What percent of 88 is 33?

### Concept & Logic The phrasing "what percent of X is Y" means you are finding the ratio of Y to X, and then scaling it to a percentage format. It is a fundamental part-to-whole relationship. $$ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 $$ ### Step-by-Step Solution **Given:** * Whole (Base) = $88$ * Part = $33$ **Calculation / Deduction:** * Construct the fraction representing the ratio of the part to the whole: $$ \frac{33}{88} $$ * Notice that both the numerator and the denominator are multiples of $11$. Simplify the fraction by dividing both by $11$: $$ \frac{3}{8} $$ * To convert this simplified fraction to a percentage, multiply by $100$: $$ \frac{3}{8} \times 100 $$ * This becomes: $$ \frac{300}{8} $$ * Divide $300$ by $8$: $300 \div 2 = 150$ $150 \div 2 = 75$ $75 \div 2 = 37.5$ ### Exam Strategy & Shortcut Memorizing standard fraction-to-percentage conversions is essential for speed. You should immediately recognize $\frac{33}{88}$ as $\frac{3}{8}$. You must know that $\frac{1}{8} = 12.5\%$. Therefore, $\frac{3}{8}$ is simply $3 \times 12.5\%$, which instantly yields $37.5\%$. This completely bypasses the need to multiply by $100$ or perform long division. ### Common Pitfall The most frequent mistake in this type of phrasing is reversing the numerator and denominator, incorrectly calculating $\frac{88}{33}$ instead of $\frac{33}{88}$. Always identify the number immediately following the word "of" as the base (denominator). ### Final Answer Therefore, the correct answer is **37.5%**.