Question

Add & Subtract Rational Numbers Sample Work

Answer 1

Sure! Let's go through some sample problems involving adding and subtracting rational numbers step by step.

### Sample Problem 1: Adding Rational Numbers

**Problem:**
Add \( \frac{3}{4} + \frac{5}{8} \).

**Step 1: Find a common denominator.**
The denominators are 4 and 8. The least common denominator (LCD) is 8.

**Step 2: Convert fractions to have the same denominator.**
- \( \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \)
- \( \frac{5}{8} \) already has the denominator of 8.

**Step 3: Add the fractions.**
\[
\frac{6}{8} + \frac{5}{8} = \frac{6 + 5}{8} = \frac{11}{8}
\]

**Step 4: Simplify if necessary.**
\( \frac{11}{8} \) is an improper fraction, which can also be written as \( 1 \frac{3}{8} \).

### Final Answer for Addition:
\[
\frac{3}{4} + \frac{5}{8} = \frac{11}{8} \text{ or } 1 \frac{3}{8}
\]

---

### Sample Problem 2: Subtracting Rational Numbers

**Problem:**
Subtract \( \frac{7}{10} - \frac{1}{5} \).

**Step 1: Find a common denominator.**
The denominators are 10 and 5. The least common denominator (LCD) is 10.

**Step 2: Convert fractions to have the same denominator.**
- \( \frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10} \)

**Step 3: Subtract the fractions.**
\[
\frac{7}{10} - \frac{2}{10} = \frac{7 - 2}{10} = \frac{5}{10}
\]

**Step 4: Simplify if necessary.**
\( \frac{5}{10} \) simplifies to \( \frac{1}{2} \).

### Final Answer for Subtraction:
\[
\frac{7}{10} - \frac{1}{5} = \frac{1}{2}
\]

---

### Summary of Processes

1. **Adding:**
- Find a common denominator.
- Convert fractions to that common denominator.
- Add the numerators and keep the common denominator.
- Simplify if possible.

2. **Subtracting:**
- Find a common denominator.
- Convert fractions to that common denominator.
- Subtract the numerators and keep the common denominator.
- Simplify if possible.

These steps can be used for any addition and subtraction of rational numbers! If you'd like more practice problems or different examples, feel free to ask!