To add the mixed numbers \(3 \frac{2}{3}\) and \(4 \frac{5}{8}\), we will first convert them into improper fractions.
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Convert \(3 \frac{2}{3}\) to an improper fraction: \[ 3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \]
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Convert \(4 \frac{5}{8}\) to an improper fraction: \[ 4 \frac{5}{8} = \frac{4 \times 8 + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8} \]
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Now, we need to add \( \frac{11}{3} + \frac{37}{8} \). To do this, we need a common denominator. The least common multiple (LCM) of 3 and 8 is 24.
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Convert \( \frac{11}{3} \) to a fraction with a denominator of 24: \[ \frac{11}{3} = \frac{11 \times 8}{3 \times 8} = \frac{88}{24} \]
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Convert \( \frac{37}{8} \) to a fraction with a denominator of 24: \[ \frac{37}{8} = \frac{37 \times 3}{8 \times 3} = \frac{111}{24} \]
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Now add the two fractions: \[ \frac{88}{24} + \frac{111}{24} = \frac{88 + 111}{24} = \frac{199}{24} \]
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Finally, convert \( \frac{199}{24} \) to a mixed number. Divide 199 by 24:
- \(199 ÷ 24 = 8\) remainder \(7\)
Thus, \( \frac{199}{24} \) can be written as: \[ 8 \frac{7}{24} \]
In simplest form, \(7\) and \(24\) have no common factors other than \(1\).
The answer is: \[ 8 \frac{7}{24} \]
In the boxes, you would enter:
- Whole number: 8
- Numerator: 7
- Denominator: 24
6 answers