6th Grade Common Core Math Worksheets - Free Printable

Let's solve each problem step by step from the worksheet titled "6.EE.A.2 Evaluating Expressions (Part 2)".

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1. Evaluate: $ 22 + k $ for $ k = 25 $

Substitute $ k = 25 $:

$$
22 + 25 = 47
$$

✔ Answer: 47

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2. Complete the table for $ 3x + 3 $

We plug in values of $ x $ into the expression $ 3x + 3 $:

- For $ x = 0 $: $ 3(0) + 3 = 0 + 3 = 3 $
- For $ x = 1 $: $ 3(1) + 3 = 3 + 3 = 6 $
- For $ x = 2 $: $ 3(2) + 3 = 6 + 3 = 9 $
- For $ x = 3 $: $ 3(3) + 3 = 9 + 3 = 12 $

| $ x $ | $ 3x + 3 $ |
|--------|-------------|
| 0 | 3 |
| 1 | 6 |
| 2 | 9 |
| 3 | 12 |

✔ Completed Table

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3. Evaluate $ 2d + 5e $, where $ d = 6 $ and $ e = 6.9 $

$$
2(6) + 5(6.9) = 12 + 34.5 = 46.5
$$

✔ Answer: 46.5

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4. Use $ a = -2 $, $ b = -3 $, and $ c = 6 $ to write an expression that has a value of 12

We need to create an expression using these values that evaluates to 12.

Try:
$$
a + b + c = (-2) + (-3) + 6 = -5 + 6 = 1 \quad \text{Too small}
$$

Try:
$$
c - a = 6 - (-2) = 6 + 2 = 8
$$

Try:
$$
c + a + b = 6 + (-2) + (-3) = 1
$$

Try:
$$
c \times (a + b) = 6 \times (-2 + (-3)) = 6 \times (-5) = -30
$$

Try:
$$
c \times 2 = 12 \Rightarrow \text{So maybe } 2c = 12
$$

Yes! $ 2c = 2 \times 6 = 12 $

But we must use all three variables? The prompt says "use $ a = -2 $, $ b = -3 $, $ c = 6 $" — but doesn't say we must use all in one expression.

However, often such problems expect you to combine them.

Try:
$$
a \times b + c = (-2)(-3) + 6 = 6 + 6 = 12
$$

✔ That works!

So one possible expression is:
$$
ab + c = (-2)(-3) + 6 = 6 + 6 = 12
$$

✔ Answer: $ ab + c $ or $ (-2)(-3) + 6 $

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5. Evaluate $ -a - a - (b - b) $ for $ a = -5 $, $ b = -4 $

First simplify:
$$
-a - a - (b - b) = -2a - (0) = -2a
$$

Now plug in $ a = -5 $:
$$
-2(-5) = 10
$$

✔ Answer: [B] 10

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6. Evaluate $ \frac{x}{y} $ for $ x = -\frac{1}{7} $, $ y = -\frac{1}{11} $

$$
\frac{-\frac{1}{7}}{-\frac{1}{11}} = \frac{-1/7}{-1/11} = \frac{1/7}{1/11} = \frac{1}{7} \times \frac{11}{1} = \frac{11}{7}
$$

✔ Answer: $ \frac{11}{7} $

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7. Evaluate $ \frac{np}{n + p} $ when $ n = 9 $, $ p = 15 $

$$
\frac{9 \cdot 15}{9 + 15} = \frac{135}{24} = \frac{45}{8} = 5.625
$$

✔ Answer: $ \frac{45}{8} $ or 5.625

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8. Evaluate $ \frac{2}{3}u - v $ for $ u = 2.1 $, $ v = 1.8 $

$$
\frac{2}{3}(2.1) - 1.8 = \left(\frac{2 \cdot 2.1}{3}\right) - 1.8 = \frac{4.2}{3} - 1.8 = 1.4 - 1.8 = -0.4
$$

✔ Answer: [B] –0.4

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9. Evaluate $ \frac{ef}{e + f} $ for $ e = 6 $, $ f = 11 $

$$
\frac{6 \cdot 11}{6 + 11} = \frac{66}{17}
$$

✔ Answer: [A] $ \frac{66}{17} $

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10. Evaluate $ \frac{y}{4x} - z $ for $ x = 2 $, $ y = 24 $, $ z = 1 $

$$
\frac{24}{4 \cdot 2} - 1 = \frac{24}{8} - 1 = 3 - 1 = 2
$$

✔ Answer: [B] 2

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11. Evaluate $ 2y^2(x + y) $ when $ x = 1 $, $ y = 5 $

First compute $ y^2 = 5^2 = 25 $

Then $ x + y = 1 + 5 = 6 $

Now:
$$
2 \cdot 25 \cdot 6 = 50 \cdot 6 = 300
$$

✔ Answer: [B] 300

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✔ Final Answers Summary:

1. 47
2. Table:
- $ x = 0 $ → 3
- $ x = 1 $ → 6
- $ x = 2 $ → 9
- $ x = 3 $ → 12
3. 46.5
4. Example: $ ab + c $ → $ (-2)(-3) + 6 = 12 $
5. [B] 10
6. $ \frac{11}{7} $
7. $ \frac{45}{8} $ or 5.625
8. [B] –0.4
9. [A] $ \frac{66}{17} $
10. [B] 2
11. [B] 300

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