7th Grade Algebraic Expressions Worksheets - Math Monks - Free Printable

Let's evaluate each expression step by step using the given values of the variables.

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1. $\frac{3}{s - t} - 1$ at $s = 2$, $t = -6$

$$
\frac{3}{2 - (-6)} - 1 = \frac{3}{2 + 6} - 1 = \frac{3}{8} - 1 = \frac{3}{8} - \frac{8}{8} = -\frac{5}{8}
$$

✔ Answer: $-\frac{5}{8}$

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2. $\frac{x + 1}{y^2}$ at $x = 8$, $y = \frac{3}{5}$

First, compute $y^2 = \left(\frac{3}{5}\right)^2 = \frac{9}{25}$

Now:
$$
\frac{8 + 1}{\frac{9}{25}} = \frac{9}{\frac{9}{25}} = 9 \cdot \frac{25}{9} = 25
$$

✔ Answer: $25$

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3. $\frac{3}{u}(u^2 + 68)$ at $u = -12$

$$
\frac{3}{-12}((-12)^2 + 68) = -\frac{1}{4}(144 + 68) = -\frac{1}{4}(212) = -53
$$

✔ Answer: $-53$

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4. $21r(63r + 3)$ at $r = -\frac{3}{7}$

First, plug in $r = -\frac{3}{7}$:

$$
21 \cdot \left(-\frac{3}{7}\right) \left(63 \cdot \left(-\frac{3}{7}\right) + 3\right)
$$

Step-by-step:

- $21 \cdot \left(-\frac{3}{7}\right) = -9$
- $63 \cdot \left(-\frac{3}{7}\right) = -27$
- So: $-27 + 3 = -24$

Now: $-9 \cdot (-24) = 216$

✔ Answer: $216$

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5. $6n^2 + 4n^2 - 19$ at $n = -3$

Note: Combine like terms first:
$$
(6n^2 + 4n^2) = 10n^2
$$
So expression becomes: $10n^2 - 19$

Now plug in $n = -3$:
$n^2 = 9$, so:
$$
10(9) - 19 = 90 - 19 = 71
$$

✔ Answer: $71$

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6. $\frac{12q - 34}{4}$ at $q = -\frac{1}{3}$

Plug in:
$$
\frac{12 \cdot \left(-\frac{1}{3}\right) - 34}{4} = \frac{-4 - 34}{4} = \frac{-38}{4} = -\frac{19}{2}
$$

✔ Answer: $-\frac{19}{2}$ or $-9.5$

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7. $\frac{5t}{3t - s} - 1$ at $s = 2$, $t = -6$

Plug in:
$$
\frac{5(-6)}{3(-6) - 2} - 1 = \frac{-30}{-18 - 2} - 1 = \frac{-30}{-20} - 1 = \frac{3}{2} - 1 = \frac{1}{2}
$$

✔ Answer: $\frac{1}{2}$

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8. $\frac{s - 4}{t^2}$ at $s = 5$, $t = -5$

$t^2 = (-5)^2 = 25$

$$
\frac{5 - 4}{25} = \frac{1}{25}
$$

✔ Answer: $\frac{1}{25}$

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9. $\frac{6q - g}{4}$ at $q = -4$, $g = 1$

$$
\frac{6(-4) - 1}{4} = \frac{-24 - 1}{4} = \frac{-25}{4} = -6.25
$$

✔ Answer: $-\frac{25}{4}$

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10. $(10p - 4)^2$ at $p = 2$

$$
10(2) - 4 = 20 - 4 = 16
$$
$$
16^2 = 256
$$

✔ Answer: $256$

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✔ Final Answers:

1. $-\frac{5}{8}$
2. $25$
3. $-53$
4. $216$
5. $71$
6. $-\frac{19}{2}$
7. $\frac{1}{2}$
8. $\frac{1}{25}$
9. $-\frac{25}{4}$
10. $256$

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