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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.

Arizona Academic Standards learning standard: A1.A-CED.A.4; A1.A-REI.A.1 · rearranging formulas and equations 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 Arizona

In the Arizona 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: Arizona Department of Education

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

    To solve 7x + 15 = 78, Mia first subtracts 15 from both sides. What equation comes next?

    • 7x = 63
    • x + 15 = 78
    • 7x = 78
    • 7x = 93

  2. Question 2

    Solve F = 1.8C + 32 for C.

    • C = F/1.8 − 32
    • C = (F − 32)/1.8
    • C = 1.8(F − 32)
    • C = (F + 32)/1.8

  3. Question 3

    Use d = rt. A car travels 100 miles at 50 miles per hour. How many hours does it take?

    • 3 h
    • 2 h
    • 48 h
    • 5000 h

  4. Question 4

    Solve V = lwh for h.

    • h = Vlw
    • h = V/(lw)
    • h = lw/V
    • h = V − lw

  5. Question 5

    To solve 3x + 9 = 15, Priya first subtracts 9 from both sides. What equation comes next?

    • 3x = 6
    • 3x = 15
    • x + 9 = 6
    • 3x = 24

  6. Question 6

    Use d = rt. A car travels 80 miles at 40 miles per hour. How many hours does it take?

    • 2 h
    • 3200 h
    • 38 h
    • 3 h

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