What is the value of 7/32 * 8/21? Give your answer as an integer or as a fraction in its simplest form.
Understand the Problem
The question asks us to multiply two fractions, 7/32 and 8/21. After multiplying, the answer should be simplified and provided as either an integer or a fraction in its simplest form.
Answer
$\frac{1}{12}$
Answer for screen readers
$\frac{1}{12}$
Steps to Solve
- Multiply the fractions
Multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
$ \frac{7}{32} \times \frac{8}{21} = \frac{7 \times 8}{32 \times 21} = \frac{56}{672} $
- Simplify the fraction
Find the greatest common divisor (GCD) of 56 and 672. $56 = 2^3 * 7$ $672 = 2^5 * 3 * 7$
Thus, GCD$(56, 672) = 2^3 * 7 = 56$. Divide both the numerator and the denominator by their GCD:
$ \frac{56 \div 56}{672 \div 56} = \frac{1}{12} $
$\frac{1}{12}$
More Information
The simplified form of $\frac{56}{672}$ is $\frac{1}{12}$. This means that 56 is 1/12 of 672.
Tips
A common mistake is not simplifying the fraction completely. For example, a student might simplify $\frac{56}{672}$ to $\frac{28}{336}$ by dividing by 2, but then forget to continue simplifying. Another common mistake is incorrectly multiplying the numerators or denominators.
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