Write and Interpret Numerical Expressions - 5th Grade Math

1. What is the numerical expression for "add $8$ and $7$, then multiply by $2$"?

   $2(8+7)$. Parentheses show to add first, then multiply.

2. What does the expression $\frac{48+16}{8}$ mean in words, without calculating?

   The sum $48+16$ divided by $8$. Describes division without evaluating the sum.

3. Which expression represents "$4$ groups of $(m+2)$"?

   $4 \times (m+2)$. "Groups of" means multiply the entire quantity in parentheses.

4. Which expression matches: "Add $6$ to the product of $4$ and $9$"?

   $(4 \times 9)+6$. "Product of" means multiply first, then add $6$.

5. What is the numerical expression for "divide $24$ by $6$, then add $10$"?

   $\frac{24}{6}+10$. Division happens first, then addition.

6. What is the numerical expression for "multiply $9$ by $5$, then subtract $3$"?

   $9\cdot 5-3$. Order of operations: multiply first, then subtract.

7. Find and correct the expression for "multiply $2$ by the sum of $8$ and $7$": $2\cdot 8+7$.

   $2(8+7)$. Parentheses needed to multiply the entire sum.

8. Which expression matches: "Subtract $5$ from $12$, then multiply by $4$"?

   $4 \times (12-5)$. Parentheses ensure subtraction occurs before multiplication.

9. What is the meaning of $(x+7) \div 2$ without evaluating it?

   The sum of $x$ and $7$, divided by $2$. Parentheses ensure addition happens before division.

10. What is the numerical expression for "double the difference of $30$ and $11$"?

    $2(30-11)$. Double means multiply by $2$; parentheses group the difference.

11. What do parentheses mean in an expression such as $2 \times (8+7)$?

    Do the operation inside parentheses first. Order of operations requires parentheses to be evaluated first.

12. Which expression shows "$4$ times as large as $a+b$": $4a+b$ or $4(a+b)$?

    $4(a+b)$. Parentheses multiply the entire sum, not just $a$.

13. How many times as large is $3 \times (18932+921)$ compared to $(18932+921)$?

    It is $3$ times as large. Multiplying by $3$ makes the expression $3$ times larger.

14. What is the meaning of $2 \times (x+7)$ without evaluating it?

    Twice the sum of $x$ and $7$. "Twice" means multiply by $2$; parentheses show sum first.

15. Which expression represents "the total of $m$ and $2$, taken $4$ times"?

    $4 \times (m+2)$. "Taken $4$ times" means multiply the sum by $4$.

16. Find and correct the expression for "add $10$ and $3$, then divide by $2$": $10+3 \div 2$.

    $(10+3) \div 2$. Parentheses needed to add before dividing.

17. What is the numerical expression for "subtract $4$ from $18$, then divide by $7$"?

    $\frac{18-4}{7}$. Fraction bar groups the subtraction before dividing.

18. What is the numerical expression for "add $6$ to the product of $7$ and $8$"?

    $7\cdot 8+6$. Product means multiply; it's calculated before adding.

19. Which is larger: $3 \times (18932+921)$ or $(18932+921)$?

    $3 \times (18932+921)$. Multiplying by $3$ makes it larger than without multiplication.

20. Find and correct the expression for "multiply $6$ by the difference of $20$ and $4$": $6 \times 20-4$.

    $6 \times (20-4)$. Parentheses needed to subtract before multiplying.

21. Which expression matches: "Multiply $4$ by the sum of $9$ and $6$"?

    $4 \times (9+6)$. "Sum of" means add first, shown by parentheses.

22. What is the numerical expression for "multiply the sum of $12$ and $3$ by $4$"?

    $4(12+3)$. Parentheses group the sum before multiplying.

23. Which expression matches: "Divide $18$ by $3$, then add $6$"?

    $(18 \div 3)+6$. Parentheses show division happens first, then addition.

24. Find and correct the expression for "subtract $6$ from the product of $9$ and $4$": $9(4-6)$.

    $9\cdot 4-6$. Product first, then subtract; not multiply the difference.

25. Which expression matches "add $9$ and $2$, then multiply by $6$": $6+9+2$ or $6(9+2)$?

    $6(9+2)$. Parentheses ensure addition happens before multiplication.

26. Which expression matches: "Multiply $2$ by $8$, then add $7$"?

    $(2 \times 8)+7$. Parentheses show multiplication happens first, then addition.

27. Identify the expression that is "$3$ times the quantity $n$ minus $5$".

    $3 \times (n-5)$. "The quantity" indicates parentheses around $n-5$.

28. Identify the expression that is "$5$ less than $3$ times $n$".

    $(3 \times n)-5$. "Less than" means subtract from the result of $3 \times n$.

29. What is the numerical expression for "half of the sum of $14$ and $6$"?

    $\frac{1}{2}(14+6)$. Half means multiply by $\frac{1}{2}$.

30. Which expression matches: "Add $8$ and $7$, then multiply the result by $2$"?

    $2 \times (8+7)$. Parentheses ensure addition happens before multiplication.

31. How many times as large is $\frac{1}{2} \times (a+b)$ compared to $(a+b)$?

    It is $\frac{1}{2}$ as large. Multiplying by $\frac{1}{2}$ makes it half as large.

32. What does the expression $3 \times (a+b)$ mean in words?

    Three times the sum of $a$ and $b$. Parentheses show that $a$ and $b$ are added before multiplying by $3$.

33. What is the numerical expression for "take $5$ away from the quotient of $40$ and $8$"?

    $\frac{40}{8}-5$. Quotient means divide; subtract after dividing.

34. What does the expression $(a+b) \times 3$ mean in words?

    The sum of $a$ and $b$, multiplied by $3$. Parentheses indicate addition happens before multiplication.

35. What does the expression $18-\frac{20}{5}$ mean in words, without calculating?

    $18$ minus the quotient $20\div 5$. Describes subtraction without evaluating the quotient.

36. Identify which is larger without evaluating: $2(50+1)$ or $(50+1)$?

    $2(50+1)$. Multiplying by $2$ makes it twice as large.

37. Identify the factor that makes $7(300+25)$ "times as large as" $(300+25)$.

    $7$. The coefficient shows how many times larger.

38. What does the expression $5(12-7)$ mean in words, without calculating?

    Five times the difference $12-7$. Describes multiplication without evaluating the difference.

39. What does the expression $3(18932+921)$ mean in words, without calculating?

    Three times the sum $18932+921$. Describes multiplication without evaluating the sum.

40. Identify the expression for "the sum of $15$ and $5$ divided by $4$": $15+\frac{5}{4}$ or $\frac{15+5}{4}$?

    $\frac{15+5}{4}$. Fraction bar groups the entire sum before dividing.

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