Expressions and Equations 6th Grade - Free Printable

Let's solve each expression by combining like terms. Like terms are terms that have the same variable raised to the same power (e.g., $ 7a $ and $ 4a $ are like terms, but $ 7a $ and $ 4b $ are not).

We'll go step-by-step through each problem.

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1) $ 7a + 4 + 8 $

- Combine constants: $ 4 + 8 = 12 $
- Only one term with $ a $: $ 7a $
- Answer: $ 7a + 12 $

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2) $ b + 5 + b + b $

- Combine $ b $ terms: $ b + b + b = 3b $
- Constant: $ 5 $
- Answer: $ 3b + 5 $

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3) $ 2c + 3 + c + 1 $

- Combine $ c $ terms: $ 2c + c = 3c $
- Constants: $ 3 + 1 = 4 $
- Answer: $ 3c + 4 $

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4) $ d + 7 + d - 8 $

- $ d + d = 2d $
- Constants: $ 7 - 8 = -1 $
- Answer: $ 2d - 1 $

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5) $ 3e + 2 + 4e + 6 $

- $ 3e + 4e = 7e $
- $ 2 + 6 = 8 $
- Answer: $ 7e + 8 $

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6) $ 5 + 3f + 1 - f $

- $ 3f - f = 2f $
- $ 5 + 1 = 6 $
- Answer: $ 2f + 6 $

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7) $ 3g - 5 - 2g + 2 $

- $ 3g - 2g = g $
- $ -5 + 2 = -3 $
- Answer: $ g - 3 $

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8) $ 3 - 2h + 8 - h $

- $ -2h - h = -3h $
- $ 3 + 8 = 11 $
- Answer: $ -3h + 11 $

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9) $ 2i - 8 + 4i + 1 $

- $ 2i + 4i = 6i $
- $ -8 + 1 = -7 $
- Answer: $ 6i - 7 $

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10) $ 2j + k + 3j + 3k $

- $ 2j + 3j = 5j $
- $ k + 3k = 4k $
- Answer: $ 5j + 4k $

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11) $ 5l + 4 - 7l + 2 $

- $ 5l - 7l = -2l $
- $ 4 + 2 = 6 $
- Answer: $ -2l + 6 $

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12) $ -4 + 5m - 5 - 3m $

- $ 5m - 3m = 2m $
- $ -4 - 5 = -9 $
- Answer: $ 2m - 9 $

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13) $ 2n + 3o - 6n + 2o $

Wait — there’s a typo in your image? It says $ 2n + 3o - 6n + 2o $. But if it's supposed to be $ 2n + 3o - 6n + 2o $, then:

- $ 2n - 6n = -4n $
- $ 3o + 2o = 5o $
- Answer: $ -4n + 5o $

But in your original, it says $ 2n + 3o - 6n + 2o $? Wait, actually looking at the image again:
It says: 13) $ 2n + 3o - 6n + 2o $ → yes, so it's two different variables.

So:
- $ 2n - 6n = -4n $
- $ 3o + 2o = 5o $
- Answer: $ -4n + 5o $

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14) $ 10 - 7p - 8 + 3p $

- $ -7p + 3p = -4p $
- $ 10 - 8 = 2 $
- Answer: $ -4p + 2 $

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15) $ 4q - (2 + q) $

Distribute the negative sign:
- $ 4q - 2 - q $
- $ 4q - q = 3q $
- So: $ 3q - 2 $
- Answer: $ 3q - 2 $

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16) $ (4 + 2r) + (7 - 6r) $

Remove parentheses:
- $ 4 + 2r + 7 - 6r $
- Combine: $ 4 + 7 = 11 $
- $ 2r - 6r = -4r $
- Answer: $ -4r + 11 $

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17) $ (4 + 2s) - (7 - 6s) $

Distribute the minus sign:
- $ 4 + 2s - 7 + 6s $
- $ 4 - 7 = -3 $
- $ 2s + 6s = 8s $
- Answer: $ 8s - 3 $

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18) $ 9t - (6 - 4t) $

Distribute the negative:
- $ 9t - 6 + 4t $
- $ 9t + 4t = 13t $
- So: $ 13t - 6 $
- Answer: $ 13t - 6 $

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19) $ (4u + 7) - (5 + 7u) $

Distribute the minus:
- $ 4u + 7 - 5 - 7u $
- $ 4u - 7u = -3u $
- $ 7 - 5 = 2 $
- Answer: $ -3u + 2 $

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20) $ 2v + 8w - (4w + 5v) $

Distribute the negative:
- $ 2v + 8w - 4w - 5v $
- Combine $ v $: $ 2v - 5v = -3v $
- Combine $ w $: $ 8w - 4w = 4w $
- Answer: $ -3v + 4w $

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✔ Final Answers Table:

| Expression | Simplified |
|----------|------------|
| 1) $ 7a + 4 + 8 $ | $ 7a + 12 $ |
| 2) $ b + 5 + b + b $ | $ 3b + 5 $ |
| 3) $ 2c + 3 + c + 1 $ | $ 3c + 4 $ |
| 4) $ d + 7 + d - 8 $ | $ 2d - 1 $ |
| 5) $ 3e + 2 + 4e + 6 $ | $ 7e + 8 $ |
| 6) $ 5 + 3f + 1 - f $ | $ 2f + 6 $ |
| 7) $ 3g - 5 - 2g + 2 $ | $ g - 3 $ |
| 8) $ 3 - 2h + 8 - h $ | $ -3h + 11 $ |
| 9) $ 2i - 8 + 4i + 1 $ | $ 6i - 7 $ |
| 10) $ 2j + k + 3j + 3k $ | $ 5j + 4k $ |
| 11) $ 5l + 4 - 7l + 2 $ | $ -2l + 6 $ |
| 12) $ -4 + 5m - 5 - 3m $ | $ 2m - 9 $ |
| 13) $ 2n + 3o - 6n + 2o $ | $ -4n + 5o $ |
| 14) $ 10 - 7p - 8 + 3p $ | $ -4p + 2 $ |
| 15) $ 4q - (2 + q) $ | $ 3q - 2 $ |
| 16) $ (4 + 2r) + (7 - 6r) $ | $ -4r + 11 $ |
| 17) $ (4 + 2s) - (7 - 6s) $ | $ 8s - 3 $ |
| 18) $ 9t - (6 - 4t) $ | $ 13t - 6 $ |
| 19) $ (4u + 7) - (5 + 7u) $ | $ -3u + 2 $ |
| 20) $ 2v + 8w - (4w + 5v) $ | $ -3v + 4w $ |

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✔ Key Tips:
- Always group like terms (same variable and exponent).
- Be careful with signs when distributing negatives.
- Remember: subtraction is the same as adding a negative.

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