Multiply. Reduce to lowest terms.
$2 \frac{1}{7} \times 4 \frac{3}{8}=$
A. $9 \frac{3}{8}$
B. $9 \frac{5}{8}$
C. $8 \frac{1}{5}$
D. $8 \frac{3}{56}$
Answer (2)
Convert the mixed numbers to improper fractions: 2 7 1 = 7 15 and 4 8 3 = 8 35 .
Multiply the improper fractions: 7 15 × 8 35 = 7 × 8 15 × 35 .
Simplify the fraction: 7 × 8 15 × 35 = 8 15 × 5 = 8 75 .
Convert the improper fraction back to a mixed number: 8 75 = 9 8 3 .
9 8 3
Explanation
Problem Analysis We are asked to multiply two mixed numbers, 2 7 1 and 4 8 3 , and reduce the result to lowest terms.
Convert to Improper Fractions First, we need to convert the mixed numbers to improper fractions. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. This result becomes the new numerator, and we keep the same denominator.
For 2 7 1 , we have 2 × 7 + 1 = 14 + 1 = 15 . So, 2 7 1 = 7 15 .
For 4 8 3 , we have 4 × 8 + 3 = 32 + 3 = 35 . So, 4 8 3 = 8 35 .
Multiply Improper Fractions Now, we multiply the improper fractions: 7 15 × 8 35 = 7 × 8 15 × 35
Simplify the Fraction We can simplify before multiplying by noticing that 35 is divisible by 7. 35 = 7 × 5 . So we have: 7 × 8 15 × 35 = 7 × 8 15 × ( 7 × 5 ) = 8 15 × 5 = 8 75
Convert back to Mixed Number Now, we convert the improper fraction 8 75 back to a mixed number. To do this, we divide 75 by 8.
75 ÷ 8 = 9 with a remainder of 3 . So, 8 75 = 9 8 3 .
Final Answer Therefore, 2 7 1 × 4 8 3 = 9 8 3 .
Examples
Mixed number multiplication is useful in everyday situations, such as when you're baking and need to adjust a recipe. For example, if a recipe calls for 2 7 1 cups of flour and you want to multiply the recipe by 4 8 3 , you would need to multiply these mixed numbers to find the new amount of flour needed. This ensures your ingredients are properly scaled for the desired quantity of the final product, maintaining the recipe's proportions and taste.
After multiplying the mixed numbers 2 7 1 and 4 8 3 , we convert them to improper fractions and find their product as 56 525 . Simplifying this gives us 9 8 3 . Thus, the correct answer is option A: 9 8 3 .
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