Rearranging Formulas to Highlight Quantities - Algebra 1

1. What is $I$ in terms of $V$ and $R$ if $V = IR$?

   $I =$. Divide both sides by $R$ to isolate $I$.

2. What is $x$ in terms of $A$, $B$, and $C$ if $A = Bx + C$?

   $x = \frac{A - C}{B}$. Subtract $C$, then divide by $B$ to isolate $x$.

3. Find and correct the isolation error: from $V = IR$ to $R = V/I$.

   $R = \frac{V}{I}$. Divide both sides by $I$ to isolate resistance.

4. What is $r$ in terms of $d$ and $t$ if $d = rt$?

   $r = \frac{d}{t}$. Divide both sides by $t$ to isolate $r$.

5. What is $x$ in terms of $y$ if $y = x^2 + k$?

   $x =$. Subtract $k$, then take the square root.

6. What is $x$ in terms of $A$, $B$, and $C$ if $A = \frac{x + B}{C}$?

   $x = AC - B$. Multiply by $C$, then subtract $B$ to isolate $x$.

7. What is $x$ in terms of $A$, $B$, and $C$ if $A = \frac{B}{C - x}$?

   $x = C - \frac{B}{A}$. Multiply by $ (C - x) $, divide by $A$, then subtract from $C$.

8. What is $x$ in terms of $A$ and $B$ if $A = \frac{B}{x}$?

   $x = \frac{B}{A}$. Cross-multiply to get $x = \frac{B}{A}$.

9. What is $x$ in terms of $A$ and $B$ if $A = \frac{1}{2}Bx$?

   $x = \frac{2A}{B}$. Multiply by $2$ to clear the fraction coefficient.

10. What is $r$ in terms of $C$ if $C = 2\pi r$?

    $r = \frac{C}{2\pi}$. Divide both sides by $2\pi$ to isolate $r$.

11. What is $x$ in terms of $A$, $B$, and $C$ if $A = C - Bx$?

    $x = \frac{C - A}{B}$. Rearrange: $Bx = C - A$, then divide by $B$.

12. What is $a$ in terms of $F$ and $m$ if $F = ma$?

    $a =$. Divide both sides by $m$ to isolate $a$.

13. What does it mean to "highlight" a quantity of interest in a formula?

    Rewrite the formula with that variable isolated. Making the desired variable the subject of the equation.

14. What is $x$ in terms of $y$ if $y = \frac{1}{x}$?

    $x = \frac{1}{y}$. Take the reciprocal of both sides.

15. What is $P$ in terms of $A$ and $r$ if $A = Pr$?

    $P = \frac{A}{r}$. Divide both sides by $r$ to isolate $P$.

16. What is $B$ in terms of $A$ and $x$ if $A = \frac{B}{x}$?

    $B = Ax$. Cross-multiply to get $B = Ax$.

17. What is $x$ in terms of $A$, $B$, and $C$ if $A = x + C$?

    $x =$. Subtract $C$, then multiply by $B$ to isolate $x$.

18. What is $x$ in terms of $A$, $B$, and $C$ if $A = B(C - x)$?

    $x = C - \frac{A}{B}$. Divide by $B$, then subtract from $C$ to isolate $x$.

19. What is $m$ in terms of $y$, $b$, and $x$ if $y = mx + b$?

    $m = \frac{y - b}{x}$. Subtract $b$, then divide by $x$ to isolate $m$.

20. What operation should you use to isolate a variable in a sum like $A = B + C$?

    Subtract the other term from both sides. Subtraction removes the unwanted term from the isolated variable's side.

21. What is $C$ in terms of $A$, $B$, and $x$ if $A = B(C - x)$?

    $C = x + \frac{A}{B}$. Add $x$, then divide by $B$ to isolate $C$.

22. What is $x$ in terms of $y$, $m$, and $b$ if $y = mx + b$?

    $x = \frac{y - b}{m}$. Subtract $b$, then divide by $m$ to isolate $x$.

23. Identify the property used when you multiply or divide both sides of an equation by the same nonzero number.

    Multiplication/Division Property of Equality. Maintains equality when multiplying or dividing by the same value.

24. What is $r$ in terms of $A$ and $P$ if $A = Pr$?

    $r =$. Divide both sides by $P$ to isolate $r$.

25. What is $r$ in terms of $V$ and $h$ if $V = \pi r^2 h$?

    $r = \sqrt{\frac{V}{\pi h}}$. Divide by $\pi h$, then take the square root.

26. What is $x$ in terms of $y$ if $y = (x - h)^2$?

    $x = h$. Take the square root, then add $h$.

27. What is $x$ in terms of $y$ if $y = x + b$?

    $x = \frac{y - b}{a}$. Subtract $b$, then divide by $a$ to isolate $x$.

28. What is $w$ in terms of $P$ and $l$ if $P = 2l + 2w$?

    $w = \frac{P - 2l}{2}$. Subtract $2l$, then divide by $2$ to isolate $w$.

29. What is $x$ in terms of $y$ if $y = \frac{x}{a} + b$?

    $x = a(y - b)$. Subtract $b$, then multiply by $a$ to isolate $x$.

30. What is $b$ in terms of $y$, $m$, and $x$ if $y = mx + b$?

    $b = y - mx$. Subtract $mx$ from both sides to isolate $b$.

31. What is $x$ in terms of $A$, $B$, and $C$ if $A = \frac{Bx}{C}$?

    $x = \frac{AC}{B}$. Multiply by $C$, then divide by $B$ to isolate $x$.

32. What is $x$ in terms of $A$ and $B$ if $A = \frac{x}{B}$?

    $x = AB$. Multiply both sides by $B$ to isolate $x$.

33. What is $C$ in terms of $A$, $x$, and $B$ if $A = \frac{x + B}{C}$?

    $C = \frac{x + B}{A}$. Multiply by $C$, then divide by $A$ to isolate $C$.

34. What is $m$ in terms of $F$ and $a$ if $F = ma$?

    $m =$. Divide both sides by $a$ to isolate $m$.

35. What is $R$ in terms of $V$ and $I$ if $V = IR$?

    $R = \frac{V}{I}$. Divide both sides by $I$ to isolate $R$.

36. What is $B$ in terms of $A$ and $x$ if $A = \frac{x}{B}$?

    $B = \frac{x}{A}$. Cross-multiply to get $B = \frac{x}{A}$.

37. What is $x$ in terms of $A$, $B$, and $C$ if $A = \frac{B}{x} + C$?

    $x = \frac{B}{A - C}$. Subtract $C$, then take the reciprocal.

38. What is the inverse operation used to undo squaring in $y = x^2$ when solving for $x$?

    Take the square root: $x =$. Square root undoes the squaring operation.

39. What operation should you use to isolate the denominator in $A = \frac{B}{C}$ (solve for $C$)?

    Multiply by $C$, then divide by $A$. First clear the fraction, then divide to isolate $C$.

40. What is $h$ in terms of $A$ and $b$ if $A = bh$?

    $h =$. Divide both sides by $\frac{1}{2}b$ to isolate $h$.

41. What is $l$ in terms of $P$ and $w$ if $P = 2l + 2w$?

    $l =$. Subtract $2w$, then divide by $2$ to isolate $l$.

42. What operation should you use to isolate a variable multiplied by a constant in $A = kB$?

    Divide both sides by $k$. Dividing by the coefficient isolates the variable.

43. Identify the property used when you add or subtract the same expression on both sides of an equation.

    Addition/Subtraction Property of Equality. Maintains equality when adding or subtracting the same value.

44. What is $b$ in terms of $A$ and $h$ if $A = bh$?

    $b =$. Divide both sides by $\frac{1}{2}h$ to isolate $b$.

45. What operation should you use to isolate a variable in $A =$ form like $A = \frac{B}{C}$ (solve for $B$)?

    Multiply both sides by $C$. Multiplying by the denominator clears the fraction.

46. Find and correct the isolation error: from $V = IR$ to $R = \frac{V}{I}$.

    $R = \frac{V}{I}$. Divide both sides by $I$ to isolate resistance.

47. What is $x$ in terms of $A$, $B$, and $C$ if $A = Bx - C$?

    $x = \frac{A + C}{B}$. Add $C$, then divide by $B$ to isolate $x$.

48. What is $h$ in terms of $V$ and $r$ if $V = r^2 h$?

    $h =$. Divide both sides by $\pi r^2$ to isolate $h$.

49. What is $t$ in terms of $d$ and $r$ if $d = rt$?

    $t =$. Divide both sides by $r$ to isolate $t$.

50. What is $C$ in terms of $A$, $B$, and $x$ if $A = \frac{Bx}{C}$?

    $C = \frac{Bx}{A}$. Multiply by $C$, then divide by $A$ to isolate $C$.

51. What operation should you use to isolate a variable in a difference like $A = B - C$ (solve for $B$)?

    Add $C$ to both sides. Adding $C$ cancels the subtraction to isolate $B$.

52. What is $h$ in terms of $V$ and $r$ if $V = \pi r^2 h$?

    $h = \frac{V}{\pi r^2}$. Divide both sides by $\pi r^2$ to isolate $h$.

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