Rewrite Expressions in Different Forms - 7th Grade Math

1. What is the factored form of $9x - 9$?

   $9(x - 1)$. Factor out the GCF of $9$ from both terms.

2. What is the simplified form of $3x + 7x - 2$?

   $10x - 2$. Combine like terms: $3x + 7x = 10x$.

3. What multiplier represents an increase of $5\%$?

   $1.05$. To increase by $5\%$, multiply by $1 + 0.05 = 1.05$.

4. What expression is equivalent to "$p$ percent of $a$" using decimals?

   $\left(\frac{p}{100}\right)a$. Convert percent to decimal by dividing by $100$.

5. Identify the equivalent expression for "$n$ increased by $40\%$": $n+0.4n$ or $0.6n$?

   $n+0.4n$. Increase by $40\%$ means add $0.4n$ to original $n$.

6. What is $5x+10$ rewritten by factoring out the greatest common factor?

   $5(x+2)$. Both terms share factor $5$: $5 \cdot x + 5 \cdot 2$.

7. What is the factored form of $3x + 12$?

   $3(x + 4)$. Factor out the GCF of $3$ from both terms.

8. What is the expanded form of $5(2x - 3)$?

   $10x - 15$. Distribute $5$ to each term inside the parentheses.

9. What is $x+0.2x$ rewritten as a single term?

   $1.2x$. Factor out $x$: $x(1 + 0.2) = 1.2x$.

10. What is the factored form of $12x + 18$ using the GCF?

    $6(2x + 3)$. The GCF of $12$ and $18$ is $6$, so factor it out.

11. What is the simplified form of $\left(1 + \frac{3}{10}\right)x$?

    $\frac{13}{10}x$. Convert to improper fraction: $1 + \frac{3}{10} = \frac{13}{10}$.

12. What multiplier represents an increase of $5\%$ of an amount $a$?

    $1.05$. To increase by $5\%$, multiply by $1 + 0.05 = 1.05$.

13. What is the equivalent form of $x + 0.3x$ as a single term?

    $1.3x$. Factor out $x$: $x(1 + 0.3) = x(1.3) = 1.3x$.

14. What multiplier represents "decrease by $p\%$" in an expression?

    $1-\frac{p}{100}$. To decrease by $p\%$, multiply by $1$ minus the decimal form.

15. What expression represents "decrease $x$ by $35\%$" in one term?

    $0.65x$. Decreasing by $35\%$ means multiplying by $1 - 0.35 = 0.65$.

16. What is $2(x-7)$ rewritten using the distributive property?

    $2x-14$. Multiply $2$ by each term: $2 \cdot x - 2 \cdot 7$.

17. What is the simplified form of $\frac{1}{3}x + \frac{2}{3}x$?

    $x$. Add fractions: $\frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1$.

18. What multiplier represents a decrease of $12\%$ of an amount $a$?

    $0.88$. To decrease by $12\%$, multiply by $1 - 0.12 = 0.88$.

19. What is the simplified form of $a + 0.05a$?

    $1.05a$. Factor out $a$: $a(1 + 0.05) = a(1.05) = 1.05a$.

20. What is $\frac{3}{5}x$ rewritten using a decimal coefficient?

    $0.6x$. Convert fraction to decimal: $\frac{3}{5} = 0.6$.

21. What is the expanded form of $4(x - 2)$?

    $4x - 8$. Distribute $4$ to each term: $4 \cdot x - 4 \cdot 2$.

22. What is the equivalent expression for "$15\%$ more than $n$"?

    $1.15n$. $15\%$ more means multiply by $1 + 0.15 = 1.15$.

23. What is the equivalent expression for "$25\%$ of $m$"?

    $0.25m$. $25\% = 0.25$, so $25\%$ of $m$ is $0.25m$.

24. What is "$20\%$ of $x$" written as an algebraic expression?

    $0.2x$. Convert percent to decimal: $20\% = 0.2$.

25. What is the simplified form of $0.2x + 0.8x$?

    $x$. Combine coefficients: $0.2 + 0.8 = 1$, so $1x = x$.

26. What is the expanded form of $2(x + 7) + 3x$?

    $5x + 14$. Distribute $2$, then combine like terms: $2x + 14 + 3x = 5x + 14$.

27. What is $x+x+x+x$ rewritten using multiplication?

    $4x$. Four copies of $x$ equals $4$ times $x$.

28. What is $6x-18$ rewritten by factoring out $6$?

    $6(x-3)$. Both terms divisible by $6$: $6 \cdot x - 6 \cdot 3$.

29. What is the equivalent one-term expression for $x - 0.08x$?

    $0.92x$. Factor out $x$: $x(1 - 0.08) = x(0.92) = 0.92x$.

30. What is the simplified form of $\frac{1}{4}x + \frac{3}{4}x$?

    $x$. Add fractions with same denominator: $\frac{1+3}{4}x = \frac{4}{4}x = x$.

31. What is "decrease by $15\%$" written as a multiplication expression on $x$?

    $0.85x$. Decrease by $15\%$ means multiply by $1 - 0.15 = 0.85$.

32. What expression represents "increase $x$ by $20\%$" in one term?

    $1.2x$. Increasing by $20\%$ means multiplying by $1.2$.

33. What is "increase by $12\%$" written as a multiplication expression on $x$?

    $1.12x$. Increase by $12\%$ means multiply by $1.12$.

34. What is $y-0.3y$ rewritten as a single term?

    $0.7y$. Factor out $y$: $y(1 - 0.3) = 0.7y$.

35. Find and correct the expression for "decrease $a$ by $9\%$": $a + 0.09a$.

    $a - 0.09a$. To decrease, subtract the percent: $a - 0.09a$.

36. What property lets you rewrite $a+0.05a$ as $(1+0.05)a$?

    Distributive property (factoring out $a$). Factoring out common factor $a$ from both terms.

37. What is the simplified form of $2x + 3 + 5x - 1$?

    $7x + 2$. Combine like terms: $(2x + 5x) + (3 - 1) = 7x + 2$.

38. What multiplier represents a decrease of $12\%$?

    $0.88$. To decrease by $12\%$, multiply by $1 - 0.12 = 0.88$.

39. What is the simplified form of $5(x + 3) - 2(x - 1)$?

    $3x + 17$. Expand both: $5x + 15 - 2x + 2 = 3x + 17$.

40. What is $0.25x$ rewritten using a fraction coefficient?

    $\frac{1}{4}x$. Convert decimal to fraction: $0.25 = \frac{1}{4}$.

41. What is "$\frac{3}{4}$ of $x$" written as an algebraic expression?

    $\frac{3}{4}x$. "Of" means multiply in mathematical expressions.

42. What is "add a $7$ dollar fee to $m$ dollars" written as an expression?

    $m+7$. Add the fee to the original amount.

43. What is the equivalent expression for $15\%$ of $x$ added to $x$?

    $1.15x$. $15\%$ of $x$ is $0.15x$, plus $x$ gives $1.15x$.

44. What is $3(x+4)$ rewritten using the distributive property?

    $3x+12$. Multiply $3$ by each term inside parentheses.

45. What is the simplified form of $0.4x + 0.6x$?

    $x$. Combine coefficients: $0.4 + 0.6 = 1$, so result is $1x = x$.

46. What is an equivalent expression for "$7$ less than twice $n$"?

    $2n - 7$. "Twice $n$" is $2n$, then subtract $7$.

47. What is $a+0.05a$ rewritten as a single coefficient times $a$?

    $1.05a$. Combine like terms: $a + 0.05a = (1 + 0.05)a = 1.05a$.

48. What is an equivalent expression for "$3$ more than $5$ times $p$"?

    $5p + 3$. "$5$ times $p$" is $5p$, then add $3$.

49. What is the simplified form of $7(x - 2) - 3(x - 2)$?

    $4(x - 2)$. Factor out $(x - 2)$: $7(x - 2) - 3(x - 2) = (7 - 3)(x - 2)$.

50. What is the equivalent expression for "$\frac{3}{5}$ of $y$"?

    $\frac{3}{5}y$. "Of" means multiply: $\frac{3}{5} \times y = \frac{3}{5}y$.

51. What is the factored form of $6x + 9$ using the GCF?

    $3(2x + 3)$. Factor out the GCF of $3$ from both terms.

52. What is the equivalent expression for "$25\%$ less than $n$"?

    $0.75n$. $25\%$ less means multiply by $1 - 0.25 = 0.75$.

53. What percent change is represented by multiplying by $1.18$?

    Increase by $18\%$. Multiplying by $1.18 = 1 + 0.18$ means adding $18\%$.

54. What multiplier represents "increase by $p\%$" in an expression?

    $1+\frac{p}{100}$. To increase by $p\%$, multiply by $1$ plus the decimal form.

55. What is "$5$ dollars per ticket for $t$ tickets" written as an expression?

    $5t$. Rate times quantity gives total cost.

56. What is the expanded form of $4(2x - 5)$?

    $8x - 20$. Distribute $4$ to each term: $4(2x) - 4(5) = 8x - 20$.

57. What percent change is represented by multiplying by $0.73$?

    Decrease by $27\%$. Multiplying by $0.73 = 1 - 0.27$ means subtracting $27\%$.

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