Question

which expression is equivalent to \\(\frac{7}{12}\times 2\\)?
a. \\(7\div 2\times 12\\)
b. \\(7\times 12\div 5\\)
c. \\(12\div 7\times 2\\)
d. \\(7\times 2\div 12\\)

Explanation:

Step1: Recall fraction multiplication rule

When multiplying a fraction $\frac{a}{b}$ by a number $c$, it is equivalent to $\frac{a\times c}{b}$, which can also be written as $a\times c\div b$. For the expression $\frac{7}{12}\times2$, here $a = 7$, $b = 12$, and $c = 2$.

Step2: Apply the rule to the given expression

Using the rule from Step 1, $\frac{7}{12}\times2$ is equivalent to $7\times2\div12$. Now let's check the options:

• Option A: $7\div2\times12=\frac{7\times12}{2}$, which is not equivalent.
• Option B: $7\times12\div5=\frac{7\times12}{5}$, not equivalent.
• Option C: $12\div7\times2=\frac{12\times2}{7}$, not equivalent.
• Option D: $7\times2\div12=\frac{7\times2}{12}$, which matches the equivalent form we derived.

Answer:

D. $7 \times 2 \div 12$