Expressions and Equations 6th Grade - Free Printable

Let's solve each problem step by step and explain the reasoning.

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1) What is the value of the expression $3a$ when $a = 7$?

Solution:
Substitute $a = 7$ into the expression:
$$
3a = 3 \times 7 = 21
$$

✔ Answer: 21

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2) Solve the equation $5b = 35$.

Solution:
Divide both sides by 5:
$$
b = \frac{35}{5} = 7
$$

✔ Answer: $b = 7$

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3) Write the expression that matches the statement: "5 more than $c$"

Solution:
"More than" means addition. So, 5 more than $c$ is:
$$
c + 5
$$

✔ Answer: $c + 5$

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4) What is the value of the expression $2d - 3$ when $d = 11$?

Solution:
Substitute $d = 11$:
$$
2(11) - 3 = 22 - 3 = 19
$$

✔ Answer: 19

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5) Solve the equation $e - 12 = 19$.

Solution:
Add 12 to both sides:
$$
e = 19 + 12 = 31
$$

✔ Answer: $e = 31$

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6) Write the expression that matches the statement: "multiply $f$ by 3"

Solution:
Multiply $f$ by 3:
$$
3f
$$

✔ Answer: $3f$

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7) What is the value of the expression $\frac{1}{2}g$ when $g = 28$?

Solution:
$$
\frac{1}{2} \times 28 = 14
$$

✔ Answer: 14

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8) Solve the equation: $h \div 3 = 12$

Solution:
Multiply both sides by 3:
$$
h = 12 \times 3 = 36
$$

✔ Answer: $h = 36$

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9) Write the expression that matches the statement: "subtract 8 from $i$"

Solution:
Subtracting 8 from $i$:
$$
i - 8
$$

✔ Answer: $i - 8$

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10) What is the value of the expression: $100 - j$ when $j = 76$?

Solution:
$$
100 - 76 = 24
$$

✔ Answer: 24

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11) Solve the equation: $4k = 120$

Solution:
Divide both sides by 4:
$$
k = \frac{120}{4} = 30
$$

✔ Answer: $k = 30$

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12) Write the expression that matches the statement: "divide $l$ by 3"

Solution:
Dividing $l$ by 3:
$$
\frac{l}{3}
$$

✔ Answer: $\frac{l}{3}$

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13) What is the value of the expression $2m + 3$ when $m = 4$?

Solution:
$$
2(4) + 3 = 8 + 3 = 11
$$

✔ Answer: 11

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14) Solve the equation: $20 - n = 3$

Solution:
Subtract 20 from both sides:
$$
-n = 3 - 20 = -17
$$
Multiply both sides by $-1$:
$$
n = 17
$$

✔ Answer: $n = 17$

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15) Write the expression that matches the statement: "double $o$ and then add 1"

Solution:
Double $o$ → $2o$, then add 1 →
$$
2o + 1
$$

✔ Answer: $2o + 1$

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16) What is the value of the expression: $3p - 5$ when $p = 6$?

Solution:
$$
3(6) - 5 = 18 - 5 = 13
$$

✔ Answer: 13

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17) Solve the equation: $\frac{1}{2}q = 10$

Solution:
Multiply both sides by 2:
$$
q = 10 \times 2 = 20
$$

✔ Answer: $q = 20$

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18) Write the expression that matches the statement: "subtract $r$ from 15"

Solution:
Subtracting $r$ from 15:
$$
15 - r
$$

✔ Answer: $15 - r$

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✔ Final Answers Summary:

| # | Answer |
|---|--------|
| 1 | 21 |
| 2 | $b = 7$ |
| 3 | $c + 5$ |
| 4 | 19 |
| 5 | $e = 31$ |
| 6 | $3f$ |
| 7 | 14 |
| 8 | $h = 36$ |
| 9 | $i - 8$ |
| 10 | 24 |
| 11 | $k = 30$ |
| 12 | $\frac{l}{3}$ |
| 13 | 11 |
| 14 | $n = 17$ |
| 15 | $2o + 1$ |
| 16 | 13 |
| 17 | $q = 20$ |
| 18 | $15 - r$ |

Let me know if you'd like this formatted as a printable answer sheet!