practice
find each sum.
4. $4\frac{7}{8} + 5\frac{7}{8}$
step 1: add the mixed numbers. step 2: simplify by rewriting the improper fraction as a mixed number.
5. $5\frac{2}{3} + 1\frac{2}{3}$
step 1: add the mixed numbers. step 2: simplify by rewriting the improper fraction as a mixed number.
6. $\begin{array}{r}2\frac{3}{5}\\ + 4\frac{3}{5}\\ \hline\end{array}$
7. $\begin{array}{r}3\frac{5}{8}\\ + 1\frac{7}{8}\\ \hline\end{array}$
8. $\begin{array}{r}5\frac{6}{10}\\ + 2\frac{6}{10}\\ \hline\end{array}$
9. $\begin{array}{r}4\frac{5}{6}\\ + 4\frac{4}{6}\\ \hline\end{array}$
reflect
name two ways to convert an improper fraction to a mixed number.

Question

Accepted Answer

### Problem 4: $ 4\frac{7}{8} + 5\frac{7}{8} $
# Explanation:
## Step 1: Add the mixed numbers.
Add the whole numbers and the fractions separately: $ 4 + 5 = 9 $ and $ \frac{7}{8} + \frac{7}{8} = \frac{14}{8} $. So, $ 4\frac{7}{8} + 5\frac{7}{8} = 9 + \frac{14}{8} = 9\frac{14}{8} $.
## Step 2: Simplify the improper fraction.
Divide the numerator by the denominator: $ 14 \div 8 = 1 $ with a remainder of $ 6 $. So, $ \frac{14}{8} = 1\frac{6}{8} = 1\frac{3}{4} $. Then, add the whole number: $ 9 + 1\frac{3}{4} = 10\frac{3}{4} $.
# Answer: $ 10\frac{3}{4} $

### Problem 5: $ 5\frac{2}{3} + 1\frac{2}{3} $
# Explanation:
## Step 1: Add the mixed numbers.
Add the whole numbers and the fractions: $ 5 + 1 = 6 $ and $ \frac{2}{3} + \frac{2}{3} = \frac{4}{3} $. So, $ 5\frac{2}{3} + 1\frac{2}{3} = 6 + \frac{4}{3} = 6\frac{4}{3} $.
## Step 2: Simplify the improper fraction.
$ 4 \div 3 = 1 $ with a remainder of $ 1 $, so $ \frac{4}{3} = 1\frac{1}{3} $. Then, $ 6 + 1\frac{1}{3} = 7\frac{1}{3} $.
# Answer: $ 7\frac{1}{3} $

### Problem 6: $ 2\frac{3}{5} + 4\frac{3}{5} $
# Explanation:
## Step 1: Add the mixed numbers.
Whole numbers: $ 2 + 4 = 6 $, fractions: $ \frac{3}{5} + \frac{3}{5} = \frac{6}{5} $. So, $ 2\frac{3}{5} + 4\frac{3}{5} = 6 + \frac{6}{5} = 6\frac{6}{5} $.
## Step 2: Simplify the improper fraction.
$ 6 \div 5 = 1 $ remainder $ 1 $, so $ \frac{6}{5} = 1\frac{1}{5} $. Then, $ 6 + 1\frac{1}{5} = 7\frac{1}{5} $.
# Answer: $ 7\frac{1}{5} $

### Problem 7: $ 3\frac{5}{8} + 1\frac{7}{8} $
# Explanation:
## Step 1: Add the mixed numbers.
Whole numbers: $ 3 + 1 = 4 $, fractions: $ \frac{5}{8} + \frac{7}{8} = \frac{12}{8} $. So, $ 3\frac{5}{8} + 1\frac{7}{8} = 4 + \frac{12}{8} = 4\frac{12}{8} $.
## Step 2: Simplify the improper fraction.
$ 12 \div 8 = 1 $ remainder $ 4 $, so $ \frac{12}{8} = 1\frac{4}{8} = 1\frac{1}{2} $. Then, $ 4 + 1\frac{1}{2} = 5\frac{1}{2} $.
# Answer: $ 5\frac{1}{2} $

### Problem 8: $ 5\frac{6}{10} + 2\frac{6}{10} $
# Explanation:
## Step 1: Add the mixed numbers.
Whole numbers: $ 5 + 2 = 7 $, fractions: $ \frac{6}{10} + \frac{6}{10} = \frac{12}{10} $. So, $ 5\frac{6}{10} + 2\frac{6}{10} = 7 + \frac{12}{10} = 7\frac{12}{10} $.
## Step 2: Simplify the improper fraction.
$ 12 \div 10 = 1 $ remainder $ 2 $, so $ \frac{12}{10} = 1\frac{2}{10} = 1\frac{1}{5} $. Then, $ 7 + 1\frac{1}{5} = 8\frac{1}{5} $.
# Answer: $ 8\frac{1}{5} $

### Problem 9: $ 4\frac{5}{6} + 4\frac{4}{6} $
# Explanation:
## Step 1: Add the mixed numbers.
Whole numbers: $ 4 + 4 = 8 $, fractions: $ \frac{5}{6} + \frac{4}{6} = \frac{9}{6} $. So, $ 4\frac{5}{6} + 4\frac{4}{6} = 8 + \frac{9}{6} = 8\frac{9}{6} $.
## Step 2: Simplify the improper fraction.
$ 9 \div 6 = 1 $ remainder $ 3 $, so $ \frac{9}{6} = 1\frac{3}{6} = 1\frac{1}{2} $. Then, $ 8 + 1\frac{1}{2} = 9\frac{1}{2} $.
# Answer: $ 9\frac{1}{2} $

### Reflect: Two ways to convert an improper fraction to a mixed number
# Brief Explanations:
1. **Division Method**: Divide the numerator by the denominator. The quotient becomes the whole number part, the remainder becomes the numerator of the fractional part, and the denominator remains the same. For example, $ \frac{14}{8} $: $ 14 \div 8 = 1 $ with a remainder of $ 6 $, so $ \frac{14}{8} = 1\frac{6}{8} = 1\frac{3}{4} $.
2. **Subtraction Method**: Subtract the denominator from the numerator repeatedly until the numerator is less than the denominator. The number of times you subtract is the whole number part, and the remaining numerator over the original denominator is the fractional part. For example, $ \frac{14}{8} $: Subtract $ 8 $ from $ 14 $, we get $ 6 $. So we subtracted once, so the whole number is $ 1 $, and the fraction is $ \frac{6}{8} $, resulting in $ 1\frac{6}{8} = 1\frac{3}{4} $.
# Answer:
1. Division Method: Divide numerator by denominator (quotient = whole number, remainder = new numerator, same denominator).
2. Subtraction Method: Subtract denominator from numerator repeatedly (number of subtractions = whole number, remaining numerator/denominator = fraction).

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QUESTION IMAGE

Question

Explanation:

Problem 4: \( 4\frac{7}{8} + 5\frac{7}{8} \)

Step 1: Add the mixed numbers.

Step 2: Simplify the improper fraction.

Step 1: Add the mixed numbers.

Step 2: Simplify the improper fraction.

Step 1: Add the mixed numbers.

Step 2: Simplify the improper fraction.

Answer:

Problem 5: \( 5\frac{2}{3} + 1\frac{2}{3} \)