7/8 ÷ 7/16 = _. Reduce your answer to the lowest terms.
A. 7/32
B. 7/2
C. 1
D. 2
The Correct Answer and Explanation is :
The correct answser is: 2
To solve the equation ( \frac{7}{8} \div \frac{7}{16} ), we can use the rule of dividing fractions, which states that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we can rewrite the equation as follows:
[
\frac{7}{8} \div \frac{7}{16} = \frac{7}{8} \times \frac{16}{7}
]
Now, we can multiply the fractions:
- Multiply the numerators: ( 7 \times 16 = 112 )
- Multiply the denominators: ( 8 \times 7 = 56 )
So we have:
[
\frac{7}{8} \times \frac{16}{7} = \frac{112}{56}
]
Next, we need to simplify ( \frac{112}{56} ). We can do this by finding the greatest common divisor (GCD) of 112 and 56, which is 56. We can then divide both the numerator and the denominator by their GCD:
[
\frac{112 \div 56}{56 \div 56} = \frac{2}{1} = 2
]
Thus, the simplified answer to ( \frac{7}{8} \div \frac{7}{16} ) is:
[
\boxed{2}
]
Explanation:
Dividing fractions can seem complicated at first, but remembering that dividing by a fraction means multiplying by its reciprocal simplifies the process significantly. In this case, by multiplying ( \frac{7}{8} ) by ( \frac{16}{7} ), we were able to cancel out the ( 7 ) in the numerator and denominator, which often helps reduce the fractions quickly. Additionally, finding the GCD for further simplification ensures that we express the result in the lowest terms. The final answer, 2, is a whole number, confirming that the initial fraction division results in a value greater than 1, aligning with our calculation.