Question

*Work the problems out in your notebook. First find a common denominator and rewrite the fractions using equivalent fractions. Then subtract.

7 ⅔ - 3 5/6
Answer:

6 3/10 - 1 4/5
Answer:

9 ⅓ - 4 ¾

Answer 1

Let's work through each of the problems step-by-step, following the method you described.

### Problem 1: \( 7 \frac{2}{3} - 3 \frac{5}{6} \)

**Step 1: Find a common denominator.**
The denominators are 3 and 6. The least common denominator (LCD) is 6.

**Step 2: Rewrite the fractions using equivalent fractions.**
- Convert \( 7 \frac{2}{3} \) to have a denominator of 6:
\[
7 \frac{2}{3} = 7 \frac{4}{6} = 7 + \frac{4}{6} = \frac{42}{6} + \frac{4}{6} = \frac{46}{6}
\]
- Convert \( 3 \frac{5}{6} \) (already has the denominator of 6):
\[
3 \frac{5}{6} = 3 + \frac{5}{6} = \frac{18}{6} + \frac{5}{6} = \frac{23}{6}
\]

**Step 3: Subtract the fractions.**
\[
\frac{46}{6} - \frac{23}{6} = \frac{46 - 23}{6} = \frac{23}{6}
\]

Convert \( \frac{23}{6} \) back to a mixed number:
\[
\frac{23}{6} = 3 \frac{5}{6}
\]

**Answer:**
\[
7 \frac{2}{3} - 3 \frac{5}{6} = 3 \frac{5}{6}
\]

### Problem 2: \( 6 \frac{3}{10} - 1 \frac{4}{5} \)

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

**Step 2: Rewrite the fractions using equivalent fractions.**
- Convert \( 1 \frac{4}{5} \) to have a denominator of 10:
\[
1 \frac{4}{5} = 1 \frac{8}{10} = 1 + \frac{8}{10} = \frac{10}{10} + \frac{8}{10} = \frac{18}{10}
\]

**Step 3: Subtract the fractions.**
\[
6 \frac{3}{10} - 1 \frac{4}{5} = \frac{63}{10} - \frac{18}{10} = \frac{63 - 18}{10} = \frac{45}{10}
\]

Convert \( \frac{45}{10} \) back to a mixed number:
\[
\frac{45}{10} = 4 \frac{5}{10} = 4 \frac{1}{2}
\]

**Answer:**
\[
6 \frac{3}{10} - 1 \frac{4}{5} = 4 \frac{1}{2}
\]

### Problem 3: \( 9 \frac{1}{3} - 4 \frac{3}{4} \)

**Step 1: Find a common denominator.**
The denominators are 3 and 4. The least common denominator is 12.

**Step 2: Rewrite the fractions using equivalent fractions.**
- Convert \( 9 \frac{1}{3} \) to have a denominator of 12:
\[
9 \frac{1}{3} = 9 \frac{4}{12} = 9 + \frac{4}{12} = \frac{108}{12} + \frac{4}{12} = \frac{112}{12}
\]

- Convert \( 4 \frac{3}{4} \) to have a denominator of 12:
\[
4 \frac{3}{4} = 4 \frac{9}{12} = 4 + \frac{9}{12} = \frac{48}{12} + \frac{9}{12} = \frac{57}{12}
\]

**Step 3: Subtract the fractions.**
\[
\frac{112}{12} - \frac{57}{12} = \frac{112 - 57}{12} = \frac{55}{12}
\]

Convert \( \frac{55}{12} \) back to a mixed number:
\[
\frac{55}{12} = 4 \frac{7}{12}
\]

**Answer:**
\[
9 \frac{1}{3} - 4 \frac{3}{4} = 4 \frac{7}{12}
\]

### Summary of Answers

1. \( 7 \frac{2}{3} - 3 \frac{5}{6} = 3 \frac{5}{6} \)
2. \( 6 \frac{3}{10} - 1 \frac{4}{5} = 4 \frac{1}{2} \)
3. \( 9 \frac{1}{3} - 4 \frac{3}{4} = 4 \frac{7}{12} \)