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Math  /  Numbers & Operations

Question645+4236 \frac{4}{5}+4 \frac{2}{3}

Studdy Solution

STEP 1

1. The expression 645+4236 \frac{4}{5}+4 \frac{2}{3} involves the addition of two mixed numbers.
2. Mixed numbers can be converted to improper fractions for easier addition.
3. The final result should be converted back to a mixed number if necessary.

STEP 2

1. Convert each mixed number to an improper fraction.
2. Find a common denominator for the addition of fractions.
3. Add the fractions.
4. Convert the result back to a mixed number if necessary.

STEP 3

Convert 6456 \frac{4}{5} to an improper fraction.
645=6+45=6×5+45=30+45=345 6 \frac{4}{5} = 6 + \frac{4}{5} = \frac{6 \times 5 + 4}{5} = \frac{30 + 4}{5} = \frac{34}{5}

STEP 4

Convert 4234 \frac{2}{3} to an improper fraction.
423=4+23=4×3+23=12+23=143 4 \frac{2}{3} = 4 + \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}

STEP 5

Find a common denominator for the fractions 345\frac{34}{5} and 143\frac{14}{3}.
The least common multiple (LCM) of 5 and 3 is 15.

STEP 6

Convert 345\frac{34}{5} and 143\frac{14}{3} to have a common denominator of 15.
345=34×35×3=10215 \frac{34}{5} = \frac{34 \times 3}{5 \times 3} = \frac{102}{15} 143=14×53×5=7015 \frac{14}{3} = \frac{14 \times 5}{3 \times 5} = \frac{70}{15}

STEP 7

Add the fractions 10215\frac{102}{15} and 7015\frac{70}{15}.
10215+7015=102+7015=17215 \frac{102}{15} + \frac{70}{15} = \frac{102 + 70}{15} = \frac{172}{15}

STEP 8

Convert the improper fraction 17215\frac{172}{15} back to a mixed number.
17215=11715 \frac{172}{15} = 11 \frac{7}{15}
Solution: 645+423=11715 6 \frac{4}{5} + 4 \frac{2}{3} = 11 \frac{7}{15}

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