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9th grade · Math · Unit 15 of 22

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.

New York State Learning Standards learning standard: AI-A.CED.4; AI-A.REI.1 · 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 New York

In the New York State Learning Standards, this is unit 15 of 22 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: New York State Education Department (NYSED)

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 d = rt. A car travels 175 miles at 35 miles per hour. How many hours does it take?

    • 30 h
    • 5 h
    • 6125 h
    • 6 h

  2. Question 2

    To solve 8x + 5 = 77, Lena first subtracts 5 from both sides. What equation comes next?

    • 8x = 82
    • 8x = 72
    • 8x = 77
    • x + 5 = 77

  3. Question 3

    Solve A = ½bh for h.

    • h = A/(2b)
    • h = 2A/b
    • h = A − ½b
    • h = 2b/A

  4. Question 4

    Use P = 2l + 2w. A rectangle has perimeter 32 ft and width 2 ft. What is its length?

    • 14 ft
    • 28 ft
    • 30 ft
    • 16 ft

  5. Question 5

    Solve d = rt for t.

    • t = r/d
    • t = dr
    • t = d − r
    • t = d/r

  6. Question 6

    To solve 8x + 9 = 49, Ana first subtracts 9 from both sides. What equation comes next?

    • x + 9 = 49
    • 8x = 40
    • 8x = 49
    • 8x = 58

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