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Math  /  Numbers & Operations

Question658−214=6 \frac{5}{8}-2 \frac{1}{4}=

Studdy Solution

STEP 1

1. The expression 658−2146 \frac{5}{8}-2 \frac{1}{4} involves the subtraction of two mixed numbers.
2. Mixed numbers can be converted to improper fractions for easier manipulation.
3. The fractions should have a common denominator for subtraction.

STEP 2

1. Convert the mixed numbers to improper fractions.
2. Find a common denominator for the fractions.
3. Subtract the fractions.
4. Simplify the result, if necessary, and convert back to a mixed number.

STEP 3

Convert the mixed number 6586 \frac{5}{8} to an improper fraction. 658=6+58=6×88+58=488+58=538 6 \frac{5}{8} = 6 + \frac{5}{8} = \frac{6 \times 8}{8} + \frac{5}{8} = \frac{48}{8} + \frac{5}{8} = \frac{53}{8}

STEP 4

Convert the mixed number 2142 \frac{1}{4} to an improper fraction. 214=2+14=2×44+14=84+14=94 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{2 \times 4}{4} + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}

STEP 5

Find a common denominator for the fractions 538\frac{53}{8} and 94\frac{9}{4}. The lowest common denominator (LCD) of 8 and 4 is 8.

STEP 6

Convert 94\frac{9}{4} to a fraction with the common denominator 8. 94=9×24×2=188 \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8}

STEP 7

Subtract the fractions: 538−188\frac{53}{8} - \frac{18}{8}. 538−188=53−188=358 \frac{53}{8} - \frac{18}{8} = \frac{53 - 18}{8} = \frac{35}{8}

STEP 8

Convert the improper fraction 358\frac{35}{8} back to a mixed number. 358=438 \frac{35}{8} = 4 \frac{3}{8}
Solution: 658−214=438 6 \frac{5}{8} - 2 \frac{1}{4} = 4 \frac{3}{8}

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