301 Moved Permanently - Free Printable

Let’s solve each problem step by step. We’ll add the rational numbers carefully, finding common denominators when needed.

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Problem 1:
$\frac{3}{2} + \frac{5}{4} + \frac{6}{5}$

Step 1: Find LCD of 2, 4, and 5 → LCD = 20
Convert each fraction:

- $\frac{3}{2} = \frac{30}{20}$
- $\frac{5}{4} = \frac{25}{20}$
- $\frac{6}{5} = \frac{24}{20}$

Add: $\frac{30 + 25 + 24}{20} = \frac{79}{20}$

✔ Answer: C) $\frac{79}{20}$

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Problem 2:
$2 + \frac{9}{8} + \frac{3}{2}$

Step 1: Convert whole number to fraction with denominator 8:
$2 = \frac{16}{8}$

$\frac{3}{2} = \frac{12}{8}$

Now add: $\frac{16}{8} + \frac{9}{8} + \frac{12}{8} = \frac{37}{8}$

✔ Answer: D) $\frac{37}{8}$

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Problem 3:
$\left(-\frac{1}{2}\right) + (-1) + \frac{5}{3}$

Step 1: Write -1 as $-\frac{1}{1}$

LCD of 2, 1, 3 → LCD = 6

Convert:

- $-\frac{1}{2} = -\frac{3}{6}$
- $-1 = -\frac{6}{6}$
- $\frac{5}{3} = \frac{10}{6}$

Add: $-\frac{3}{6} - \frac{6}{6} + \frac{10}{6} = \frac{1}{6}$

✔ Answer: D) $\frac{1}{6}$

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Problem 4:
$\left(-\frac{5}{3}\right) + (-1) + \left(-\frac{3}{2}\right)$

LCD of 3, 1, 2 → LCD = 6

Convert:

- $-\frac{5}{3} = -\frac{10}{6}$
- $-1 = -\frac{6}{6}$
- $-\frac{3}{2} = -\frac{9}{6}$

Add: $-\frac{10}{6} - \frac{6}{6} - \frac{9}{6} = -\frac{25}{6}$

✔ Answer: D) $-\frac{25}{6}$

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Problem 5:
$\left(-\frac{4}{3}\right) + \frac{9}{8} + \frac{2}{7}$

Find LCD of 3, 8, 7 → LCD = 168

Convert:

- $-\frac{4}{3} = -\frac{224}{168}$
- $\frac{9}{8} = \frac{189}{168}$
- $\frac{2}{7} = \frac{48}{168}$

Add: $-224 + 189 + 48 = 13$ → $\frac{13}{168}$

✔ Answer: D) $\frac{13}{168}$

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Problem 6:
$\left(-\frac{1}{8}\right) + \left(-\frac{4}{3}\right) + \frac{11}{8}$

Group terms with same denominator first:

$\left(-\frac{1}{8} + \frac{11}{8}\right) + \left(-\frac{4}{3}\right) = \frac{10}{8} - \frac{4}{3}$

Simplify $\frac{10}{8} = \frac{5}{4}$

Now: $\frac{5}{4} - \frac{4}{3}$

LCD = 12

$\frac{5}{4} = \frac{15}{12}, \quad \frac{4}{3} = \frac{16}{12}$

So: $\frac{15}{12} - \frac{16}{12} = -\frac{1}{12}$

✔ Answer: A) $-\frac{1}{12}$

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Problem 7:
$8 + (-1) + \frac{1}{2}$

First: $8 - 1 = 7$

Then: $7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2}$

✔ Answer: D) $\frac{15}{2}$

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Problem 8:
$(-5) + 2 + \left(-\frac{3}{8}\right)$

First: $-5 + 2 = -3$

Then: $-3 - \frac{3}{8} = -\frac{24}{8} - \frac{3}{8} = -\frac{27}{8}$

✔ Answer: C) $-\frac{27}{8}$

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Final Answer:
1) C
2) D
3) D
4) D
5) D
6) A
7) D
8) C