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Answer :
To solve the problem of evaluating [tex]\(29 \frac{4}{5} \times 20 \frac{1}{6}\)[/tex], follow these steps:
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(29 \frac{4}{5}\)[/tex]:
- Multiply the whole number (29) by the denominator (5): [tex]\(29 \times 5 = 145\)[/tex].
- Add the numerator (4) to this result: [tex]\(145 + 4 = 149\)[/tex].
- Thus, [tex]\(29 \frac{4}{5}\)[/tex] converts to the improper fraction [tex]\(\frac{149}{5}\)[/tex].
- For [tex]\(20 \frac{1}{6}\)[/tex]:
- Multiply the whole number (20) by the denominator (6): [tex]\(20 \times 6 = 120\)[/tex].
- Add the numerator (1) to this result: [tex]\(120 + 1 = 121\)[/tex].
- Thus, [tex]\(20 \frac{1}{6}\)[/tex] converts to the improper fraction [tex]\(\frac{121}{6}\)[/tex].
2. Multiply the Improper Fractions:
[tex]\[
\frac{149}{5} \times \frac{121}{6} = \frac{149 \times 121}{5 \times 6}
\][/tex]
- Calculate the numerator: [tex]\(149 \times 121 = 18029\)[/tex].
- Calculate the denominator: [tex]\(5 \times 6 = 30\)[/tex].
- So, the product is [tex]\(\frac{18029}{30}\)[/tex].
3. Convert the Result to a Mixed Number:
- Divide the numerator by the denominator to find the whole number part: [tex]\(18029 \div 30 = 600\)[/tex] (with a remainder).
- Calculate the remainder: [tex]\(18029 - 600 \times 30 = 29\)[/tex].
Therefore, the result as a mixed number is [tex]\(600 \frac{29}{30}\)[/tex].
4. Identify the Correct Option:
Based on the choices provided:
- (A) [tex]\(599 \frac{14}{15}\)[/tex]
- (B) [tex]\(601 \frac{29}{30}\)[/tex]
- (C) [tex]\(600 \frac{29}{30}\)[/tex]
- (D) [tex]\(600 \frac{14}{15}\)[/tex]
The correct answer is [tex]\(600 \frac{29}{30}\)[/tex], which corresponds to option (C).
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(29 \frac{4}{5}\)[/tex]:
- Multiply the whole number (29) by the denominator (5): [tex]\(29 \times 5 = 145\)[/tex].
- Add the numerator (4) to this result: [tex]\(145 + 4 = 149\)[/tex].
- Thus, [tex]\(29 \frac{4}{5}\)[/tex] converts to the improper fraction [tex]\(\frac{149}{5}\)[/tex].
- For [tex]\(20 \frac{1}{6}\)[/tex]:
- Multiply the whole number (20) by the denominator (6): [tex]\(20 \times 6 = 120\)[/tex].
- Add the numerator (1) to this result: [tex]\(120 + 1 = 121\)[/tex].
- Thus, [tex]\(20 \frac{1}{6}\)[/tex] converts to the improper fraction [tex]\(\frac{121}{6}\)[/tex].
2. Multiply the Improper Fractions:
[tex]\[
\frac{149}{5} \times \frac{121}{6} = \frac{149 \times 121}{5 \times 6}
\][/tex]
- Calculate the numerator: [tex]\(149 \times 121 = 18029\)[/tex].
- Calculate the denominator: [tex]\(5 \times 6 = 30\)[/tex].
- So, the product is [tex]\(\frac{18029}{30}\)[/tex].
3. Convert the Result to a Mixed Number:
- Divide the numerator by the denominator to find the whole number part: [tex]\(18029 \div 30 = 600\)[/tex] (with a remainder).
- Calculate the remainder: [tex]\(18029 - 600 \times 30 = 29\)[/tex].
Therefore, the result as a mixed number is [tex]\(600 \frac{29}{30}\)[/tex].
4. Identify the Correct Option:
Based on the choices provided:
- (A) [tex]\(599 \frac{14}{15}\)[/tex]
- (B) [tex]\(601 \frac{29}{30}\)[/tex]
- (C) [tex]\(600 \frac{29}{30}\)[/tex]
- (D) [tex]\(600 \frac{14}{15}\)[/tex]
The correct answer is [tex]\(600 \frac{29}{30}\)[/tex], which corresponds to option (C).
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