7/8 divided by 7/16 reduce your answer to the Lowest form
The Correct Answer and Explanation is :
To solve ( \frac{7}{8} \div \frac{7}{16} ) and reduce the answer to its lowest terms, follow these steps:
Step 1: Convert Division to Multiplication
When dividing by a fraction, you multiply by the reciprocal (the flipped version) of the second fraction. The reciprocal of ( \frac{7}{16} ) is ( \frac{16}{7} ).
So, the expression becomes:
[
\frac{7}{8} \div \frac{7}{16} = \frac{7}{8} \times \frac{16}{7}
]
Step 2: Multiply the Numerators and Denominators
Now multiply the numerators (top numbers) and denominators (bottom numbers):
[
\frac{7 \times 16}{8 \times 7} = \frac{112}{56}
]
Step 3: Simplify the Fraction
Next, simplify the fraction ( \frac{112}{56} ). You can do this by finding the greatest common divisor (GCD) of 112 and 56, which is 56.
Divide both the numerator and the denominator by 56:
[
\frac{112 \div 56}{56 \div 56} = \frac{2}{1}
]
Final Answer:
[
\frac{7}{8} \div \frac{7}{16} = \frac{2}{1} = 2
]
Explanation:
- Division by a fraction is converted into multiplication by its reciprocal. This is a key property of fractions, which allows for easier manipulation.
- The multiplication of the fractions ( \frac{7}{8} \times \frac{16}{7} ) results in ( \frac{7 \times 16}{8 \times 7} ), where the 7’s cancel out, simplifying the expression to ( \frac{16}{8} ).
- After simplifying ( \frac{16}{8} ), you get 2, which is the final result.
This process shows how understanding the concept of multiplying by the reciprocal and simplifying fractions leads to the correct and simplified answer.