add the mixed numbers. simplify your answer if needed.
1
$2\frac{2}{5} + 1\frac{4}{5}$
2
$4\frac{5}{8} + 1\frac{4}{8}$
3
$3\frac{4}{7} + 2\frac{6}{7}$
4
$1\frac{4}{9} + 6\frac{6}{9}$
5
$1\frac{3}{8} + 2\frac{7}{8}$
6
$1\frac{6}{11} + 2\frac{7}{11}$
7
$7\frac{1}{8} + 2\frac{7}{8}$
8
$8\frac{8}{12} + 3\frac{6}{12}$
9
$3\frac{4}{9} + 5\frac{7}{9}$
10
$9\frac{4}{8} + 5\frac{5}{8}$
11
$2\frac{9}{15} + 6\frac{7}{15}$
12
$2\frac{5}{8} + 3\frac{7}{8}$

Question

Accepted Answer

Let's solve problem 1: $ 2\frac{2}{5} + 1\frac{4}{5} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
The whole numbers are $ 2 $ and $ 1 $, and the fractions are $ \frac{2}{5} $ and $ \frac{4}{5} $.
First, add the whole numbers: $ 2 + 1 = 3 $
Then, add the fractions: $ \frac{2}{5} + \frac{4}{5} = \frac{2 + 4}{5} = \frac{6}{5} $

## Step 2: Combine the results and simplify the fraction
Now, combine the sum of the whole numbers and the sum of the fractions: $ 3 + \frac{6}{5} $
Convert $ 3 $ to a fraction with denominator $ 5 $: $ 3 = \frac{15}{5} $
So, $ \frac{15}{5} + \frac{6}{5} = \frac{15 + 6}{5} = \frac{21}{5} $
Convert $ \frac{21}{5} $ back to a mixed number: $ \frac{21}{5} = 4\frac{1}{5} $ (since $ 21 \div 5 = 4 $ with a remainder of $ 1 $)

# Answer:
$ 4\frac{1}{5} $

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Let's solve problem 2: $ 4\frac{5}{8} + 1\frac{4}{8} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 4 + 1 = 5 $
Fractions: $ \frac{5}{8} + \frac{4}{8} = \frac{5 + 4}{8} = \frac{9}{8} $

## Step 2: Combine and simplify
Combine: $ 5 + \frac{9}{8} $
Convert $ 5 $ to eighths: $ 5 = \frac{40}{8} $
So, $ \frac{40}{8} + \frac{9}{8} = \frac{49}{8} $
Convert to mixed number: $ \frac{49}{8} = 6\frac{1}{8} $ (since $ 49 \div 8 = 6 $ with remainder $ 1 $)

# Answer:
$ 6\frac{1}{8} $

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Let's solve problem 3: $ 3\frac{4}{7} + 2\frac{6}{7} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 3 + 2 = 5 $
Fractions: $ \frac{4}{7} + \frac{6}{7} = \frac{4 + 6}{7} = \frac{10}{7} $

## Step 2: Combine and simplify
Combine: $ 5 + \frac{10}{7} $
Convert $ 5 $ to sevenths: $ 5 = \frac{35}{7} $
So, $ \frac{35}{7} + \frac{10}{7} = \frac{45}{7} $
Convert to mixed number: $ \frac{45}{7} = 6\frac{3}{7} $ (since $ 45 \div 7 = 6 $ with remainder $ 3 $)

# Answer:
$ 6\frac{3}{7} $

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Let's solve problem 4: $ 1\frac{4}{9} + 6\frac{6}{9} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 1 + 6 = 7 $
Fractions: $ \frac{4}{9} + \frac{6}{9} = \frac{4 + 6}{9} = \frac{10}{9} $

## Step 2: Combine and simplify
Combine: $ 7 + \frac{10}{9} $
Convert $ 7 $ to ninths: $ 7 = \frac{63}{9} $
So, $ \frac{63}{9} + \frac{10}{9} = \frac{73}{9} $
Convert to mixed number: $ \frac{73}{9} = 8\frac{1}{9} $ (since $ 73 \div 9 = 8 $ with remainder $ 1 $)

# Answer:
$ 8\frac{1}{9} $

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Let's solve problem 5: $ 1\frac{3}{8} + 2\frac{7}{8} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 1 + 2 = 3 $
Fractions: $ \frac{3}{8} + \frac{7}{8} = \frac{3 + 7}{8} = \frac{10}{8} $

## Step 2: Combine and simplify
Combine: $ 3 + \frac{10}{8} $
Simplify $ \frac{10}{8} = \frac{5}{4} = 1\frac{1}{4} $
Now, add $ 3 + 1\frac{1}{4} = 4\frac{1}{4} $ (or, alternatively, convert $ 3 $ to eighths: $ 3 = \frac{24}{8} $, so $ \frac{24}{8} + \frac{10}{8} = \frac{34}{8} = \frac{17}{4} = 4\frac{1}{4} $)

# Answer:
$ 4\frac{1}{4} $ (Note: The handwritten answer in the image is $ 4\frac{2}{8} $, which simplifies to $ 4\frac{1}{4} $)

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Let's solve problem 6: $ 1\frac{6}{11} + 2\frac{7}{11} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 1 + 2 = 3 $
Fractions: $ \frac{6}{11} + \frac{7}{11} = \frac{6 + 7}{11} = \frac{13}{11} $

## Step 2: Combine and simplify
Combine: $ 3 + \frac{13}{11} $
Convert $ 3 $ to elevenths: $ 3 = \frac{33}{11} $
So, $ \frac{33}{11} + \frac{13}{11} = \frac{46}{11} $
Convert to mixed number: $ \frac{46}{11} = 4\frac{2}{11} $ (since $ 46 \div 11 = 4 $ with remainder $ 2 $)

# Answer:
$ 4\frac{2}{11} $

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Let's solve problem 7: $ 7\frac{1}{8} + 2\frac{7}{8} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 7 + 2 = 9 $
Fractions: $ \frac{1}{8} + \frac{7}{8} = \frac{1 + 7}{8} = \frac{8}{8} = 1 $

## Step 2: Combine the results
Combine: $ 9 + 1 = 10 $

# Answer:
$ 10 $

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Let's solve problem 8: $ 8\frac{8}{12} + 3\frac{6}{12} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 8 + 3 = 11 $
Fractions: $ \frac{8}{12} + \frac{6}{12} = \frac{8 + 6}{12} = \frac{14}{12} $

## Step 2: Combine and simplify the fraction
Combine: $ 11 + \frac{14}{12} $
Simplify $ \frac{14}{12} = \frac{7}{6} = 1\frac{1}{6} $
Now, add $ 11 + 1\frac{1}{6} = 12\frac{1}{6} $ (or, alternatively, convert $ 11 $ to twelfths: $ 11 = \frac{132}{12} $, so $ \frac{132}{12} + \frac{14}{12} = \frac{146}{12} = \frac{73}{6} = 12\frac{1}{6} $)

# Answer:
$ 12\frac{1}{6} $ (Note: The handwritten answer in the image is $ 12 $, which is incorrect. The correct answer is $ 12\frac{1}{6} $ or simplified further, but $ \frac{14}{12} = \frac{7}{6} $, so $ 11 + \frac{7}{6} = 12\frac{1}{6} $)

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Let's solve problem 9: $ 3\frac{4}{9} + 5\frac{7}{9} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 3 + 5 = 8 $
Fractions: $ \frac{4}{9} + \frac{7}{9} = \frac{4 + 7}{9} = \frac{11}{9} $

## Step 2: Combine and simplify
Combine: $ 8 + \frac{11}{9} $
Convert $ 8 $ to ninths: $ 8 = \frac{72}{9} $
So, $ \frac{72}{9} + \frac{11}{9} = \frac{83}{9} $
Convert to mixed number: $ \frac{83}{9} = 9\frac{2}{9} $ (since $ 83 \div 9 = 9 $ with remainder $ 2 $)

# Answer:
$ 9\frac{2}{9} $

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Let's solve problem 10: $ 9\frac{4}{8} + 5\frac{5}{8} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 9 + 5 = 14 $
Fractions: $ \frac{4}{8} + \frac{5}{8} = \frac{4 + 5}{8} = \frac{9}{8} $

## Step 2: Combine and simplify
Combine: $ 14 + \frac{9}{8} $
Convert $ 14 $ to eighths: $ 14 = \frac{112}{8} $
So, $ \frac{112}{8} + \frac{9}{8} = \frac{121}{8} $
Convert to mixed number: $ \frac{121}{8} = 15\frac{1}{8} $ (since $ 121 \div 8 = 15 $ with remainder $ 1 $)

# Answer:
$ 15\frac{1}{8} $

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Let's solve problem 11: $ 2\frac{9}{15} + 6\frac{7}{15} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 2 + 6 = 8 $
Fractions: $ \frac{9}{15} + \frac{7}{15} = \frac{9 + 7}{15} = \frac{16}{15} $

## Step 2: Combine and simplify
Combine: $ 8 + \frac{16}{15} $
Convert $ 8 $ to fifteenths: $ 8 = \frac{120}{15} $
So, $ \frac{120}{15} + \frac{16}{15} = \frac{136}{15} $
Convert to mixed number: $ \frac{136}{15} = 9\frac{1}{15} $ (since $ 136 \div 15 = 9 $ with remainder $ 1 $)

# Answer:
$ 9\frac{1}{15} $

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Let's solve problem 12: $ 2\frac{5}{8} + 3\frac{7}{8} $

# Explanation:
## Step 1: Add the whole numbers and the fractions separately
Whole numbers: $ 2 + 3 = 5 $
Fractions: $ \frac{5}{8} + \frac{7}{8} = \frac{5 + 7}{8} = \frac{12}{8} $

## Step 2: Combine and simplify the fraction
Combine: $ 5 + \frac{12}{8} $
Simplify $ \frac{12}{8} = \frac{3}{2} = 1\frac{1}{2} $
Now, add $ 5 + 1\frac{1}{2} = 6\frac{1}{2} $ (or, alternatively, convert $ 5 $ to eighths: $ 5 = \frac{40}{8} $, so $ \frac{40}{8} + \frac{12}{8} = \frac{52}{8} = \frac{13}{2} = 6\frac{1}{2} $)

# Answer:
$ 6\frac{1}{2} $

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QUESTION IMAGE

Question

Explanation:

Step 1: Add the whole numbers and the fractions separately

Step 2: Combine the results and simplify the fraction

Step 1: Add the whole numbers and the fractions separately

Step 2: Combine and simplify

Step 1: Add the whole numbers and the fractions separately

Step 2: Combine and simplify

Answer: