skiis practice adding mixed fractions practice your fraction arithmetic skills by adding the following mixed fractions. be sure to show your work and simplify your answers. $1 \frac{2}{3} + 4 \frac{1}{7} = 5 \frac{17}{21}$ $3 \frac{3}{7} + 2 \frac{1}{6} = \underline{\quad\quad}$ $3 \frac{1}{4} + 4 \frac{4}{5} = \underline{\quad\quad}$ $5 \frac{2}{5} + 4 \frac{1}{2} = \underline{\quad\quad}$ $2 \frac{1}{3} + 6 \frac{3}{5} = \underline{\quad\quad}$ $6 \frac{3}{4} + 1 \frac{6}{7} = \underline{\quad\quad}$ $2 \frac{3}{7} + 2 \frac{1}{6} = \underline{\quad\quad}$

Question

Accepted Answer

### 1. Solve $ 3\frac{3}{7} + 2\frac{1}{6} $
# Explanation:
## Step1: Convert to improper fractions
$ 3\frac{3}{7}=\frac{3\times7 + 3}{7}=\frac{24}{7} $, $ 2\frac{1}{6}=\frac{2\times6 + 1}{6}=\frac{13}{6} $
## Step2: Find common denominator (42)
$ \frac{24}{7}=\frac{24\times6}{7\times6}=\frac{144}{42} $, $ \frac{13}{6}=\frac{13\times7}{6\times7}=\frac{91}{42} $
## Step3: Add the fractions
$ \frac{144}{42}+\frac{91}{42}=\frac{144 + 91}{42}=\frac{235}{42} $
## Step4: Convert back to mixed number
$ \frac{235}{42}=5\frac{25}{42} $
# Answer: $ 5\frac{25}{42} $

### 2. Solve $ 3\frac{1}{4} + 4\frac{4}{5} $
# Explanation:
## Step1: Convert to improper fractions
$ 3\frac{1}{4}=\frac{3\times4 + 1}{4}=\frac{13}{4} $, $ 4\frac{4}{5}=\frac{4\times5 + 4}{5}=\frac{24}{5} $
## Step2: Find common denominator (20)
$ \frac{13}{4}=\frac{13\times5}{4\times5}=\frac{65}{20} $, $ \frac{24}{5}=\frac{24\times4}{5\times4}=\frac{96}{20} $
## Step3: Add the fractions
$ \frac{65}{20}+\frac{96}{20}=\frac{65 + 96}{20}=\frac{161}{20} $
## Step4: Convert back to mixed number
$ \frac{161}{20}=8\frac{1}{20} $
# Answer: $ 8\frac{1}{20} $

### 3. Solve $ 5\frac{2}{5} + 4\frac{1}{2} $
# Explanation:
## Step1: Convert to improper fractions
$ 5\frac{2}{5}=\frac{5\times5 + 2}{5}=\frac{27}{5} $, $ 4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2} $
## Step2: Find common denominator (10)
$ \frac{27}{5}=\frac{27\times2}{5\times2}=\frac{54}{10} $, $ \frac{9}{2}=\frac{9\times5}{2\times5}=\frac{45}{10} $
## Step3: Add the fractions
$ \frac{54}{10}+\frac{45}{10}=\frac{54 + 45}{10}=\frac{99}{10} $
## Step4: Convert back to mixed number
$ \frac{99}{10}=9\frac{9}{10} $
# Answer: $ 9\frac{9}{10} $

### 4. Solve $ 2\frac{1}{3} + 6\frac{3}{5} $
# Explanation:
## Step1: Convert to improper fractions
$ 2\frac{1}{3}=\frac{2\times3 + 1}{3}=\frac{7}{3} $, $ 6\frac{3}{5}=\frac{6\times5 + 3}{5}=\frac{33}{5} $
## Step2: Find common denominator (15)
$ \frac{7}{3}=\frac{7\times5}{3\times5}=\frac{35}{15} $, $ \frac{33}{5}=\frac{33\times3}{5\times3}=\frac{99}{15} $
## Step3: Add the fractions
$ \frac{35}{15}+\frac{99}{15}=\frac{35 + 99}{15}=\frac{134}{15} $
## Step4: Convert back to mixed number
$ \frac{134}{15}=8\frac{14}{15} $
# Answer: $ 8\frac{14}{15} $

### 5. Solve $ 6\frac{3}{4} + 1\frac{6}{7} $
# Explanation:
## Step1: Convert to improper fractions
$ 6\frac{3}{4}=\frac{6\times4 + 3}{4}=\frac{27}{4} $, $ 1\frac{6}{7}=\frac{1\times7 + 6}{7}=\frac{13}{7} $
## Step2: Find common denominator (28)
$ \frac{27}{4}=\frac{27\times7}{4\times7}=\frac{189}{28} $, $ \frac{13}{7}=\frac{13\times4}{7\times4}=\frac{52}{28} $
## Step3: Add the fractions
$ \frac{189}{28}+\frac{52}{28}=\frac{189 + 52}{28}=\frac{241}{28} $
## Step4: Convert back to mixed number
$ \frac{241}{28}=8\frac{17}{28} $
# Answer: $ 8\frac{17}{28} $

### 6. Solve $ 2\frac{3}{7} + 2\frac{1}{6} $
# Explanation:
## Step1: Convert to improper fractions
$ 2\frac{3}{7}=\frac{2\times7 + 3}{7}=\frac{17}{7} $, $ 2\frac{1}{6}=\frac{2\times6 + 1}{6}=\frac{13}{6} $
## Step2: Find common denominator (42)
$ \frac{17}{7}=\frac{17\times6}{7\times6}=\frac{102}{42} $, $ \frac{13}{6}=\frac{13\times7}{6\times7}=\frac{91}{42} $
## Step3: Add the fractions
$ \frac{102}{42}+\frac{91}{42}=\frac{102 + 91}{42}=\frac{193}{42} $
## Step4: Convert back to mixed number
$ \frac{193}{42}=4\frac{25}{42} $
# Answer: $ 4\frac{25}{42} $

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QUESTION IMAGE

Question

Explanation:

1. Solve \( 3\frac{3}{7} + 2\frac{1}{6} \)

Step1: Convert to improper fractions

Step2: Find common denominator (42)

Step3: Add the fractions

Step4: Convert back to mixed number

Step1: Convert to improper fractions

Step2: Find common denominator (20)

Step3: Add the fractions

Step4: Convert back to mixed number

Step1: Convert to improper fractions

Step2: Find common denominator (10)

Step3: Add the fractions

Step4: Convert back to mixed number

Answer:

2. Solve \( 3\frac{1}{4} + 4\frac{4}{5} \)