Math / Numbers & Operations

Question $2 \frac{10}{12}+3 \frac{9}{12}$

Studdy Solution

STEP 1

1. The problem involves the addition of two mixed numbers.
2. The fractions in the mixed numbers have the same denominator, which simplifies the addition process.

STEP 2

1. Convert mixed numbers to improper fractions.
2. Add the improper fractions.
3. Convert the result back to a mixed number if necessary.

STEP 3

Convert the first mixed number $2 \frac{10}{12}$ to an improper fraction.
$2 \frac{10}{12} = \frac{2 \times 12 + 10}{12} = \frac{24 + 10}{12} = \frac{34}{12}$

STEP 4

Convert the second mixed number $3 \frac{9}{12}$ to an improper fraction.
$3 \frac{9}{12} = \frac{3 \times 12 + 9}{12} = \frac{36 + 9}{12} = \frac{45}{12}$

STEP 5

Add the two improper fractions $\frac{34}{12}$ and $\frac{45}{12}$ .
$\frac{34}{12} + \frac{45}{12} = \frac{34 + 45}{12} = \frac{79}{12}$

STEP 6

Convert the improper fraction $\frac{79}{12}$ back to a mixed number.
1. Divide $79$ by $12$ to find the whole number part: $79 \div 12 = 6$ remainder $7$ .
2. The mixed number is $6 \frac{7}{12}$ .
The sum of the mixed numbers is:
$\boxed{6 \frac{7}{12}}$

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