Algebra Flashcards: Rearranging Formulas To Highlight Quantities

What this deck covers

This deck focuses on Rearranging Formulas To Highlight Quantities, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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

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

Flashcard 2: What is $x$ in terms of $A$, $B$, and $C$ if $A = C - Bx$?

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

Flashcard 3: What is $x$ in terms of $A$, $B$, and $C$ if $A = Bx + C$?

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

Flashcard 4: Find and correct the isolation error: from $V = IR$ to $R = V/I$.

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

Flashcard 5: What is $r$ in terms of $d$ and $t$ if $d = rt$?

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

Flashcard 6: What is $x$ in terms of $y$ if $y = x^2 + k$?

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

Flashcard 7: What is $x$ in terms of $A$, $B$, and $C$ if A = rac{x + B}{C}?

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

Flashcard 8: What is $R$ in terms of $V$ and $I$ if $V = IR$?

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

Flashcard 9: What is $x$ in terms of $A$, $B$, and $C$ if A = rac{B}{C - x}?

Answer: x = C - rac{B}{A}. Multiply by $(C - x)$, divide by $A$, then subtract from $C$.

Flashcard 10: What is $I$ in terms of $V$ and $R$ if $V = IR$?

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

Flashcard 11: What operation should you use to isolate a variable in a sum like $A = B + C$?

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

Flashcard 12: What is $x$ in terms of $A$ and $B$ if A = rac{B}{x}?

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

Flashcard 13: What is $x$ in terms of $A$ and $B$ if A = rac{1}{2}Bx?

Answer: x = rac{2A}{B}. Multiply by $2$ to clear the fraction coefficient.

Flashcard 14: What is $r$ in terms of $C$ if $C = 2\pi r$?

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

Flashcard 15: What is $x$ in terms of $A$, $B$, and $C$ if $A = C - Bx$?

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

Flashcard 16: What is $a$ in terms of $F$ and $m$ if $F = ma$?

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

Flashcard 17: What does it mean to "highlight" a quantity of interest in a formula?

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

Flashcard 18: What is $x$ in terms of $y$ if y = rac{1}{x}?

Answer: x = rac{1}{y}. Take the reciprocal of both sides.

Flashcard 19: What is $r$ in terms of $A$ and $P$ if $A = Pr$?

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

Flashcard 20: What is $P$ in terms of $A$ and $r$ if $A = Pr$?

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

Flashcard 21: What is $B$ in terms of $A$ and $x$ if A = rac{B}{x}?

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

Flashcard 22: What is $x$ in terms of $A$, $B$, and $C$ if A =  x + C?

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

Flashcard 23: What is $x$ in terms of $A$, $B$, and $C$ if $A = B(C - x)$?

Answer: x = C - rac{A}{B}. Divide by $B$, then subtract from $C$ to isolate $x$.

Flashcard 24: What is $m$ in terms of $y$, $b$, and $x$ if $y = mx + b$?

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

Flashcard 25: What operation should you use to isolate a variable in a sum like $A = B + C$?

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

Flashcard 26: What is $C$ in terms of $A$, $B$, and $x$ if $A = B(C - x)$?

Answer: C = x + rac{A}{B}. Add $x$, then divide by $B$ to isolate $C$.

Flashcard 27: What is $x$ in terms of $y$, $m$, and $b$ if $y = mx + b$?

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

Flashcard 28: What is $x$ in terms of $y$ if $y = x^2 + k$?

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

Flashcard 29: What is $r$ in terms of $d$ and $t$ if $d = rt$?

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

Flashcard 30: What operation should you use to isolate a variable multiplied by a constant in $A = kB$?

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

Flashcard 31: Identify the property used when you multiply or divide both sides of an equation by the same nonzero number.

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

Flashcard 32: What is $r$ in terms of $A$ and $P$ if $A = Pr$?

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

Flashcard 33: What is $r$ in terms of $V$ and $h$ if $V = \pi r^2 h$?

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

Flashcard 34: What is $x$ in terms of $y$ if $y = (x - h)^2$?

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

Flashcard 35: What is $x$ in terms of $y$ if y =  x + b?

Answer: x = rac{y - b}{a}. Subtract $b$, then divide by $a$ to isolate $x$.

Flashcard 36: What is $w$ in terms of $P$ and $l$ if $P = 2l + 2w$?

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

Flashcard 37: What is $x$ in terms of $y$, $m$, and $b$ if $y = mx + b$?

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

Flashcard 38: What is $x$ in terms of $y$ if y = rac{x}{a} + b?

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

Flashcard 39: What is $b$ in terms of $y$, $m$, and $x$ if $y = mx + b$?

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

Flashcard 40: What is $x$ in terms of $A$, $B$, and $C$ if A = rac{x + B}{C}?

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

Flashcard 41: What is $x$ in terms of $A$, $B$, and $C$ if A = rac{Bx}{C}?

Answer: x = rac{AC}{B}. Multiply by $C$, then divide by $B$ to isolate $x$.

Flashcard 42: What is $x$ in terms of $A$ and $B$ if A = rac{x}{B}?

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

Flashcard 43: What is $C$ in terms of $A$, $x$, and $B$ if A = rac{x + B}{C}?

Answer: C = rac{x + B}{A}. Multiply by $C$, then divide by $A$ to isolate $C$.

Flashcard 44: What is $m$ in terms of $F$ and $a$ if $F = ma$?

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

Flashcard 45: What is $R$ in terms of $V$ and $I$ if $V = IR$?

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

Flashcard 46: What is $B$ in terms of $A$ and $x$ if A = rac{x}{B}?

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

Flashcard 47: What is $x$ in terms of $A$, $B$, and $C$ if A = rac{B}{x} + C?

Answer: x = rac{B}{A - C}. Subtract $C$, then take the reciprocal.

Flashcard 48: What is $r$ in terms of $V$ and $h$ if $V = \pi r^2 h$?

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

Flashcard 49: What is $x$ in terms of $A$, $B$, and $C$ if $A = Bx - C$?

Answer: x = rac{A + C}{B}. Add $C$, then divide by $B$ to isolate $x$.

Flashcard 50: What is the inverse operation used to undo squaring in $y = x^2$ when solving for $x$?

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

Flashcard 51: What operation should you use to isolate the denominator in A = rac{B}{C} (solve for $C$)?

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

Flashcard 52: What is $h$ in terms of $A$ and $b$ if A =  bh?

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

Flashcard 53: What is $l$ in terms of $P$ and $w$ if $P = 2l + 2w$?

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

Flashcard 54: What operation should you use to isolate a variable multiplied by a constant in $A = kB$?

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

Flashcard 55: Identify the property used when you add or subtract the same expression on both sides of an equation.

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

Flashcard 56: What is $b$ in terms of $A$ and $h$ if A =  bh?

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

Flashcard 57: What operation should you use to isolate a variable in A =   form like A = rac{B}{C} (solve for $B$)?

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

Flashcard 58: What is $x$ in terms of $y$ if y = rac{1}{x}?

Answer: x = rac{1}{y}. Take the reciprocal of both sides.

Flashcard 59: What is $l$ in terms of $P$ and $w$ if $P = 2l + 2w$?

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

Flashcard 60: Find and correct the isolation error: from $V = IR$ to $R = \frac{V}{I}$.

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

Flashcard 61: What is $x$ in terms of $A$, $B$, and $C$ if $A = Bx - C$?

Answer: x = rac{A + C}{B}. Add $C$, then divide by $B$ to isolate $x$.

Flashcard 62: What is $h$ in terms of $V$ and $r$ if V =   r^2 h?

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

Flashcard 63: What is $t$ in terms of $d$ and $r$ if $d = rt$?

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

Flashcard 64: What is $C$ in terms of $A$, $B$, and $x$ if A = rac{Bx}{C}?

Answer: C = rac{Bx}{A}. Multiply by $C$, then divide by $A$ to isolate $C$.

Flashcard 65: What is $B$ in terms of $A$ and $x$ if A = rac{x}{B}?

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

Flashcard 66: What operation should you use to isolate a variable in a difference like $A = B - C$ (solve for $B$)?

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

Flashcard 67: What is $h$ in terms of $V$ and $r$ if $V = \pi r^2 h$?

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