$5 \frac{2}{3} \times 1 \frac{7}{14} =$
Answer (2)
Convert the mixed fractions to improper fractions: 5 3 2 = 3 17 and 1 14 7 = 2 3 .
Multiply the improper fractions: 3 17 × 2 3 = 6 51 .
Simplify the resulting fraction: 6 51 = 2 17 .
Convert the improper fraction back to a mixed fraction: 2 17 = 8 2 1 . The final answer is 8 2 1 .
Explanation
Understanding the Problem We are given the expression 5 3 2 × 1 14 7 . We need to evaluate this expression. The numbers are mixed fractions.
Converting to Improper Fractions First, we convert the mixed fractions to improper fractions.
5 3 2 = 3 5 × 3 + 2 = 3 15 + 2 = 3 17
1 14 7 = 1 2 1 = 2 1 × 2 + 1 = 2 2 + 1 = 2 3
Multiplying Improper Fractions Now, we multiply the improper fractions:
3 17 × 2 3 = 3 × 2 17 × 3 = 6 51
Simplifying the Result Finally, we simplify the resulting fraction:
6 51 = 2 × 3 17 × 3 = 2 17
We can convert this improper fraction back to a mixed fraction:
2 17 = 8 2 1
Examples
Understanding fraction multiplication is crucial in everyday situations, such as when you're scaling a recipe. For instance, if a recipe calls for 2 2 1 cups of flour and you want to make 1 3 1 times the recipe, you need to multiply these mixed fractions. Converting them to improper fractions makes the multiplication easier, allowing you to accurately adjust the ingredient amounts for the desired serving size. This ensures your baked goods turn out perfectly, maintaining the correct ratios and flavors.
To find 5 3 2 × 1 14 7 , first convert both mixed numbers to improper fractions, multiply those fractions, simplify the result, and then convert back to a mixed number. This gives a final result of 8 2 1 .
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