Multi-Step Operations - ISEE Upper Level Quantitative Reasoning

1. What is the value of $\left(\frac{3}{8}\right)\div\left(\frac{1}{4}\right)+\frac{1}{2}$?

   $2$. Division of fractions is multiplication by the reciprocal, performed before adding $\frac{1}{2}$.

2. What is the value of $\frac{9-3}{2}+\frac{8}{4}$?

   $5$. Numerator subtraction precedes division, then add the result of the second division.

3. What is the value of $\left(\frac{1}{3}+\frac{1}{6}\right)\times12$?

   $6$. Parentheses require addition of fractions first, then multiplication by 12.

4. What is the value of $(18-6)\times(2+5)$?

   $84$. Parentheses dictate subtraction and addition first, then multiplication of the results.

5. What is the value of $\frac{7}{10}+\frac{3}{5}-\frac{1}{2}$?

   $\frac{4}{5}$. Convert to tenths and perform addition followed by subtraction from left to right.

6. What is the value of $\frac{3}{7}\div\frac{6}{7}+\frac{1}{4}$?

   $\frac{3}{4}$. Division of fractions is multiplication by the reciprocal, performed before adding $\frac{1}{4}$.

7. What is the value of $\left(\frac{2}{3}\right)\times\left(\frac{9}{4}\right)-\frac{1}{2}$?

   $1$. Multiplication of fractions precedes subtraction, so compute $\frac{2}{3} \times \frac{9}{4}$ first, then subtract $\frac{1}{2}$.

8. What is the value of $\frac{5}{6}-\frac{1}{3}+\frac{1}{2}$?

   $1$. Convert fractions to a common denominator of 6, then subtract and add from left to right.

9. What is the value of $\left(\frac{5}{2}-\frac{1}{4}\right)\div\frac{3}{2}$?

   $\frac{3}{2}$. Parentheses require subtraction first, then divide the result by $\frac{3}{2}$ via multiplication by its reciprocal.

10. What is the value of $\frac{2}{5}\text{ of }50+\frac{1}{2}\text{ of }20$?

    $30$. 'Of' indicates multiplication, so compute each product separately and add the results.

11. What is the value of $\frac{1}{2}\times\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{1}{8}$?

    $\frac{5}{8}$. Parentheses require addition first, then multiplication by $\frac{1}{2}$, followed by adding $\frac{1}{8}$.

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