Simplifying Mixed Numbers worksheet with 14 exercises to reduce mixed numbers to lowest terms.

Let's solve each problem step by step. The goal is to simplify each mixed number to its lowest terms. This means we need to:

1. Simplify the fractional part of the mixed number (reduce it to lowest terms).
2. If the fractional part reduces to a whole number, add it to the whole number part.
3. If the fraction simplifies to an improper fraction, convert it back to a mixed number and simplify.

We'll go through each one.

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1) $ 3 \frac{4}{8} $

- Simplify $ \frac{4}{8} $: divide numerator and denominator by GCF = 4 → $ \frac{1}{2} $
- So, $ 3 \frac{4}{8} = 3 \frac{1}{2} $

✔ Answer: $ 3 \frac{1}{2} $

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2) $ 15 \frac{2}{4} $

- Simplify $ \frac{2}{4} $: divide by 2 → $ \frac{1}{2} $
- So, $ 15 \frac{2}{4} = 15 \frac{1}{2} $

✔ Answer: $ 15 \frac{1}{2} $

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3) $ 7 \frac{5}{10} $

- Simplify $ \frac{5}{10} $: divide by 5 → $ \frac{1}{2} $
- So, $ 7 \frac{5}{10} = 7 \frac{1}{2} $

✔ Answer: $ 7 \frac{1}{2} $

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4) $ 1 \frac{21}{27} $

- Simplify $ \frac{21}{27} $: GCF of 21 and 27 is 3 → $ \frac{21 ÷ 3}{27 ÷ 3} = \frac{7}{9} $
- So, $ 1 \frac{21}{27} = 1 \frac{7}{9} $

✔ Answer: $ 1 \frac{7}{9} $

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5) $ 14 \frac{6}{8} $

- Simplify $ \frac{6}{8} $: divide by 2 → $ \frac{3}{4} $
- So, $ 14 \frac{6}{8} = 14 \frac{3}{4} $

✔ Answer: $ 14 \frac{3}{4} $

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6) $ 9 \frac{6}{9} $

- Simplify $ \frac{6}{9} $: divide by 3 → $ \frac{2}{3} $
- So, $ 9 \frac{6}{9} = 9 \frac{2}{3} $

✔ Answer: $ 9 \frac{2}{3} $

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7) $ 4 \frac{32}{40} $

- Simplify $ \frac{32}{40} $: GCF is 8 → $ \frac{32 ÷ 8}{40 ÷ 8} = \frac{4}{5} $
- So, $ 4 \frac{32}{40} = 4 \frac{4}{5} $

✔ Answer: $ 4 \frac{4}{5} $

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8) $ 10 \frac{7}{14} $

- Simplify $ \frac{7}{14} $: divide by 7 → $ \frac{1}{2} $
- So, $ 10 \frac{7}{14} = 10 \frac{1}{2} $

✔ Answer: $ 10 \frac{1}{2} $

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9) $ 5 \frac{20}{45} $

- Simplify $ \frac{20}{45} $: GCF is 5 → $ \frac{20 ÷ 5}{45 ÷ 5} = \frac{4}{9} $
- So, $ 5 \frac{20}{45} = 5 \frac{4}{9} $

✔ Answer: $ 5 \frac{4}{9} $

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10) $ 8 \frac{6}{36} $

- Simplify $ \frac{6}{36} $: divide by 6 → $ \frac{1}{6} $
- So, $ 8 \frac{6}{36} = 8 \frac{1}{6} $

✔ Answer: $ 8 \frac{1}{6} $

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11) $ 12 \frac{8}{32} $

- Simplify $ \frac{8}{32} $: divide by 8 → $ \frac{1}{4} $
- So, $ 12 \frac{8}{32} = 12 \frac{1}{4} $

✔ Answer: $ 12 \frac{1}{4} $

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12) $ 13 \frac{9}{15} $

- Simplify $ \frac{9}{15} $: divide by 3 → $ \frac{3}{5} $
- So, $ 13 \frac{9}{15} = 13 \frac{3}{5} $

✔ Answer: $ 13 \frac{3}{5} $

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13) $ 11 \frac{3}{9} $

- Simplify $ \frac{3}{9} $: divide by 3 → $ \frac{1}{3} $
- So, $ 11 \frac{3}{9} = 11 \frac{1}{3} $

✔ Answer: $ 11 \frac{1}{3} $

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14) $ 2 \frac{12}{14} $

- Simplify $ \frac{12}{14} $: divide by 2 → $ \frac{6}{7} $
- So, $ 2 \frac{12}{14} = 2 \frac{6}{7} $

✔ Answer: $ 2 \frac{6}{7} $

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✔ Final Answers:

1) $ 3 \frac{1}{2} $
2) $ 15 \frac{1}{2} $
3) $ 7 \frac{1}{2} $
4) $ 1 \frac{7}{9} $
5) $ 14 \frac{3}{4} $
6) $ 9 \frac{2}{3} $
7) $ 4 \frac{4}{5} $
8) $ 10 \frac{1}{2} $
9) $ 5 \frac{4}{9} $
10) $ 8 \frac{1}{6} $
11) $ 12 \frac{1}{4} $
12) $ 13 \frac{3}{5} $
13) $ 11 \frac{1}{3} $
14) $ 2 \frac{6}{7} $

All fractions are now in lowest terms. 🎉

Let me know if you'd like this as a printable answer sheet!