Questions: 3 3/4 + 3 1/6

Transcript text: $3 \frac{3}{4}+3 \frac{1}{6}$

Solution

Step 1: Convert Mixed Numbers to Improper Fractions

First, convert the mixed numbers $ 3 \frac{3}{4} $ and $ 3 \frac{1}{6} $ into improper fractions.

For $ 3 \frac{3}{4} $: \[ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \]

For $ 3 \frac{1}{6} $: \[ 3 \frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{18 + 1}{6} = \frac{19}{6} \]

Step 2: Find a Common Denominator

To add the fractions $ \frac{15}{4} $ and $ \frac{19}{6} $, find a common denominator. The least common denominator (LCD) of 4 and 6 is 12.

Convert each fraction to have the denominator 12:

For $ \frac{15}{4} $: \[ \frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12} \]

For $ \frac{19}{6} $: \[ \frac{19}{6} = \frac{19 \times 2}{6 \times 2} = \frac{38}{12} \]

Step 3: Add the Fractions

Now, add the two fractions: \[ \frac{45}{12} + \frac{38}{12} = \frac{45 + 38}{12} = \frac{83}{12} \]

Step 4: Convert the Improper Fraction Back to a Mixed Number

Convert $ \frac{83}{12} $ back to a mixed number: \[ \frac{83}{12} = 6 \frac{11}{12} \]

\[ \boxed{6 \frac{11}{12}} \]

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