Multi-Operation Problems - SSAT Upper Level Quantitative

1. What is the value of $\frac{12}{3}\left(5-2\right)+7$?

   $19$. Division first, then parentheses, implied multiplication, and addition per PEMDAS.

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

   $1$. Add fractions in parentheses, then divide by inverting and multiplying.

3. What is the value of $\left(0.6\times 50\right)-\left(\frac{3}{5}\times 20\right)$?

   $18$. Compute each multiplication in parentheses, then subtract decimals.

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

   $\frac{5}{36}$. Difference of squares formula applies: $(a+b)(a-b) = a^2 - b^2$ with fractions.

5. What is the value of $\left|3-8\right|+\left(-2\right)^3$?

   $-3$. Absolute value yields positive, added to negative cube of integer.

6. What is the value of $2^3\times 3+4^2\div 2$?

   $32$. Exponents first, then multiplication and division left to right, finally addition.

7. What is the value of $\frac{x^2-9}{x-3}$ when $x=6$?

   $9$. Substitute value into algebraic fraction and simplify numerator and denominator.

8. What is the value of $\left(12\div 4\right)^2-\left(3\times 2\right)$?

   $3$. Division inside parentheses, square the result, then subtract product.

9. What order of operations should you use to evaluate an expression with parentheses and exponents?

   Use $\text{PEMDAS}$: parentheses, exponents, multiply/divide, add/subtract. PEMDAS ensures consistent evaluation by prioritizing parentheses, then exponents, followed by multiplication/division left to right, and addition/subtraction left to right.

10. What is the value of $\frac{3}{4}+\frac{1}{8}\times 4$?

    $\frac{5}{4}$. Multiplication precedes addition, so compute fraction multiplication first then add.

11. What is the value of $18-6\div 3\times 4$?

    $10$. Perform division and multiplication from left to right before subtraction, per order of operations.

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

    $\frac{5}{2}$. Division of fractions involves multiplying by reciprocal, then add the integer.

13. What is the value of $7+3\left(2-\frac{5}{2}\right)$?

    $\frac{11}{2}$. Compute inside parentheses, multiply by coefficient, then add.

14. What is the value of $\frac{16}{\left(2^3\right)}+\frac{9}{3}$?

    $5$. Exponent in denominator first, then divide each term and add results.

15. What is the value of $\left(2.5\right)^2-\left(1.5\right)^2+\left(3\right)$?

    $7$. Difference of squares plus integer: $(a^2 - b^2) + c$ with decimals.

16. What is the value of $\left(\frac{5}{6}-\frac{1}{3}\right)\div\frac{1}{4}$?

    $2$. Subtract fractions in parentheses, then divide by inverting and multiplying.

17. What is the value of $\frac{9}{2}-\left(\frac{3}{4}\times 8\right)$?

    $-\frac{3}{2}$. Multiplication in parentheses first, then subtract from fraction.

18. What is the value of $\left(6-\frac{3}{2}\right)\times 4$?

    $18$. Subtract fractions within parentheses first, then multiply by the integer.

19. What is the value of $5-\left[2-\left(3-4\right)\right]$?

    $2$. Evaluate innermost parentheses first, then work outward subtracting nested brackets.

20. What is the value of $\frac{1}{2}ab$ when $a=8$ and $b=\frac{3}{4}$?

    $3$. Multiply variables by fraction after substituting given values.

21. What is the value of $\frac{2}{5}\cdot 15-\frac{3}{10}\cdot 20$?

    $0$. Compute each multiplication separately, then subtract the results.

22. What is the value of $2\left[3x-4\right]$ when $x=5$?

    $22$. Substitute variable, compute inside brackets, then multiply by coefficient.

23. What is the value of $\frac{2\left(3+7\right)}{5}-\frac{6}{5}$?

    $\frac{14}{5}$. Add inside parentheses, multiply numerator, divide, then subtract fraction.

24. What is the value of $3(4+2)^2-5$?

    $103$. Apply PEMDAS: first compute inside parentheses, then exponent, multiply, and finally subtract.

25. What is the value of $4x-3\left(x-2\right)$ when $x=7$?

    $13$. Substitute variable, distribute negative over parentheses, then combine terms.

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