What is $7 / 8 \div 7 / 16$ reduced to the lowest term?
A. 1
B. 2
C. $7 / 2$
D. $7^{1 / 32}$
Answer (2)
To divide 8 7 by 16 7 , multiply 8 7 by the reciprocal of 16 7 , which is 7 16 .
The expression becomes 8 7 × 7 16 .
Multiply the numerators and denominators: 8 × 7 7 × 16 .
Simplify the fraction by canceling common factors, resulting in 2 .
Explanation
Understanding the Problem We are asked to divide two fractions, 8 7 and 16 7 , and reduce the result to its lowest terms.
Dividing Fractions To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, we have: 8 7 ÷ 16 7 = 8 7 × 7 16
Multiplying Numerators and Denominators Now, we multiply the numerators and the denominators: 8 × 7 7 × 16
Simplifying the Fraction Next, we simplify the fraction by canceling common factors. Both the numerator and denominator have a factor of 7. Also, 16 and 8 have a common factor of 8. So we can cancel 7 from the numerator and denominator, and divide 16 by 8 to get 2: 8 × 7 7 × 16 = 8 × 7 7 × ( 2 × 8 ) = 1 2 = 2
Final Answer Therefore, the result of the division is 2.
Examples
Understanding fractions and division is crucial in many real-life situations. For instance, when you're baking and need to halve a recipe, you're essentially dividing fractions. If a recipe calls for 8 7 cup of flour and you only want to make half the recipe, you would calculate 8 7 ÷ 2 = 16 7 . Similarly, if you're splitting a pizza with friends and need to divide it into equal slices, you're using fractions and division to ensure everyone gets a fair share. These basic math skills are fundamental to everyday problem-solving.
The expression 8 7 ÷ 16 7 simplifies to 2. This is done by multiplying 8 7 by the reciprocal of 16 7 and then simplifying the result. The correct option is B: 2.
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