Question

solve for a in the proportion.
\frac{56}{84} = \frac{a}{12}

a = \square

submit

Explanation:

Step1: Cross - multiply the proportion

Given the proportion $\frac{56}{84}=\frac{a}{12}$, cross - multiplying (which is based on the property of proportions: if $\frac{m}{n}=\frac{p}{q}$, then $m\times q = n\times p$) gives us $56\times12 = 84\times a$.

Step2: Calculate the left - hand side

First, calculate $56\times12$. $56\times12=(50 + 6)\times12=50\times12+6\times12 = 600+72 = 672$. So the equation becomes $672 = 84a$.

Step3: Solve for a

To solve for $a$, divide both sides of the equation $672 = 84a$ by 84. So $a=\frac{672}{84}$. Simplify $\frac{672}{84}$: divide numerator and denominator by 12, we get $\frac{56}{7}=8$.

Answer:

8