$2 \frac{4}{7} \times \frac{11}{12} \div\left(-1 \frac{1}{21}\right)$
Answer (2)
Convert mixed numbers to improper fractions: 2 7 4 = 7 18 and − 1 21 1 = − 21 22 .
Rewrite division as multiplication by the reciprocal: 7 18 × 12 11 × ( − 22 21 ) .
Multiply the fractions: 7 × 12 × 22 18 × 11 × ( − 21 ) .
Simplify the fraction: − 4 27 .
The final answer is − 4 27 .
Explanation
Understanding the Problem We are given the expression 2 7 4 × 12 11 ÷ ( − 1 21 1 ) and we need to evaluate it. This involves mixed numbers, multiplication, and division.
Converting to Improper Fractions First, we convert the mixed numbers to improper fractions:
2 7 4 = 7 2 × 7 + 4 = 7 14 + 4 = 7 18
− 1 21 1 = − 21 1 × 21 + 1 = − 21 21 + 1 = − 21 22
Rewriting Division as Multiplication Now we rewrite the division as multiplication by the reciprocal:
7 18 × 12 11 ÷ ( − 21 22 ) = 7 18 × 12 11 × ( − 22 21 )
Multiplying the Fractions Next, we multiply the fractions:
7 18 × 12 11 × ( − 22 21 ) = 7 × 12 × 22 18 × 11 × ( − 21 )
Simplifying the Fraction Now, we simplify the resulting fraction:
7 × 12 × 22 18 × 11 × ( − 21 ) = 7 × 3 × 4 × 2 × 11 2 × 9 × 11 × ( − 3 × 7 ) = 4 9 × ( − 3 ) = − 4 27
Converting to Mixed Number Finally, we express the result as a mixed number:
− 4 27 = − 6 4 3
Final Answer Therefore, 2 7 4 × 12 11 ÷ ( − 1 21 1 ) = − 4 27 .
Examples
Understanding fraction operations is crucial in many real-life situations, such as cooking, where you might need to adjust ingredient quantities based on a recipe. For instance, if a recipe calls for 2 2 1 cups of flour, but you only want to make half the recipe, you need to calculate half of 2 2 1 , which involves multiplying fractions. Similarly, when calculating discounts or sales tax, you often need to multiply or divide fractions or mixed numbers. These skills are also essential in construction and engineering for accurate measurements and calculations.
To evaluate the expression 2 7 4 × 12 11 ÷ ( − 1 21 1 ) , we convert the mixed numbers to improper fractions, rewrite the division as multiplication by the reciprocal, then perform the multiplication and simplify. The final answer is − 4 27 , which can also be written as − 6 4 3 .
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