Simplify Improper Fractions worksheet for math practice.

Let's solve the problem step by step.

We are asked to simplify improper fractions and match them to their lowest terms. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To simplify, we convert it into a mixed number (a whole number plus a proper fraction) and reduce the fractional part to its lowest terms.

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Step-by-step simplification:

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1) $ \frac{70}{30} $

- Divide 70 ÷ 30 = 2 with remainder 10 → $ 2 \frac{10}{30} $
- Simplify $ \frac{10}{30} $: divide numerator and denominator by GCF (10) → $ \frac{1}{3} $
- So, $ \frac{70}{30} = 2 \frac{1}{3} $

✔ Match: $ \frac{7}{3} $ or $ 2 \frac{1}{3} $ → #3

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2) $ \frac{48}{20} $

- Divide 48 ÷ 20 = 2 with remainder 8 → $ 2 \frac{8}{20} $
- Simplify $ \frac{8}{20} $: GCF is 4 → $ \frac{2}{5} $
- So, $ \frac{48}{20} = 2 \frac{2}{5} $

✔ Match: $ \frac{12}{5} $ or $ 2 \frac{2}{5} $ → #7

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3) $ \frac{33}{15} $

- Divide 33 ÷ 15 = 2 with remainder 3 → $ 2 \frac{3}{15} $
- Simplify $ \frac{3}{15} $: GCF is 3 → $ \frac{1}{5} $
- So, $ \frac{33}{15} = 2 \frac{1}{5} $

Wait! But the options are:
- $ \frac{11}{5} $ or $ 2 \frac{1}{5} $ → YES!

✔ Match: $ \frac{11}{5} $ or $ 2 \frac{1}{5} $ → #2

Wait — let's check this again.

Actually, $ \frac{33}{15} $: divide numerator and denominator by 3 → $ \frac{11}{5} $, which is $ 2 \frac{1}{5} $. Correct.

So #3 → $ \frac{11}{5} $ or $ 2 \frac{1}{5} $ → #2

But wait — we need to match the left side to the right side.

So:
- Left: $ \frac{33}{15} $ → simplified to $ \frac{11}{5} $ or $ 2 \frac{1}{5} $
- That matches option: $ \frac{11}{5} $ or $ 2 \frac{1}{5} $ → so this is #2

✔ So #3 → #2

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4) $ \frac{49}{21} $

- Divide 49 ÷ 21 = 2 with remainder 7 → $ 2 \frac{7}{21} $
- Simplify $ \frac{7}{21} $: GCF is 7 → $ \frac{1}{3} $
- So $ \frac{49}{21} = 2 \frac{1}{3} $

Now look for $ 2 \frac{1}{3} $ → that’s $ \frac{7}{3} $ → yes!

✔ Match: $ \frac{7}{3} $ or $ 2 \frac{1}{3} $ → #3

So #4 → #3

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5) $ \frac{80}{45} $

- Divide 80 ÷ 45 = 1 with remainder 35 → $ 1 \frac{35}{45} $
- Simplify $ \frac{35}{45} $: GCF is 5 → $ \frac{7}{9} $
- So $ \frac{80}{45} = 1 \frac{7}{9} $

But the choices on the right don’t have $ 1 \frac{7}{9} $.

Wait — let's check the options:

Right side:
- $ \frac{16}{9} $ or $ 1 \frac{7}{9} $ → YES! That’s one of them.

So $ \frac{80}{45} $ → simplify:

Divide numerator and denominator by 5: $ \frac{16}{9} $ → $ 1 \frac{7}{9} $

✔ Match: $ \frac{16}{9} $ or $ 1 \frac{7}{9} $ → #1

So #5 → #1

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6) $ \frac{70}{42} $

- Divide 70 ÷ 42 = 1 with remainder 28 → $ 1 \frac{28}{42} $
- Simplify $ \frac{28}{42} $: GCF is 14 → $ \frac{2}{3} $
- So $ \frac{70}{42} = 1 \frac{2}{3} $

Check right side: $ \frac{5}{3} $ or $ 1 \frac{2}{3} $ → YES!

So $ \frac{70}{42} $ reduces to $ \frac{5}{3} $? Let's verify:

$ \frac{70}{42} $ → divide numerator and denominator by 14:
70 ÷ 14 = 5, 42 ÷ 14 = 3 → $ \frac{5}{3} $ → $ 1 \frac{2}{3} $

✔ Match: $ \frac{5}{3} $ or $ 1 \frac{2}{3} $ → #8

So #6 → #8

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7) $ \frac{88}{36} $

- Divide 88 ÷ 36 = 2 with remainder 16 → $ 2 \frac{16}{36} $
- Simplify $ \frac{16}{36} $: GCF is 4 → $ \frac{4}{9} $
- So $ \frac{88}{36} = 2 \frac{4}{9} $

Now check right side: $ \frac{22}{9} $ or $ 2 \frac{4}{9} $ → YES!

$ \frac{88}{36} $: divide numerator and denominator by 4 → $ \frac{22}{9} $ → $ 2 \frac{4}{9} $

✔ Match: $ \frac{22}{9} $ or $ 2 \frac{4}{9} $ → #4

So #7 → #4

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8) $ \frac{90}{25} $

- Divide 90 ÷ 25 = 3 with remainder 15 → $ 3 \frac{15}{25} $
- Simplify $ \frac{15}{25} $: GCF is 5 → $ \frac{3}{5} $
- So $ \frac{90}{25} = 3 \frac{3}{5} $

Now check right side: $ \frac{18}{5} $ or $ 3 \frac{3}{5} $ → YES!

$ \frac{90}{25} $: divide numerator and denominator by 5 → $ \frac{18}{5} $ → $ 3 \frac{3}{5} $

✔ Match: $ \frac{18}{5} $ or $ 3 \frac{3}{5} $ → #6

So #8 → #6

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Final Matching:

| Problem | Answer |
|--------|--------|
| 1) $ \frac{70}{30} $ | → $ \frac{7}{3} $ or $ 2 \frac{1}{3} $ → #3 |
| 2) $ \frac{48}{20} $ | → $ \frac{12}{5} $ or $ 2 \frac{2}{5} $ → #7 |
| 3) $ \frac{33}{15} $ | → $ \frac{11}{5} $ or $ 2 \frac{1}{5} $ → #2 |
| 4) $ \frac{49}{21} $ | → $ \frac{7}{3} $ or $ 2 \frac{1}{3} $ → #3 |
| 5) $ \frac{80}{45} $ | → $ \frac{16}{9} $ or $ 1 \frac{7}{9} $ → #1 |
| 6) $ \frac{70}{42} $ | → $ \frac{5}{3} $ or $ 1 \frac{2}{3} $ → #8 |
| 7) $ \frac{88}{36} $ | → $ \frac{22}{9} $ or $ 2 \frac{4}{9} $ → #4 |
| 8) $ \frac{90}{25} $ | → $ \frac{18}{5} $ or $ 3 \frac{3}{5} $ → #6 |

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Summary of Matches:

1) → 3
2) → 7
3) → 2
4) → 3
5) → 1
6) → 8
7) → 4
8) → 6

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✔ Answer Key:
- 1 → 3
- 2 → 7
- 3 → 2
- 4 → 3
- 5 → 1
- 6 → 8
- 7 → 4
- 8 → 6

You can now draw lines or write the matching numbers accordingly.