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Math  /  Numbers & Operations

Question238+7512=2 \frac{3}{8}+7 \frac{5}{12}=

Studdy Solution

STEP 1

1. The problem involves the addition of two mixed numbers: 2382 \frac{3}{8} and 75127 \frac{5}{12}.
2. Mixed numbers can be converted into improper fractions for ease of addition.
3. The fractions should have a common denominator for addition.

STEP 2

1. Convert the mixed numbers to improper fractions.
2. Find a common denominator for the fractions.
3. Convert the fractions to have the common denominator.
4. Add the fractions.
5. Convert the result back to a mixed number if necessary.

STEP 3

Convert 2382 \frac{3}{8} to an improper fraction.
238=2×8+38=16+38=198 2 \frac{3}{8} = \frac{2 \times 8 + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8}

STEP 4

Convert 75127 \frac{5}{12} to an improper fraction.
7512=7×12+512=84+512=8912 7 \frac{5}{12} = \frac{7 \times 12 + 5}{12} = \frac{84 + 5}{12} = \frac{89}{12}

STEP 5

Find the least common denominator (LCD) for 198\frac{19}{8} and 8912\frac{89}{12}.
The LCD of 8 and 12 is 24.

STEP 6

Convert 198\frac{19}{8} to a fraction with the denominator 24.
198=19×38×3=5724 \frac{19}{8} = \frac{19 \times 3}{8 \times 3} = \frac{57}{24}

STEP 7

Convert 8912\frac{89}{12} to a fraction with the denominator 24.
8912=89×212×2=17824 \frac{89}{12} = \frac{89 \times 2}{12 \times 2} = \frac{178}{24}

STEP 8

Add the fractions 5724\frac{57}{24} and 17824\frac{178}{24}.
5724+17824=57+17824=23524 \frac{57}{24} + \frac{178}{24} = \frac{57 + 178}{24} = \frac{235}{24}

STEP 9

Convert the improper fraction 23524\frac{235}{24} back to a mixed number.
23524=91924 \frac{235}{24} = 9 \frac{19}{24}
Solution: 238+7512=91924 2 \frac{3}{8} + 7 \frac{5}{12} = 9 \frac{19}{24}

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