Rearranging Formulas to Highlight Quantities - Algebra 1

Temperature conversion can be written as the literal equation $C = \frac{5}{9}(F - 32)$ , where $C$ is degrees Celsius and $F$ is degrees Fahrenheit. Solve $C = \frac{5}{9}(F - 32)$ for $F$ .
Answer: $F = \dfrac{9}{5}C + 32$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! To solve C = (5/9)(F - 32) for F, we first multiply both sides by 9/5 to clear the fraction: (9/5)C = F - 32. Then we add 32 to both sides: (9/5)C + 32 = F, or F = (9/5)C + 32. Choice C is correct because it properly isolates F using multiplication by 9/5 and addition of 32, giving F = (9/5)C + 32. Perfect! Choice A incorrectly keeps the 5/9 fraction, while choice B has the wrong order of operations—we need to multiply C by 9/5 first, then add 32, not subtract 32 from C before multiplying. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving C = (5/9)(F - 32) for F is like solving 20 = (5/9)(x - 32) for x: multiply by 9/5, then add 32. Common formula rearrangements to practice: d = rt becomes t = d/r (divide by rate) and r = d/t (divide by time); A = lw becomes l = A/w (divide by width); P = 2l + 2w becomes l = (P - 2w)/2 (subtract 2w, divide by 2). The same formulas show up repeatedly in math and science, so learning these rearrangements once helps you many times!
In geometry, the area of a rectangle is given by the literal equation $A = lw$ , where $A$ is area, $l$ is length, and $w$ is width. Treat the other variables like numbers and use inverse operations (as you would when solving a numeric equation) to solve for $w$ .
Answer: $w = \dfrac{A}{l}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! To solve A = l w for w, treat A and l as known and isolate w by dividing both sides by l, which gives w = A / l. Choice C is correct because it properly isolates w using division, giving w = A / l. Perfect! A common mistake like choice D multiplies instead of divides, but remember, since l and w are multiplied to get A, you need the inverse operation of division to isolate w—keep practicing those inverse steps! The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving V = I R for R is just like solving 12 = 3x for x: divide both sides by I, giving R = V / I. When checking your work, substitute back: if you rearranged A = l w to get w = A / l, multiply both sides of your answer by l: l · w = l · (A / l) = A, which gives l w = A—same as the original! This 'does it work backward?' check confirms you rearranged correctly.
In algebra, consider the literal equation $ax + by = c$ , where $a$ , $b$ , and $c$ are constants. Solve for $y$ in terms of $x$ , $a$ , $b$ , and $c$ using the same steps as solving a numeric equation.
Answer: $y = \dfrac{c - ax}{b}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with a x + b y = c, subtract a x from both sides to get b y = c - a x, then divide by b to isolate y, giving y = (c - a x)/b. Choice A is correct because it properly isolates y using subtraction and division, giving y = (c - a x)/b. Perfect! Choice B switches the signs inside, but subtracting a x correctly moves it to the other side positively—it's tricky, but treating it like numbers clarifies it! The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! When checking your work, substitute back: multiply your y expression by b and add a x to see if you get c.
In finance, simple interest is modeled by $I = Prt$ , where $I$ is interest, $P$ is principal, $r$ is annual rate, and $t$ is time. Rearrange $I = Prt$ to solve for $r$ .
Answer: $r = \dfrac{I}{Pt}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! To solve I = Prt for r, we need to isolate r on one side. Since r is being multiplied by both P and t (giving Prt), we divide both sides by Pt: I/(Pt) = Prt/(Pt), which simplifies to I/(Pt) = r, or r = I/(Pt). Choice B is correct because it properly isolates r using division by Pt, giving r = I/(Pt). Perfect! Choice A incorrectly shows r = Pt/I (the reciprocal), while choice C multiplies all three variables together—remember, we need to divide by everything that's multiplied with r. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving I = Prt for r is just like solving 100 = 20x for x: divide both sides by Pt (or 20), giving r = I/(Pt). When checking your work, substitute back: if you rearranged I = Prt to get r = I/(Pt), multiply both sides of your answer by Pt: Pt · r = Pt · (I/(Pt)) = I, which gives Prt = I—same as the original! This 'does it work backward?' check confirms you rearranged correctly.
Rearrange the formula $y = \dfrac{x - a}{b}$ (assume $b \ne 0$ ) to solve for $x$ in terms of $y$ , $a$ , and $b$ .
Answer: $x = by + a$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with y = (x - a)/b, we first multiply both sides by b: by = b · (x - a)/b, which simplifies to by = x - a. Then we add a to both sides: by + a = x - a + a, which gives us x = by + a. Choice C is correct because it properly isolates x using multiplication by b followed by addition of a, giving x = by + a. Perfect! Choice B incorrectly shows x = (y - a)/b, which seems to just swap x and y in the original formula without proper algebraic steps—remember, we need to undo the operations around x systematically. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. When you see y = (x - a)/b, think of solving 3 = (x - 2)/5: multiply by 5 to get 15 = x - 2, then add 2 to get x = 17, just like we get x = by + a!
In the rectangle area formula $A = lw$ (where $A$ is area, $l$ is length, and $w$ is width), solve for $w$ . Treat the other variables like numbers and use inverse operations as you would in a numeric equation.
Answer: $w = \dfrac{A}{l}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with A = lw, we want to isolate w, so we divide both sides by l: A/l = lw/l, which simplifies to A/l = w, or w = A/l. Choice B is correct because it properly isolates w using division by l, giving w = A/l. Perfect! Choice A incorrectly shows w = l/A, which would mean width equals length divided by area—this reverses the fraction and doesn't match our algebraic steps. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving A = lw for w is just like solving 12 = 3x for x: divide both sides by 3 (or l), giving x = 12/3 (or w = A/l).
Ohm's law is $V = IR$ , where $V$ is voltage, $I$ is current, and $R$ is resistance. Rearrange the formula to solve for $R$ .
Answer: $R = \dfrac{V}{I}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with V = IR, we want to isolate R, so we divide both sides by I: V/I = IR/I, which simplifies to V/I = R, or R = V/I. Choice A is correct because it properly isolates R using division by I, giving R = V/I. Perfect! Choice B incorrectly multiplies V by I—remember, to undo multiplication by I, we divide by I, not multiply more. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving V = IR for R is just like solving 12 = 3x for x: divide both sides by I (or 3), giving R = V/I.
In physics, Newton's second law is $F = ma$ , where $F$ is force, $m$ is mass, and $a$ is acceleration. Solve for $m$ in terms of $F$ and $a$ .
Answer: $m = \dfrac{F}{a}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with F = ma, we want to isolate m, so we divide both sides by a: F/a = ma/a, which simplifies to F/a = m, or m = F/a. Choice C is correct because it properly isolates m using division by a, giving m = F/a. Perfect! Choice A incorrectly multiplies F by a—remember, to undo multiplication by a, we divide by a, not multiply more. When checking your work, substitute back: if you rearranged F = ma to get m = F/a, multiply both sides of your answer by a: a · m = a · (F/a) = F, which gives ma = F—same as the original! This 'does it work backward?' check confirms you rearranged correctly.
In geometry, the area of a rectangle is given by the literal equation $A = lw$ , where $A$ is area, $l$ is length, and $w$ is width. Solve $A = lw$ for $w$ (width).
Answer: $w = \dfrac{A}{l}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! To solve A = lw for w, we need to isolate w on one side. Since w is being multiplied by l, we do the opposite operation—divide both sides by l: A/l = lw/l, which simplifies to A/l = w, or w = A/l. Choice B is correct because it properly isolates w using division by l, giving w = A/l. Perfect! Choice A incorrectly shows w = l/A (the reciprocal), while choice C multiplies instead of dividing—remember, we need to undo multiplication with division. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving A = lw for w is just like solving 12 = 3x for x: divide both sides by l (or 3), giving w = A/l. When checking your work, substitute back: if you rearranged A = lw to get w = A/l, multiply both sides of your answer by l: l · w = l · (A/l) = A, which gives lw = A—same as the original! This 'does it work backward?' check confirms you rearranged correctly.
In the rectangle area formula $A = lw$ (where $A$ is area, $l$ is length, and $w$ is width), solve for $w$ in terms of $A$ and $l$ .
Answer: $w = \dfrac{A}{l}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with A = lw, we want to isolate w, so we divide both sides by l: A/l = lw/l, which simplifies to A/l = w, or w = A/l. Choice B is correct because it properly isolates w using division by l, giving w = A/l. Perfect! Choice A incorrectly shows w = l/A, which would mean multiplying l by w gives l/A—but that doesn't equal A. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving A = lw for w is just like solving 12 = 3x for x: divide both sides by 3 (or l), giving x = 4 (or w = A/l).
The average (mean) of $n$ numbers is given by $m = \dfrac{S}{n}$ , where $m$ is the mean and $S$ is the sum of the numbers. Rearrange to solve for $S$ in terms of $m$ and $n$ .
Answer: $S = mn$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! From $m = \dfrac{S}{n}$ , multiply both sides by n to isolate S, since division by n is undone by multiplication, giving $S = mn$ . Choice B is correct because it properly isolates S using multiplication, giving $S = mn$ . Perfect! Choice A divides instead, but that's the reverse—since S is divided by n originally, multiplying back isolates it nicely, so keep practicing those inverses! Common formula rearrangements to practice: $A = l w$ becomes $l = \dfrac{A}{w}$ (divide by width); $P = 2 l + 2 w$ becomes $l = \dfrac{P - 2 w}{2}$ (subtract 2 w, divide by 2). The same formulas show up repeatedly in math and science, so learning these rearrangements once helps you many times! When checking your work, substitute back: divide your $S = mn$ by n to get m, matching the original.
In physics, force is given by $F = ma$ , where $F$ is force, $m$ is mass, and $a$ is acceleration. Rearrange $F = ma$ to solve for $a$ .
Answer: $a = \dfrac{F}{m}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! To solve F = ma for a, we need to isolate a on one side. Since a is being multiplied by m, we do the opposite operation—divide both sides by m: F/m = ma/m, which simplifies to F/m = a, or a = F/m. Choice A is correct because it properly isolates a using division by m, giving a = F/m. Perfect! Choice B incorrectly shows a = Fm (multiplying instead of dividing), while choice C has the fraction flipped as a = m/F—remember, force divided by mass gives acceleration according to Newton's second law. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving F = ma for a is just like solving 20 = 5x for x: divide both sides by m (or 5), giving a = F/m. When checking your work, substitute back: if you rearranged F = ma to get a = F/m, multiply both sides of your answer by m: m · a = m · (F/m) = F, which gives ma = F—same as the original! This 'does it work backward?' check confirms you rearranged correctly.
In physics, distance traveled is modeled by $d = rt$ , where $d$ is distance, $r$ is speed (rate), and $t$ is time. Solve for $t$ in terms of $d$ and $r$ using the same steps you would use to isolate a variable in a numeric equation.
Answer: $t = \dfrac{d}{r}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with d = r t, to isolate t, divide both sides by r (treating d and r like constants), resulting in t = d / r. Choice C is correct because it properly isolates t using division, giving t = d / r. Perfect! Something like choice A multiplies instead, but that's the opposite of what we need—since r and t are multiplied, division is the inverse to undo it, so double-check those operations! Common formula rearrangements to practice: d = r t becomes t = d / r (divide by rate) and r = d / t (divide by time); A = l w becomes l = A / w (divide by width). The same formulas show up repeatedly in math and science, so learning these rearrangements once helps you many times! When checking your work, substitute back: if you rearranged d = r t to get t = d / r, multiply both sides by r: r · t = r · (d / r) = d, matching the original.
The formula for the volume of a cone is $V = \frac{1}{3}\pi r^2 h$ . An engineer designing a conical funnel knows the desired volume and height, but needs to find the radius. After rearranging the formula to solve for $r$ , what additional step must be performed to find the numerical value?
Answer: Take the square root of $\frac{3V}{\pi h}$ Starting with $V = \frac{1}{3}\pi r^2 h$ , multiply by 3: $3V = \pi r^2 h$ . Divide by $\pi h$ : $\frac{3V}{\pi h} = r^2$ . To find $r$ , take the square root: $r = \sqrt{\frac{3V}{\pi h}}$ . Choice B has the 3 in the wrong position (denominator instead of numerator). Choice C suggests division instead of taking a square root. Choice D suggests a cube root instead of square root.
The simple interest formula is $I = Prt$ (where $I$ is interest, $P$ is principal, $r$ is annual rate, and $t$ is time). Rearrange the formula to solve for $r$ in terms of $I$ , $P$ , and $t$ .
Answer: $r = \dfrac{I}{Pt}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with I = Prt, we want to isolate r, so we divide both sides by Pt: I/(Pt) = Prt/(Pt), which simplifies to I/(Pt) = r, or r = I/(Pt). Choice A is correct because it properly isolates r using division by the product Pt, giving r = I/(Pt). Perfect! Choice B incorrectly shows r = Pt/I, which would flip the relationship—if we substitute back, we'd get I = P(Pt/I)t = P²t²/I, not our original formula. When checking your work, substitute back: if you rearranged I = Prt to get r = I/(Pt), multiply both sides of your answer by Pt: Pt · r = Pt · (I/(Pt)) = I, which gives Prt = I—same as the original! This 'does it work backward?' check confirms you rearranged correctly.
The average (mean) of $n$ numbers is given by $\bar{x} = \dfrac{S}{n}$ , where $S$ is the sum of the numbers. Solve for $S$ in terms of $\bar{x}$ and $n$ .
Answer: $S = \bar{x}n$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with x̄ = S/n (where x̄ is the average), we want to isolate S, so we multiply both sides by n: n · x̄ = n · (S/n), which simplifies to nx̄ = S, or S = x̄n. Choice B is correct because it properly isolates S using multiplication by n, giving S = x̄n. Perfect! Choice A incorrectly shows S = x̄/n, which would mean the sum equals the average divided by the count—this doesn't make sense because sums are larger than averages when we have multiple values. When checking your work, substitute back: if you rearranged x̄ = S/n to get S = x̄n, divide both sides by n: S/n = (x̄n)/n = x̄—same as the original! This 'does it work backward?' check confirms you rearranged correctly.
In geometry, the volume of a rectangular prism is $V = lwh$ , where $V$ is volume, $l$ is length, $w$ is width, and $h$ is height. Solve $V = lwh$ for $h$ .
Answer: $h = \dfrac{V}{lw}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! To solve V = lwh for h, we need to isolate h on one side. Since h is being multiplied by both l and w (giving lwh), we divide both sides by lw: V/(lw) = lwh/(lw), which simplifies to V/(lw) = h, or h = V/(lw). Choice A is correct because it properly isolates h using division by lw, giving h = V/(lw). Perfect! Choice B incorrectly shows h = lw/V (the reciprocal), while choice C multiplies all the variables together—remember, we need to divide volume by length times width to get height. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving V = lwh for h is just like solving 60 = 12x for x: divide both sides by lw (or 12), giving h = V/(lw). Common formula rearrangements to practice: d = rt becomes t = d/r (divide by rate) and r = d/t (divide by time); A = lw becomes l = A/w (divide by width); P = 2l + 2w becomes l = (P - 2w)/2 (subtract 2w, divide by 2). The same formulas show up repeatedly in math and science, so learning these rearrangements once helps you many times!
The perimeter of a rectangle is $P = 2l + 2w$ , where $P$ is perimeter, $l$ is length, and $w$ is width. Rearrange the formula to make $l$ the subject (solve for $l$ in terms of $P$ and $w$ ).
Answer: $l = \dfrac{P - 2w}{2}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! From P = 2 l + 2 w, subtract 2 w from both sides to get P - 2 w = 2 l, then divide by 2 to isolate l, yielding l = (P - 2 w)/2. Choice A is correct because it properly isolates l using subtraction and division, giving l = (P - 2 w)/2. Perfect! Choice C forgets the division, but since l is multiplied by 2, we must divide to undo it—great job spotting that, and remember to apply inverses fully! The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving V = I R for R is just like solving 12 = 3x for x: divide both sides by I, giving R = V / I.
Ohm's law is $V = IR$ , where $V$ is voltage, $I$ is current, and $R$ is resistance. What is $R$ in terms of $V$ and $I$ ?
Answer: $R = \dfrac{V}{I}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! To solve V = IR for R, we need to isolate R on one side. Since R is being multiplied by I, we do the opposite operation—divide both sides by I: V/I = IR/I, which simplifies to V/I = R, or R = V/I. Choice B is correct because it properly isolates R using division by I, giving R = V/I. Perfect! Choice A incorrectly shows R = VI (multiplying instead of dividing), while choice C has the fraction flipped as R = I/V—remember, voltage divided by current gives resistance, not the other way around. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving V = IR for R is just like solving 12 = 3x for x: divide both sides by I (or 3), giving R = V/I. Common formula rearrangements to practice: d = rt becomes t = d/r (divide by rate) and r = d/t (divide by time); A = lw becomes l = A/w (divide by width); P = 2l + 2w becomes l = (P - 2w)/2 (subtract 2w, divide by 2). The same formulas show up repeatedly in math and science, so learning these rearrangements once helps you many times!
In the rectangle area formula $A = lw$ (where $A$ is area, $l$ is length, and $w$ is width), solve for $w$ . Treat the other variables like numbers as you would in a numeric equation.
Answer: $w = \dfrac{A}{l}$ This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! Starting with A = lw, we want to isolate w, so we divide both sides by l: A/l = lw/l, which simplifies to A/l = w, or w = A/l. Choice A is correct because it properly isolates w using division by l, giving w = A/l. Perfect! Choice B incorrectly multiplies A by l instead of dividing—remember, we need to undo multiplication with division, not more multiplication. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving A = lw for w is just like solving 12 = 3x for x: divide both sides by l (or 3), giving w = A/l.

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