$\frac{2}{7} \times\left[\frac{7}{16}-\frac{21}{4}\right]$
Answer (2)
Find a common denominator and subtract the fractions inside the brackets: 16 7 − 4 21 = 16 − 77 .
Multiply the result by 7 2 : 7 2 × 16 − 77 = 112 − 154 .
Simplify the fraction: 112 − 154 = 8 − 11 .
The final answer is − 8 11 .
Explanation
Understanding the Problem We are asked to evaluate the expression 7 2 × [ 16 7 − 4 21 ] . This involves basic arithmetic operations with fractions. To solve this, we first need to perform the subtraction inside the brackets and then multiply the result by 7 2 .
Subtracting Fractions First, we find a common denominator for the fractions inside the brackets. The least common multiple of 16 and 4 is 16. So we rewrite 4 21 with a denominator of 16: 4 21 = 4 × 4 21 × 4 = 16 84 Now we can perform the subtraction: 16 7 − 16 84 = 16 7 − 84 = 16 − 77
Multiplying Fractions Next, we multiply the result by 7 2 : 7 2 × 16 − 77 = 7 × 16 2 × − 77 = 112 − 154
Simplifying the Result Finally, we simplify the fraction. We can divide both the numerator and the denominator by their greatest common divisor, which is 14: 112 − 154 = 112 ÷ 14 − 154 ÷ 14 = 8 − 11 So, the final answer is − 8 11 . As a decimal, this is -1.375.
Examples
Fractions are used in everyday life, such as when calculating proportions in recipes, determining discounts while shopping, or understanding probabilities in games. This problem demonstrates how to perform arithmetic operations with fractions, a fundamental skill for various real-world applications. For instance, if you are baking a cake and need to halve a recipe that calls for 16 7 cup of flour, you would need to calculate 2 1 × 16 7 , which involves multiplying fractions.
We evaluated the expression 7 2 × [ 16 7 − 4 21 ] step-by-step, first finding a common denominator to subtract the fractions, then multiplying the result by 7 2 . The final answer is − 8 11 , which is equal to -1.375 when expressed as a decimal.
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