To convert a mixed number (like 2 and 1/3) into an improper fraction, we need to count all the total parts based on the size of the slice.
Here is how you do it for each problem:
1) 2 1/3
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Whole numbers: There are 2 whole circles. Each circle has 3 slices. So, $2 \times 3 = 6$ slices.
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Fraction part: Add the extra 1 slice. Total = $6 + 1 = 7$.
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Denominator: The size of the slice stays the same (3).
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Result: 7/3
2) 3 3/4
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Whole numbers: 3 circles $\times$ 4 slices each = 12 slices.
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Fraction part: Add 3 more slices. Total = $12 + 3 = 15$.
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Result: 15/4
3) 1 4/7
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Whole numbers: 1 circle $\times$ 7 slices = 7 slices.
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Fraction part: Add 4 slices. Total = $7 + 4 = 11$.
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Result: 11/7
4) 2 4/5
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Whole numbers: 2 circles $\times$ 5 slices = 10 slices.
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Fraction part: Add 4 slices. Total = $10 + 4 = 14$.
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Result: 14/5
5) 2 1/6
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Whole numbers: 2 circles $\times$ 6 slices = 12 slices.
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Fraction part: Add 1 slice. Total = $12 + 1 = 13$.
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Result: 13/6
6) 1 7/8
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Whole numbers: 1 circle $\times$ 8 slices = 8 slices.
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Fraction part: Add 7 slices. Total = $8 + 7 = 15$.
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Result: 15/8
7) 3 1/2
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Whole numbers: 3 circles $\times$ 2 slices = 6 slices.
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Fraction part: Add 1 slice. Total = $6 + 1 = 7$.
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Result: 7/2
8) 2 5/8
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Whole numbers: 2 circles $\times$ 8 slices = 16 slices.
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Fraction part: Add 5 slices. Total = $16 + 5 = 21$.
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Result: 21/8
9) 2 2/7
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Whole numbers: 2 circles $\times$ 7 slices = 14 slices.
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Fraction part: Add 2 slices. Total = $14 + 2 = 16$.
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Result: 16/7
10) 3 5/6
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Whole numbers: 3 circles $\times$ 6 slices = 18 slices.
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Fraction part: Add 5 slices. Total = $18 + 5 = 23$.
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Result: 23/6
11) 1 7/10
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Whole numbers: 1 circle $\times$ 10 slices = 10 slices.
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Fraction part: Add 7 slices. Total = $10 + 7 = 17$.
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Result: 17/10
12) 3 7/8
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Whole numbers: 3 circles $\times$ 8 slices = 24 slices.
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Fraction part: Add 7 slices. Total = $24 + 7 = 31$.
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Result: 31/8
Final Answer:
1) 7/3
2) 15/4
3) 11/7
4) 14/5
5) 13/6
6) 15/8
7) 7/2
8) 21/8
9) 16/7
10) 23/6
11) 17/10
12) 31/8
Parent Tip: Review the logic above to help your child master the concept of improper fractions to mixed numbers worksheets.
