Grade 7 Math Rational Number Operations 7.NS.3 Worksheets by The ... - Free Printable

Let's solve each problem in the worksheet "The Number System: Rational Number Operations" step by step.

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Problem 1:

-2 + 2 ÷ 0.4

We follow the order of operations (PEMDAS):
Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

1. Division first:
$ 2 ÷ 0.4 = 5 $
(Because $ 0.4 \times 5 = 2 $)

2. Now:
$ -2 + 5 = 3 $

✔ Answer: 3

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Problem 2:

0.8 + 2 + 3

Add from left to right:
$ 0.8 + 2 = 2.8 $
$ 2.8 + 3 = 5.8 $

✔ Answer: 5.8

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Problem 3:

-6 + 81 ÷ 15

Division first:
$ 81 ÷ 15 = 5.4 $

Now:
$ -6 + 5.4 = -0.6 $

✔ Answer: -0.6

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Problem 4:

-3 + 6 ÷ 2

Division first:
$ 6 ÷ 2 = 3 $

Now:
$ -3 + 3 = 0 $

✔ Answer: 0

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Problem 5:

4 ÷ 0.3 - 2

Division first:
$ 4 ÷ 0.3 = \frac{4}{0.3} = \frac{40}{3} \approx 13.\overline{3} $

Now subtract:
$ 13.\overline{3} - 2 = 11.\overline{3} $

Or as a fraction:
$ \frac{40}{3} - 2 = \frac{40}{3} - \frac{6}{3} = \frac{34}{3} $

✔ Answer: $ \frac{34}{3} $ or $ 11.\overline{3} $

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Problem 6:

(2 + 8) ÷ (-2)

Parentheses first:
$ 2 + 8 = 10 $

Now divide:
$ 10 ÷ (-2) = -5 $

✔ Answer: -5

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Problem 7:

1 - 0.5 - 0.4 - 0.5

Subtract left to right:
$ 1 - 0.5 = 0.5 $
$ 0.5 - 0.4 = 0.1 $
$ 0.1 - 0.5 = -0.4 $

✔ Answer: -0.4

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Problem 8:

-(-5) + (-5) - (-4)

Simplify signs:
$ -(-5) = +5 $
$ +(-5) = -5 $
$ -(-4) = +4 $

So:
$ 5 - 5 + 4 = 0 + 4 = 4 $

✔ Answer: 4

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Problem 9:

-0.2 + 0.5

$ -0.2 + 0.5 = 0.3 $

✔ Answer: 0.3

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Problem 10:

-(-4.3 + 0.5) + (4 + 8)

First simplify inside parentheses:

1. $ -4.3 + 0.5 = -3.8 $
Then: $ -(-3.8) = +3.8 $

2. $ 4 + 8 = 12 $

Now add:
$ 3.8 + 12 = 15.8 $

✔ Answer: 15.8

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Problem 11:

(3 - 3.5) ÷ (-2)

First: $ 3 - 3.5 = -0.5 $

Then: $ -0.5 ÷ (-2) = 0.25 $

✔ Answer: 0.25

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Problem 12:

8 ÷ 2 + 4 × 3

Order of operations: Division and multiplication before addition.

$ 8 ÷ 2 = 4 $
$ 4 × 3 = 12 $

Now: $ 4 + 12 = 16 $

✔ Answer: 16

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Problem 13:

-0.2 - (3 + (-2))

First: $ 3 + (-2) = 1 $

Then: $ -0.2 - 1 = -1.2 $

✔ Answer: -1.2

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Problem 14:

-10 ÷ 2 - 2 × (-5)

Division and multiplication first (left to right):

$ -10 ÷ 2 = -5 $
$ 2 × (-5) = -10 $

Now: $ -5 - (-10) = -5 + 10 = 5 $

✔ Answer: 5

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Problem 15:

0.25 × (-10) + 1

Multiply first:
$ 0.25 × (-10) = -2.5 $

Then: $ -2.5 + 1 = -1.5 $

✔ Answer: -1.5

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Problem 16:

-(8 + 2) + 2 × 3

Parentheses first: $ 8 + 2 = 10 $
Then: $ -(10) = -10 $

Multiplication: $ 2 × 3 = 6 $

Now: $ -10 + 6 = -4 $

✔ Answer: -4

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Problem 17:

-0.1 - (-2.5 + 2)

Inside parentheses: $ -2.5 + 2 = -0.5 $

Now: $ -0.1 - (-0.5) = -0.1 + 0.5 = 0.4 $

✔ Answer: 0.4

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Problem 18:

0.4 + 2 - 0.3

Left to right:
$ 0.4 + 2 = 2.4 $
$ 2.4 - 0.3 = 2.1 $

✔ Answer: 2.1

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Problem 19:

-0.5 + (-0.5) - (-10)

Simplify:
$ -0.5 - 0.5 = -1 $
Then: $ -1 - (-10) = -1 + 10 = 9 $

✔ Answer: 9

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Problem 20:

10 ÷ 2 - 0.1

Division first:
$ 10 ÷ 2 = 5 $

Then: $ 5 - 0.1 = 4.9 $

✔ Answer: 4.9

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------------|
| 1 | 3 |
| 2 | 5.8 |
| 3 | -0.6 |
| 4 | 0 |
| 5 | $ \frac{34}{3} $ or $ 11.\overline{3} $ |
| 6 | -5 |
| 7 | -0.4 |
| 8 | 4 |
| 9 | 0.3 |
| 10 | 15.8 |
| 11 | 0.25 |
| 12 | 16 |
| 13 | -1.2 |
| 14 | 5 |
| 15 | -1.5 |
| 16 | -4 |
| 17 | 0.4 |
| 18 | 2.1 |
| 19 | 9 |
| 20 | 4.9 |

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