If $\frac{3}{5} w=\frac{4}{3}$, what is the value of $w ?$
SAT · Math · previous-year question
- A.$\frac{9}{20}$
- B.$\frac{4}{5}$
- C.$\frac{5}{4}$
- D.$\frac{20}{9}$correct
Answer
D. $\frac{20}{9}$
Explanation
Choice D is correct. To solve the equation for $w$, multiply both sides of the equation by the reciprocal of $\frac{3}{5}$, which is $\frac{5}{3}$. This gives $\left(\frac{5}{3}\right) \cdot \frac{3}{5} w=\frac{4}{3} \cdot\left(\frac{5}{3}\right)$, which simplifies to $w=\frac{20}{9}$.Choices A, B, and C are incorrect and may be the result of errors in arithmetic when simplifying the given equation.
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