Evaluating Expressions with Rational Numbers Worksheets - Free Printable

Let's evaluate each of the 10 numerical expressions step by step, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). We'll handle rational numbers (fractions, decimals) carefully.

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1) $ 39 - \frac{7}{8} \times 16 $

First, perform multiplication:
$$
\frac{7}{8} \times 16 = \frac{7 \times 16}{8} = \frac{112}{8} = 14
$$
Now subtract:
$$
39 - 14 = 25
$$

✔ Answer: 25

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2) $ (-8.1) + 3 - 2.63 $

Add and subtract left to right:
$$
-8.1 + 3 = -5.1
$$
$$
-5.1 - 2.63 = -7.73
$$

✔ Answer: -7.73

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3) $ 36.5 - 4 \times 3.14 - (-9.06) $

First, multiplication:
$$
4 \times 3.14 = 12.56
$$
Now substitute:
$$
36.5 - 12.56 - (-9.06)
$$
Subtracting a negative is adding:
$$
36.5 - 12.56 + 9.06
$$
Now compute:
$$
36.5 - 12.56 = 23.94
$$
$$
23.94 + 9.06 = 33.00
$$

✔ Answer: 33

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4) $ \frac{3}{4} \times 8 \div \left(-\frac{2}{3}\right) - 6 $

Start with multiplication and division from left to right.

First:
$$
\frac{3}{4} \times 8 = \frac{24}{4} = 6
$$

Now divide by $-\frac{2}{3}$:
$$
6 \div \left(-\frac{2}{3}\right) = 6 \times \left(-\frac{3}{2}\right) = -\frac{18}{2} = -9
$$

Now subtract 6:
$$
-9 - 6 = -15
$$

✔ Answer: -15

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5) $ 28 - \frac{6}{7} \div \left(-\frac{2}{7}\right) $

First, division:
$$
\frac{6}{7} \div \left(-\frac{2}{7}\right) = \frac{6}{7} \times \left(-\frac{7}{2}\right) = -\frac{42}{14} = -3
$$

Now:
$$
28 - (-3) = 28 + 3 = 31
$$

✔ Answer: 31

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6) $ 4.2 \times 8 - (-0.09) $

First, multiply:
$$
4.2 \times 8 = 33.6
$$

Then subtract $-0.09$:
$$
33.6 - (-0.09) = 33.6 + 0.09 = 33.69
$$

✔ Answer: 33.69

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7) $ 11.7 + 3.9 \times 5.6 + (-17) $

Multiplication first:
$$
3.9 \times 5.6 = ?
$$

Let’s compute:
$$
3.9 \times 5.6 = (39/10) \times (56/10) = (39 \times 56)/100
$$
$$
39 \times 56 = (40 - 1)(56) = 40×56 - 56 = 2240 - 56 = 2184
$$
So:
$$
2184 / 100 = 21.84
$$

Now plug back in:
$$
11.7 + 21.84 + (-17) = 11.7 + 21.84 - 17
$$
$$
11.7 + 21.84 = 33.54
$$
$$
33.54 - 17 = 16.54
$$

✔ Answer: 16.54

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8) $ 42 \times \frac{3}{7} - 36 \times \frac{1}{3} $

Compute each term:

First:
$$
42 \times \frac{3}{7} = \frac{126}{7} = 18
$$

Second:
$$
36 \times \frac{1}{3} = 12
$$

Now subtract:
$$
18 - 12 = 6
$$

✔ Answer: 6

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9) $ (-2) \times 3 + \left(-\frac{3}{4}\right) $

First, multiply:
$$
-2 \times 3 = -6
$$

Now add:
$$
-6 + \left(-\frac{3}{4}\right) = -6 - \frac{3}{4} = -\frac{24}{4} - \frac{3}{4} = -\frac{27}{4}
$$

Or as a mixed number: $-6\frac{3}{4}$

✔ Answer: $-\frac{27}{4}$ or $-6\frac{3}{4}$

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10) $ 7 - 2.5 + (-6.8) - 1.3 $

Work left to right:
$$
7 - 2.5 = 4.5
$$
$$
4.5 + (-6.8) = 4.5 - 6.8 = -2.3
$$
$$
-2.3 - 1.3 = -3.6
$$

✔ Answer: -3.6

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✔ Final Answers:

1) 25
2) -7.73
3) 33
4) -15
5) 31
6) 33.69
7) 16.54
8) 6
9) $-\frac{27}{4}$ or $-6\frac{3}{4}$
10) -3.6

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