If one-third of one-fourth of a number is $15$, then three-tenths of that number is

### Concept & Logic The word "of" in fractional word problems translates to multiplication. We can chain these fractions together to form a single coefficient for our unknown variable, solve for the variable, and then apply the final requested fraction. ### Step-by-step Solution **Step 1: Find the original number** Let the unknown number be $x$. Set up the equation based on the given sequence: $$ \frac{1}{3} \times \frac{1}{4} \times x = 15 $$ Multiply the fractions: $$ \frac{1}{12}x = 15 $$ Multiply both sides by $12$ to isolate $x$: $$ x = 15 \times 12 $$ $$ x = 180 $$ **Step 2: Calculate the required final value** The question asks for three-tenths ($\frac{3}{10}$) of the original number. $$ \text{Result} = \frac{3}{10} \times 180 $$ $$ \text{Result} = 3 \times 18 $$ $$ \text{Result} = 54 $$ ### Exam Strategy & Shortcut **Direct Chain Multiplication:** You can combine everything into a single line without finding the intermediate number $x$. You know $x = 15 \times 3 \times 4$. You need $\frac{3}{10} \times x$. So, calculate: $\frac{3}{10} \times (15 \times 3 \times 4)$. Cancel out a $5$ and $2$ from the denominator ($10 = 5 \times 2$): Cancel $5$ from $15$ (leaves $3$). Cancel $2$ from $4$ (leaves $2$). Result = $3 \times (3 \times 3 \times 2) = 3 \times 18 = 54$. This minimizes large numbers and reduces calculation errors. ### Common Pitfall A common mistake is forgetting the second part of the question. A student might calculate the original number ($180$) and panic if it's not in the options, or accidentally pick a distractor if one matches. Always highlight what the question is ultimately asking for. ### Final Answer **Therefore, the correct answer is 54.**