Question

*Subtract the mixed numbers. Work the problems out in your notebook. First you need to find a common denominator. Next you will rewrite the fractions using equivalent fractions with a common denominator. Then check to make sure your first numerator is larger than the second numerator. If the first numerator is smaller than the second numerator, you will need to borrow from your whole numerator.

-Example: 7 7/10 - 2 ⅘
7 7/10 - 2 8/10
(7 is smaller than 8 so I need to borrow from my whole number 7. The 7 becomes a 6 and I trade 1 whole for fraction pieces 10/10 + 7/10 = 17/10 so 6 17/10 - 2 8/10 = 4 9/10)
Answer: 4 9/10

4 ⅚ - 2 ⅓
Answer:

4 ⅛ - 3 ¾
Answer:

5 ½ - 3 ⅚
Answer:

Answer 1

Let's solve each mixed number subtraction step by step.

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

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

2. **Rewrite the fractions**:
- The first fraction is already \(\frac{5}{6}\).
- Convert \(\frac{1}{3}\) to have the denominator of 6:
\[
\frac{1}{3} = \frac{2}{6}
\]
So we now have:
\[
4 \frac{5}{6} - 2 \frac{2}{6}
\]

3. **Subtract the fractions**:
The whole numbers: \(4 - 2 = 2\)
The fractions:
\[
\frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}
\]
So we get:
\[
2 \frac{1}{2}
\]

**Answer:** \(2 \frac{1}{2}\)

---

### Problem 2: \( 4 \frac{1}{8} - 3 \frac{3}{4} \)

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

2. **Rewrite the fractions**:
- The first fraction is already \(\frac{1}{8}\).
- Convert \(\frac{3}{4}\) to have the denominator of 8:
\[
\frac{3}{4} = \frac{6}{8}
\]
So we now have:
\[
4 \frac{1}{8} - 3 \frac{6}{8}
\]

3. **Subtract the fractions**:
The whole numbers: \(4 - 3 = 1\)
The fractions:
\[
\frac{1}{8} - \frac{6}{8}
\]
Since \(\frac{1}{8} < \frac{6}{8}\), we need to borrow:
- Borrow 1 from 1 (the whole number), turning it into 0, and adding 8/8 to 1/8.
\[
\frac{1}{8} + \frac{8}{8} = \frac{9}{8}
\]
Now we calculate:
\[
\frac{9}{8} - \frac{6}{8} = \frac{3}{8}
\]
Therefore, our final result is:
\[
0 \frac{3}{8} = \frac{3}{8}
\]

**Answer:** \(\frac{3}{8}\)

---

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

1. **Find a common denominator**: The denominators are 2 and 6. The least common denominator (LCD) is 6.

2. **Rewrite the fractions**:
- Convert \(\frac{1}{2}\) to have the denominator of 6:
\[
\frac{1}{2} = \frac{3}{6}
\]
So we now have:
\[
5 \frac{3}{6} - 3 \frac{5}{6}
\]

3. **Subtract the fractions**:
The whole numbers: \(5 - 3 = 2\)
The fractions:
\[
\frac{3}{6} - \frac{5}{6}
\]
Since \(\frac{3}{6} < \frac{5}{6}\), we need to borrow:
- Borrow 1 from 2 (the whole number), turning it into 1, and adding \(6/6\) to \(3/6\).
\[
\frac{3}{6} + \frac{6}{6} = \frac{9}{6}
\]
Now we can calculate:
\[
\frac{9}{6} - \frac{5}{6} = \frac{4}{6} = \frac{2}{3}
\]
Our final result is:
\[
1 \frac{2}{3}
\]

**Answer:** \(1 \frac{2}{3}\)

---

### Summary of Answers:
1. \( 2 \frac{1}{2} \)
2. \( \frac{3}{8} \)
3. \( 1 \frac{2}{3} \)