Rearranging Equations Worksheet: Complete with ease | airSlate SignNow - Free Printable

Let's solve each equation from the worksheet by rearranging to make "p" the subject (i.e., isolate *p* on one side of the equation).

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1. $ t = 3py $

We want to solve for $ p $.
Divide both sides by $ 3y $:

$$
p = \frac{t}{3y}
$$

✔ Answer: $ p = \frac{t}{3y} $

---

2. $ t = kp $

Solve for $ p $.
Divide both sides by $ k $:

$$
p = \frac{t}{k}
$$

✔ Answer: $ p = \frac{t}{k} $

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3. $ t = 7yp $

Solve for $ p $.
Divide both sides by $ 7y $:

$$
p = \frac{t}{7y}
$$

✔ Answer: $ p = \frac{t}{7y} $

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4. $ \frac{a + 12}{p} = 7 $

Multiply both sides by $ p $:

$$
a + 12 = 7p
$$

Now divide both sides by 7:

$$
p = \frac{a + 12}{7}
$$

✔ Answer: $ p = \frac{a + 12}{7} $

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5. $ \frac{6 + 12}{p} = 12 $

First simplify numerator:

$$
\frac{18}{p} = 12
$$

Multiply both sides by $ p $:

$$
18 = 12p
$$

Divide by 12:

$$
p = \frac{18}{12} = \frac{3}{2}
$$

✔ Answer: $ p = \frac{3}{2} $ or $ 1.5 $

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6. $ \frac{7 + 4p}{5} = 10 $

Multiply both sides by 5:

$$
7 + 4p = 50
$$

Subtract 7:

$$
4p = 43
$$

Divide by 4:

$$
p = \frac{43}{4}
$$

✔ Answer: $ p = \frac{43}{4} $ or $ 10.75 $

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7. $ 40 = \frac{2}{5}(5y - 8p) $

Multiply both sides by 5 to eliminate denominator:

$$
200 = 2(5y - 8p)
$$

Divide both sides by 2:

$$
100 = 5y - 8p
$$

Now isolate $ p $:

$$
8p = 5y - 100
$$

$$
p = \frac{5y - 100}{8}
$$

✔ Answer: $ p = \frac{5y - 100}{8} $

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8. $ 40 = \frac{2}{3}(5y - 5p) $

Multiply both sides by 3:

$$
120 = 2(5y - 5p)
$$

Divide by 2:

$$
60 = 5y - 5p
$$

Rearrange:

$$
5p = 5y - 60
$$

$$
p = y - 12
$$

✔ Answer: $ p = y - 12 $

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9. $ 30 = \frac{2}{3}(7y - 8p) $

Multiply both sides by 3:

$$
90 = 2(7y - 8p)
$$

Divide by 2:

$$
45 = 7y - 8p
$$

Now solve for $ p $:

$$
8p = 7y - 45
$$

$$
p = \frac{7y - 45}{8}
$$

✔ Answer: $ p = \frac{7y - 45}{8} $

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10. $ 2x = \frac{2}{3}(7y + 3p) $

Multiply both sides by 3:

$$
6x = 2(7y + 3p)
$$

Divide by 2:

$$
3x = 7y + 3p
$$

Now isolate $ p $:

$$
3p = 3x - 7y
$$

$$
p = x - \frac{7y}{3}
$$

Or write as:

$$
p = \frac{3x - 7y}{3}
$$

✔ Answer: $ p = \frac{3x - 7y}{3} $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ p = \frac{t}{3y} $ |
| 2 | $ p = \frac{t}{k} $ |
| 3 | $ p = \frac{t}{7y} $ |
| 4 | $ p = \frac{a + 12}{7} $ |
| 5 | $ p = \frac{3}{2} $ |
| 6 | $ p = \frac{43}{4} $ |
| 7 | $ p = \frac{5y - 100}{8} $ |
| 8 | $ p = y - 12 $ |
| 9 | $ p = \frac{7y - 45}{8} $ |
| 10 | $ p = \frac{3x - 7y}{3} $ |

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