Rearranging formulas

Solving a formula for the letter you want — one operation to undo, then two, then mixed, then the abstract ax + by = c.

4 sheets · 32 questions · one answer key · 6 pages

Recommended for grades 8–9

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One step Sheet 1 of 4

Rearranging formulasOne step

Name: Date:

Rearrange each formula to make the named letter the subject.

1W = Fdfor F

2F = mafor m

3n = 360efor e

4C = πdfor d

5E = mc²for m

6P = a + b + cfor a

7V = IRfor I

8D = mVfor V

Rearranging formulasTwo steps

Name: Date:

Rearrange each formula to make the named letter the subject.

1y − k = m(x − h)for m

2P = 2(l + w)for l

3A = 12(a + b)hfor h

4V = 13Bhfor h

5v = u + atfor t

6F = 95C + 32for C

7K = 12mv²for m

8P = 2l + 2wfor l

Rearranging formulasOne and two steps

Name: Date:

Rearrange each formula to make the named letter the subject.

1P = 2(l + w)for l

2V = lwhfor l

3d = rtfor t

4A = P + Prtfor r

5V = πr²hfor h

6K = 12mv²for m

7y − k = m(x − h)for m

8y = mx + bfor b

Rearranging formulasTwo variables

Name: Date:

Rearrange each equation to make the named letter the subject.

13x + 7y = 12for x

25x + 4y = 10for y

39x + 5y = 12for y

48x + 6y = 10for y

53x + 2y = 24for y

63x + 9y = 6for x

74x + 7y = 10for y

89x + 7y = 24for y

Power Pack · Rearranging formulasAnswer key

One step

1. W = Fd (work done), for F → F = Wd2. F = ma (force), for m → m = Fa3. n = 360e (sides from an exterior angle), for e → e = 360n4. C = πd (circumference from the diameter), for d → d = Cπ5. E = mc² (mass and energy), for m → m = Ec²6. P = a + b + c (perimeter of a triangle), for a → a = P − b − c7. V = IR (Ohm's law), for I → I = VR8. D = mV (density), for V → V = mD

Two steps

1. y − k = m(x − h) (point-slope form), for m → m = y − kx − h2. P = 2(l + w) (perimeter, factored), for l → l = P2 − w3. A = 12(a + b)h (area of a trapezoid), for h → h = 2Aa + b4. V = 13Bh (volume of a cone or pyramid), for h → h = 3VB5. v = u + at (velocity after accelerating), for t → t = v − ua6. F = 95C + 32 (Fahrenheit from Celsius), for C → C = 5(F − 32)97. K = 12mv² (kinetic energy), for m → m = 2Kv²8. P = 2l + 2w (perimeter of a rectangle), for l → l = P − 2w2

Mixed

1. P = 2(l + w) (perimeter, factored), for l → l = P2 − w2. V = lwh (volume of a box), for l → l = Vwh3. d = rt (distance traveled), for t → t = dr4. A = P + Prt (amount with simple interest), for r → r = A − PPt5. V = πr²h (volume of a cylinder), for h → h = Vπr²6. K = 12mv² (kinetic energy), for m → m = 2Kv²7. y − k = m(x − h) (point-slope form), for m → m = y − kx − h8. y = mx + b (equation of a line), for b → b = y − mx

ax + by = c

1. 3x + 7y = 12 (a linear equation in two variables), for x → x = 12 − 7y32. 5x + 4y = 10 (a linear equation in two variables), for y → y = 10 − 5x43. 9x + 5y = 12 (a linear equation in two variables), for y → y = 12 − 9x54. 8x + 6y = 10 (a linear equation in two variables), for y → y = 5 − 4x3

Power Pack · Rearranging formulasAnswer key

ax + by = c

5. 3x + 2y = 24 (a linear equation in two variables), for y → y = 24 − 3x26. 3x + 9y = 6 (a linear equation in two variables), for x → x = 2 − 3y7. 4x + 7y = 10 (a linear equation in two variables), for y → y = 10 − 4x78. 9x + 7y = 24 (a linear equation in two variables), for y → y = 24 − 9x7

Rearranging formulas

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