Algebra 2 Worksheets | Dynamically Created Algebra 2 Worksheets - Free Printable

Problem: Adding and Subtracting Rational Numbers

We are tasked with solving each sum or difference in the given problems. Let's solve them step by step.

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#### 1) \((-9) + (-19)\)
- Add the two negative numbers:
\[
-9 + (-19) = -9 - 19 = -28
\]
- Answer: \(\boxed{-28}\)

---

#### 2) \((- \frac{3}{8}) + \frac{9}{4} + (-\frac{5}{8})\)
- Combine the fractions. First, convert \(\frac{9}{4}\) to a fraction with a denominator of 8:
\[
\frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8}
\]
- Now add the fractions:
\[
-\frac{3}{8} + \frac{18}{8} + \left(-\frac{5}{8}\right) = \frac{-3 + 18 - 5}{8} = \frac{10}{8} = \frac{5}{4}
\]
- Answer: \(\boxed{\frac{5}{4}}\)

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#### 3) \((-3.8) - 5.6\)
- Subtract the two numbers:
\[
-3.8 - 5.6 = -9.4
\]
- Answer: \(\boxed{-9.4}\)

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#### 4) \((-15) - (-16) - (-32)\)
- Simplify the expression by converting subtraction of negatives to addition:
\[
-15 - (-16) - (-32) = -15 + 16 + 32
\]
- Add the numbers:
\[
-15 + 16 = 1 \quad \text{and} \quad 1 + 32 = 33
\]
- Answer: \(\boxed{33}\)

---

#### 5) \(1.6 + 3.0\)
- Add the two decimal numbers:
\[
1.6 + 3.0 = 4.6
\]
- Answer: \(\boxed{4.6}\)

---

#### 6) \(5.7 + (-7.4) + 4.1\)
- Add the numbers step by step:
\[
5.7 + (-7.4) = 5.7 - 7.4 = -1.7
\]
\[
-1.7 + 4.1 = 2.4
\]
- Answer: \(\boxed{2.4}\)

---

#### 7) \(1.5 - 5.7\)
- Subtract the two decimal numbers:
\[
1.5 - 5.7 = -4.2
\]
- Answer: \(\boxed{-4.2}\)

---

#### 8) \((-3.0) - (-5.7) - (-5.2)\)
- Simplify the expression by converting subtraction of negatives to addition:
\[
-3.0 - (-5.7) - (-5.2) = -3.0 + 5.7 + 5.2
\]
- Add the numbers:
\[
-3.0 + 5.7 = 2.7 \quad \text{and} \quad 2.7 + 5.2 = 7.9
\]
- Answer: \(\boxed{7.9}\)

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#### 9) \((-38) + 31\)
- Add the two integers:
\[
-38 + 31 = -7
\]
- Answer: \(\boxed{-7}\)

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#### 10) \((- \frac{3}{5}) + (- \frac{4}{8}) + \frac{7}{5}\)
- Simplify \(-\frac{4}{8}\):
\[
-\frac{4}{8} = -\frac{1}{2}
\]
- Convert all fractions to have a common denominator (the least common multiple of 5 and 2 is 10):
\[
-\frac{3}{5} = -\frac{3 \times 2}{5 \times 2} = -\frac{6}{10}, \quad -\frac{1}{2} = -\frac{1 \times 5}{2 \times 5} = -\frac{5}{10}, \quad \frac{7}{5} = \frac{7 \times 2}{5 \times 2} = \frac{14}{10}
\]
- Add the fractions:
\[
-\frac{6}{10} + \left(-\frac{5}{10}\right) + \frac{14}{10} = \frac{-6 - 5 + 14}{10} = \frac{3}{10}
\]
- Answer: \(\boxed{\frac{3}{10}}\)

---

#### 11) \(\frac{8}{9} - \frac{7}{4}\)
- Find a common denominator for \(\frac{8}{9}\) and \(\frac{7}{4}\). The least common multiple of 9 and 4 is 36:
\[
\frac{8}{9} = \frac{8 \times 4}{9 \times 4} = \frac{32}{36}, \quad \frac{7}{4} = \frac{7 \times 9}{4 \times 9} = \frac{63}{36}
\]
- Subtract the fractions:
\[
\frac{32}{36} - \frac{63}{36} = \frac{32 - 63}{36} = \frac{-31}{36}
\]
- Answer: \(\boxed{-\frac{31}{36}}\)

---

#### 12) \((- \frac{8}{9}) - \frac{3}{2} - (- \frac{7}{9})\)
- Simplify the expression by converting subtraction of negatives to addition:
\[
-\frac{8}{9} - \frac{3}{2} - \left(-\frac{7}{9}\right) = -\frac{8}{9} - \frac{3}{2} + \frac{7}{9}
\]
- Find a common denominator for \(\frac{8}{9}\), \(\frac{3}{2}\), and \(\frac{7}{9}\). The least common multiple of 9 and 2 is 18:
\[
-\frac{8}{9} = -\frac{8 \times 2}{9 \times 2} = -\frac{16}{18}, \quad -\frac{3}{2} = -\frac{3 \times 9}{2 \times 9} = -\frac{27}{18}, \quad \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}
\]
- Add the fractions:
\[
-\frac{16}{18} - \frac{27}{18} + \frac{14}{18} = \frac{-16 - 27 + 14}{18} = \frac{-29}{18}
\]
- Answer: \(\boxed{-\frac{29}{18}}\)

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#### 13) \(40 + (-24)\)
- Add the two integers:
\[
40 + (-24) = 40 - 24 = 16
\]
- Answer: \(\boxed{16}\)

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#### 14) \((- \frac{6}{3}) + (- \frac{8}{9}) + \frac{7}{3}\)
- Simplify \(-\frac{6}{3}\):
\[
-\frac{6}{3} = -2
\]
- Convert all terms to have a common denominator. The least common multiple of 3 and 9 is 9:
\[
-2 = -\frac{2 \times 9}{1 \times 9} = -\frac{18}{9}, \quad -\frac{8}{9} = -\frac{8}{9}, \quad \frac{7}{3} = \frac{7 \times 3}{3 \times 3} = \frac{21}{9}
\]
- Add the fractions:
\[
-\frac{18}{9} + \left(-\frac{8}{9}\right) + \frac{21}{9} = \frac{-18 - 8 + 21}{9} = \frac{-5}{9}
\]
- Answer: \(\boxed{-\frac{5}{9}}\)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & -28 \\
2) & \frac{5}{4} \\
3) & -9.4 \\
4) & 33 \\
5) & 4.6 \\
6) & 2.4 \\
7) & -4.2 \\
8) & 7.9 \\
9) & -7 \\
10) & \frac{3}{10} \\
11) & -\frac{31}{36} \\
12) & -\frac{29}{18} \\
13) & 16 \\
14) & -\frac{5}{9}
\end{array}
}
\]