Using and rearranging formulas

A formula is a rule written using variables that connects different quantities — like the formula for the area of a rectangle, A = l × w (length times width). You substitute known values into a formula to find the unknown, or rearrange it to make a different variable the subject, so you can solve for whatever you need. Rearranging works the same way as solving an equation: do the same operation to both sides to isolate the variable you want.

Key terms

Formula:

A rule connecting different quantities, written using variables.

Subject:

The variable that is alone on one side of a formula, e.g. A in "A = l × w".

Rearrange:

To change which variable is the subject of a formula.

Questions

1. 1. A formula connects:

   • Only one quantity
   • Different quantities using variables
   • Only numbers
   • Only colours

2. 2. The formula for the area of a rectangle is:

   • A = l + w
   • A = l × w
   • A = l - w
   • A = l ÷ w

3. 3. In a formula, the "subject" is:

   • Always a number
   • The variable alone on one side
   • The formula's name
   • A random letter

4. 4. To find an unknown in a formula, you:

   • Ignore the formula
   • Substitute known values
   • Guess randomly
   • Multiply everything by zero

5. 5. If A = l × w, and l=5, w=3, what is A?

   • 8
   • 15
   • 2
   • 53

6. 6. The formula for speed is s = d ÷ t. What does d stand for?

   • Speed
   • Distance
   • Time
   • Density

7. 7. Rearranging a formula means:

   • Deleting it
   • Changing which variable is the subject
   • Multiplying by 100
   • Ignoring the variables

8. 8. If A = l × w and A=20, l=4, what is w?

   • 5
   • 16
   • 24
   • 80

9. 9. Using s = d ÷ t, if d=100km and t=2 hours, what is s?

   • 50km/h
   • 200km/h
   • 98km/h
   • 102km/h

10. 10. Rearrange A = l × w to make w the subject:

    • w = A × l
    • w = A ÷ l
    • w = A + l
    • w = A - l

11. 11. Rearrange s = d ÷ t to make d the subject:

    • d = s ÷ t
    • d = s × t
    • d = s + t
    • d = t ÷ s

12. 12. If the perimeter formula is P = 2l + 2w, and l=6, w=4, what is P?

    • 10
    • 20
    • 24
    • 48

13. 13. Using P = 2l + 2w, if P=30 and l=8, what is w?

    • 7
    • 11
    • 14
    • 22

14. 14. The formula for the area of a triangle is A = ½ × b × h. If b=10, h=6, what is A?

    • 16
    • 30
    • 60
    • 120

15. 15. Rearrange A = ½ × b × h to make h the subject:

    • h = 2A ÷ b
    • h = A ÷ 2b
    • h = 2A × b
    • h = A ÷ b

16. 16. Using A = ½ × b × h, if A=24 and b=8, what is h?

    • 3
    • 6
    • 12
    • 48

17. 17. The formula for converting Celsius to Fahrenheit is F = (9/5)C + 32. What is F when C=20?

    • 52
    • 68
    • 72
    • 88

18. 18. Rearrange F = (9/5)C + 32 to make C the subject:

    • C = (F-32) × 5/9
    • C = (F+32) × 5/9
    • C = F × 5/9 - 32
    • C = (F-32) × 9/5

19. 19. A formula for cost is C = 5n + 20, where n is the number of items. If C=70, what is n?

    • 10
    • 14
    • 50
    • 90

20. 20. Why is rearranging a formula useful?

    • It changes the actual quantities
    • It lets you solve for a different variable using the same relationship
    • It removes the need for maths
    • It only works once