
Flip ³⁄₇ → becomes 7/3
Multiply: 3 × 7/3 = (3×7)/3 = 21/3 = 7
✔ Answer:
7
*(Model: Each whole has 7 sevenths. 3 wholes = 21 sevenths. Group into sets of 3 sevenths → 21 ÷ 3 = 7 groups.)*
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Problem 5:
2 ÷ ¹⁄₆ = ?
How many sixths in 2 wholes?
Each whole has 6 sixths → 2 × 6 = 12
✔ Answer:
12
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Problem 6:
4 ÷ ⁴⁄₇ = ?
Flip ⁴⁄₇ → becomes 7/4
Multiply: 4 × 7/4 = (4×7)/4 = 28/4 = 7
✔ Answer:
7
*(Model: Each whole has 7 sevenths → 4 wholes = 28 sevenths. Group into sets of 4 sevenths → 28 ÷ 4 = 7 groups.)*
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Problem 7:
5 ÷ ¹⁄₃ = ?
How many thirds in 5 wholes?
Each whole has 3 thirds → 5 × 3 = 15
✔ Answer:
15
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Problem 8:
6 ÷ ³₅ = ?
Flip ³⁄₅ → becomes 5/3
Multiply: 6 × 5/3 = (6×5)/3 = 30/3 = 10
✔ Answer:
10
*(Model: Each whole has 5 fifths → 6 wholes = 30 fifths. Group into sets of 3 fifths → 30 ÷ 3 = 10 groups.)*
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Final Answer:
1) 8
2) 5
3) 8
4) 7
5) 12
6) 7
7) 15
8) 10
Parent Tip: Review the logic above to help your child master the concept of dividing fractions by whole numbers worksheet.
