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9th grade · Math · Unit 15 of 17

Rearranging Formulas

Solve for any letter

What your child practices

Rearranging a formula to solve for one quantity (d = rt for t, P = 2l + 2w for l) and using it, plus justifying each step in solving an equation.

Minnesota K-12 Academic Standards benchmark: 9.3.5.7 · rearranging formulas to highlight a quantity

How we explain it

Children can open this short lesson before they practice.

  1. Treat the other letters like numbers.
  2. Undo each operation on the letter you want, in reverse order.
  3. Do the same thing to both sides.

Example: Solve d = rt for t. t is multiplied by r. Divide both sides by r. Answer: t = d/r

Rearranging Formulas in Minnesota

In the Minnesota K-12 Academic Standards, this is unit 15 of 17 in 9th grade Math, after Factoring & Quadratics and before Two-Way Tables & Causation.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Minnesota Department of Education (MDE)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Use P = 2l + 2w. A rectangle has perimeter 42 ft and width 9 ft. What is its length?

    • 21 ft
    • 24 ft
    • 12 ft
    • 33 ft

  2. Question 2

    Solve P = 2l + 2w for l.

    • l = (P − 2w)/2
    • l = P − 2w
    • l = P/2 − 2w
    • l = (P + 2w)/2

  3. Question 3

    To solve 2x + 4 = 16, Leo first subtracts 4 from both sides. What equation comes next?

    • 2x = 16
    • 2x = 20
    • x + 4 = 9
    • 2x = 12

  4. Question 4

    Use A = ½bh. A triangle has area 36 cm² and base 8 cm. What is its height?

    • 11 cm
    • 9 cm
    • 72 cm
    • 4.5 cm

  5. Question 5

    Solve 2x + 3y = 12 for y.

    • y = (12 + 2x)/3
    • y = (12 − 2x)/3
    • y = 12 − 2x/3
    • y = 4 − 2x

  6. Question 6

    To solve 2x + 1 = 13, Priya first subtracts 1 from both sides. What equation comes next?

    • 2x = 12
    • 2x = 13
    • 2x = 14
    • x + 1 = 13

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