Simplify Expressions Worksheets - Free Printable

Let's solve each expression step by step using the given value: y = 56.

We'll substitute y = 56 into each expression and simplify, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

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1. $ 96 \div (y + 90) $

Substitute $ y = 56 $:

$$
96 \div (56 + 90) = 96 \div 146
$$

Now divide:

$$
96 \div 146 = \frac{96}{146} = \frac{48}{73} \approx 0.6575
$$

✔ Answer: $ \frac{48}{73} $ or approximately $ 0.6575 $

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2. $ 96 \div (y + 7) $

Substitute $ y = 56 $:

$$
96 \div (56 + 7) = 96 \div 63
$$

Simplify:

$$
\frac{96}{63} = \frac{32}{21} \approx 1.5238
$$

✔ Answer: $ \frac{32}{21} $ or approximately $ 1.5238 $

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3. $ 47 \div (y + 70) $

Substitute $ y = 56 $:

$$
47 \div (56 + 70) = 47 \div 126
$$

$$
\frac{47}{126} \approx 0.3730
$$

✔ Answer: $ \frac{47}{126} $ or approximately $ 0.3730 $

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4. $ (y + 5) \div 43 $

Substitute $ y = 56 $:

$$
(56 + 5) \div 43 = 61 \div 43
$$

$$
\frac{61}{43} \approx 1.4186
$$

✔ Answer: $ \frac{61}{43} $ or approximately $ 1.4186 $

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5. $ (y + 46) \div 11 $

Substitute $ y = 56 $:

$$
(56 + 46) \div 11 = 102 \div 11
$$

$$
\frac{102}{11} \approx 9.2727
$$

✔ Answer: $ \frac{102}{11} $ or approximately $ 9.2727 $

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6. $ 4 \div (y + 51) $

Substitute $ y = 56 $:

$$
4 \div (56 + 51) = 4 \div 107
$$

$$
\frac{4}{107} \approx 0.0374
$$

✔ Answer: $ \frac{4}{107} $ or approximately $ 0.0374 $

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7. $ (y + 14) \div 9 $

Substitute $ y = 56 $:

$$
(56 + 14) \div 9 = 70 \div 9
$$

$$
\frac{70}{9} \approx 7.777...
$$

✔ Answer: $ \frac{70}{9} $ or approximately $ 7.\overline{7} $

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8. $ 7 \div (y + 36) $

Substitute $ y = 56 $:

$$
7 \div (56 + 36) = 7 \div 92
$$

$$
\frac{7}{92} \approx 0.0761
$$

✔ Answer: $ \frac{7}{92} $ or approximately $ 0.0761 $

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9. $ (y + 2) \div 45 $

Substitute $ y = 56 $:

$$
(56 + 2) \div 45 = 58 \div 45
$$

$$
\frac{58}{45} \approx 1.2889
$$

✔ Answer: $ \frac{58}{45} $ or approximately $ 1.2889 $

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10. $ 16 \div (y + 86) $

Substitute $ y = 56 $:

$$
16 \div (56 + 86) = 16 \div 142
$$

$$
\frac{16}{142} = \frac{8}{71} \approx 0.1127
$$

✔ Answer: $ \frac{8}{71} $ or approximately $ 0.1127 $

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✔ Final Answers (Summary):

| Problem | Answer (Exact) | Decimal Approximation |
|--------|------------------|------------------------|
| 1 | $ \frac{48}{73} $ | ≈ 0.6575 |
| 2 | $ \frac{32}{21} $ | ≈ 1.5238 |
| 3 | $ \frac{47}{126} $ | ≈ 0.3730 |
| 4 | $ \frac{61}{43} $ | ≈ 1.4186 |
| 5 | $ \frac{102}{11} $ | ≈ 9.2727 |
| 6 | $ \frac{4}{107} $ | ≈ 0.0374 |
| 7 | $ \frac{70}{9} $ | ≈ 7.777... |
| 8 | $ \frac{7}{92} $ | ≈ 0.0761 |
| 9 | $ \frac{58}{45} $ | ≈ 1.2889 |
| 10 | $ \frac{8}{71} $ | ≈ 0.1127 |

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📝 Tips:

- Always substitute the variable first.
- Simplify inside parentheses before dividing.
- Reduce fractions when possible.
- Show work as required — this helps in checking your steps.

Let me know if you'd like these answers formatted neatly for printing or submission!