Solving Equations with Fractions: A worksheet with 15 algebra problems requiring students to solve equations involving fractions.

Let's solve each of these equations step by step. These are linear equations involving fractions. The goal is to isolate the variable on one side of the equation.

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1) $\frac{f}{5} + 2 = 8$

Step 1: Subtract 2 from both sides
$$
\frac{f}{5} = 8 - 2 = 6
$$

Step 2: Multiply both sides by 5
$$
f = 6 \times 5 = 30
$$

✔ Answer: $f = 30$

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2) $\frac{w}{3} - 5 = 2$

Step 1: Add 5 to both sides
$$
\frac{w}{3} = 2 + 5 = 7
$$

Step 2: Multiply both sides by 3
$$
w = 7 \times 3 = 21
$$

✔ Answer: $w = 21$

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3) $\frac{x}{8} + 3 = 12$

Step 1: Subtract 3 from both sides
$$
\frac{x}{8} = 12 - 3 = 9
$$

Step 2: Multiply both sides by 8
$$
x = 9 \times 8 = 72
$$

✔ Answer: $x = 72$

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4) $\frac{5t}{4} + 3 = 18$

Step 1: Subtract 3 from both sides
$$
\frac{5t}{4} = 18 - 3 = 15
$$

Step 2: Multiply both sides by 4
$$
5t = 15 \times 4 = 60
$$

Step 3: Divide by 5
$$
t = \frac{60}{5} = 12
$$

✔ Answer: $t = 12$

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5) $\frac{3y}{2} - 1 = 8$

Step 1: Add 1 to both sides
$$
\frac{3y}{2} = 8 + 1 = 9
$$

Step 2: Multiply both sides by 2
$$
3y = 9 \times 2 = 18
$$

Step 3: Divide by 3
$$
y = \frac{18}{3} = 6
$$

✔ Answer: $y = 6$

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6) $\frac{2x}{3} + 5 = 12$

Step 1: Subtract 5 from both sides
$$
\frac{2x}{3} = 12 - 5 = 7
$$

Step 2: Multiply both sides by 3
$$
2x = 7 \times 3 = 21
$$

Step 3: Divide by 2
$$
x = \frac{21}{2} = 10.5
$$

✔ Answer: $x = \frac{21}{2}$ or $10.5$

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7) $\frac{t}{5} + 3 = 1$

Step 1: Subtract 3 from both sides
$$
\frac{t}{5} = 1 - 3 = -2
$$

Step 2: Multiply both sides by 5
$$
t = -2 \times 5 = -10
$$

✔ Answer: $t = -10$

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8) $\frac{x + 3}{2} = 5$

Step 1: Multiply both sides by 2
$$
x + 3 = 5 \times 2 = 10
$$

Step 2: Subtract 3
$$
x = 10 - 3 = 7
$$

✔ Answer: $x = 7$

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9) $\frac{t - 5}{2} = 3$

Step 1: Multiply both sides by 2
$$
t - 5 = 3 \times 2 = 6
$$

Step 2: Add 5
$$
t = 6 + 5 = 11
$$

✔ Answer: $t = 11$

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10) $\frac{x + 10}{2} = 3$

Step 1: Multiply both sides by 2
$$
x + 10 = 3 \times 2 = 6
$$

Step 2: Subtract 10
$$
x = 6 - 10 = -4
$$

✔ Answer: $x = -4$

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11) $\frac{2x + 1}{3} = 5$

Step 1: Multiply both sides by 3
$$
2x + 1 = 5 \times 3 = 15
$$

Step 2: Subtract 1
$$
2x = 15 - 1 = 14
$$

Step 3: Divide by 2
$$
x = \frac{14}{2} = 7
$$

✔ Answer: $x = 7$

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12) $\frac{5y - 2}{4} = 3$

Step 1: Multiply both sides by 4
$$
5y - 2 = 3 \times 4 = 12
$$

Step 2: Add 2
$$
5y = 12 + 2 = 14
$$

Step 3: Divide by 5
$$
y = \frac{14}{5} = 2.8
$$

✔ Answer: $y = \frac{14}{5}$ or $2.8$

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13) $\frac{6y + 3}{9} = 1$

Step 1: Multiply both sides by 9
$$
6y + 3 = 1 \times 9 = 9
$$

Step 2: Subtract 3
$$
6y = 9 - 3 = 6
$$

Step 3: Divide by 6
$$
y = \frac{6}{6} = 1
$$

✔ Answer: $y = 1$

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14) $\frac{2x - 3}{5} = 4$

Step 1: Multiply both sides by 5
$$
2x - 3 = 4 \times 5 = 20
$$

Step 2: Add 3
$$
2x = 20 + 3 = 23
$$

Step 3: Divide by 2
$$
x = \frac{23}{2} = 11.5
$$

✔ Answer: $x = \frac{23}{2}$ or $11.5$

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15) $\frac{5t + 3}{4} = 1$

Step 1: Multiply both sides by 4
$$
5t + 3 = 1 \times 4 = 4
$$

Step 2: Subtract 3
$$
5t = 4 - 3 = 1
$$

Step 3: Divide by 5
$$
t = \frac{1}{5} = 0.2
$$

✔ Answer: $t = \frac{1}{5}$ or $0.2$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $f = 30$ |
| 2) | $w = 21$ |
| 3) | $x = 72$ |
| 4) | $t = 12$ |
| 5) | $y = 6$ |
| 6) | $x = \frac{21}{2}$ or $10.5$ |
| 7) | $t = -10$ |
| 8) | $x = 7$ |
| 9) | $t = 11$ |
| 10) | $x = -4$ |
| 11) | $x = 7$ |
| 12) | $y = \frac{14}{5}$ or $2.8$ |
| 13) | $y = 1$ |
| 14) | $x = \frac{23}{2}$ or $11.5$ |
| 15) | $t = \frac{1}{5}$ or $0.2$ |

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