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$10 \frac{1}{2}$ of what number is $30$

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Percents of numbers: fractional and decimal percents

Full solution

Q.

10 \frac{1}{2}

of what number is

30

Prompt: question_prompt: What number do you multiply by $10 \frac{1}{2}$ to get $30$ ?
Divide by $10$ $1$ / $2$ : To find the number, divide $30$ by $10 \frac{1}{2}$ .
Convert to Improper Fraction: Convert $10\frac{1}{2}$ to an improper fraction: $10\frac{1}{2} = (10 \times 2 + 1)/2 = \frac{21}{2}$ .
Multiply by Reciprocal: Now divide $30$ by $\frac{21}{2}$ by multiplying $30$ by the reciprocal of $\frac{21}{2}$ , which is $\frac{2}{21}$ .
Calculate Result: So, $30 \times \left(\frac{2}{21}\right) = \frac{60}{21}.$
Simplify Fraction: Simplify $\frac{60}{21}$ to get the final answer.
Final Answer: $\frac{60}{21}$ simplifies to $\frac{20}{7}$ , which is approximately $2.857$ .

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