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Math  /  Numbers & Operations

Question12. 178+5141 \frac{7}{8}+5 \frac{1}{4}

Studdy Solution

STEP 1

1. We are adding two mixed numbers: 1781 \frac{7}{8} and 5145 \frac{1}{4}.
2. We need to express both mixed numbers in a common form to perform the addition.

STEP 2

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

STEP 3

Convert the mixed number 1781 \frac{7}{8} to an improper fraction.
178=1×8+78=158 1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{15}{8}

STEP 4

Convert the mixed number 5145 \frac{1}{4} to an improper fraction.
514=5×4+14=214 5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4}

STEP 5

Find a common denominator for the fractions 158\frac{15}{8} and 214\frac{21}{4}.
The least common denominator of 88 and 44 is 88.

STEP 6

Convert 214\frac{21}{4} to a fraction with a denominator of 88.
214=21×24×2=428 \frac{21}{4} = \frac{21 \times 2}{4 \times 2} = \frac{42}{8}

STEP 7

Add the fractions 158\frac{15}{8} and 428\frac{42}{8}.
158+428=15+428=578 \frac{15}{8} + \frac{42}{8} = \frac{15 + 42}{8} = \frac{57}{8}

STEP 8

Convert 578\frac{57}{8} to a mixed number.
578=718 \frac{57}{8} = 7 \frac{1}{8}
The sum of 1781 \frac{7}{8} and 5145 \frac{1}{4} is:
718\boxed{7 \frac{1}{8}}

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