Rearranging formulae

The Maths Habit

What undoes it?

Switch on the light→Switch off the light
Lock the door→Unlock the door
Put the lid on→Take the lid off

What went in?

  1. ?  →  + 5  →  12

    7 (12 − 5)

  2. ?  →  − 3  →  6

    9 (6 + 3)

  3. ?  →  × 4  →  20

    5 (20 ÷ 4)

  4. ?  →  ÷ 2  →  6

    12 (6 × 2)

y = x + 5
Formula
A rule that links letters with an equals sign.
y = x + 5
Subject
The letter on its own on one side of a formula.
+ 5undoes− 5
× 4undoes÷ 4
Inverse
The step that undoes another step.

Make x the subject of y = x + 3

1Fill in the machine.
x+ 3y
2Undo the step.
x− 3y
3Write the formula.
x =y − 3

Make x the subject of y = x + 8

1Fill in the machine.
x+ 8y
2Undo the step.
x− 8y
3Write the formula.
x =y − 8

Make x the subject of y = x + 3

1Fill in the machine.
x+ 3y
2Undo the step.
x− 3y
3Write the formula.
x =y − 3

Make x the subject of y = x − 5

1Fill in the machine.
x− 5y
2Undo the step.
x+ 5y
3Write the formula.
x =y + 5
Remember1Fill in the machine.2Undo the step.3Write the formula.

Make x the subject of y = x + 3

1Fill in the machine.
x+ 3y
2Undo the step.
x− 3y
3Write the formula.
x =y − 3

Make q the subject of p = q + 2

1Fill in the machine.
q+ 2p
2Undo the step.
q− 2p
3Write the formula.
q =p − 2
Remember1Fill in the machine.2Undo the step.3Write the formula.

Make x the subject of y = x + 3

1Fill in the machine.
x+ 3y
2Undo the step.
x− 3y
3Write the formula.
x =y − 3

Make g the subject of h = g − 3

1Fill in the machine.
g− 3h
2Undo the step.
g+ 3h
3Write the formula.
g =h + 3
Remember1Fill in the machine.2Undo the step.3Write the formula.

  1. Write y ÷ 4 as a fraction.

    y4

  2. Write m ÷ 2 as a fraction.

    m2

  3. Write P ÷ 5 as a fraction.

    P5

Make x the subject of y = 6x

1Fill in the machine.
x× 6y
2Undo the step.
x÷ 6y
3Write the formula.
x =y6

Make x the subject of y = 5x

1Fill in the machine.
x× 5y
2Undo the step.
x÷ 5y
3Write the formula.
x =y5

Make x the subject of y = 6x

1Fill in the machine.
x× 6y
2Undo the step.
x÷ 6y
3Write the formula.
x =y6

Make a the subject of b = 3a

1Fill in the machine.
a× 3b
2Undo the step.
a÷ 3b
3Write the formula.
a =b3
Remember1Fill in the machine.2Undo the step.3Write the formula.

Make x the subject of y = 6x

1Fill in the machine.
x× 6y
2Undo the step.
x÷ 6y
3Write the formula.
x =y6

Make c the subject of d = 2c

1Fill in the machine.
c× 2d
2Undo the step.
c÷ 2d
3Write the formula.
c =d2
Remember1Fill in the machine.2Undo the step.3Write the formula.

Make x the subject of y = 6x

1Fill in the machine.
x× 6y
2Undo the step.
x÷ 6y
3Write the formula.
x =y6

Make x the subject of y = 7x

1Fill in the machine.
x× 7y
2Undo the step.
x÷ 7y
3Write the formula.
x =y7
Remember1Fill in the machine.2Undo the step.3Write the formula.

Rearranging formulae worksheet, page 1

Rearranging formulae worksheet, page 2

Answer sheet

Is it right? Thumbs up: yes. Thumbs down: no.

  1. y = x + 2   so   x = y − 2

    Yes

  2. y = x − 7   so   x = y − 7

    No: x = y + 7

  3. y = 12x   so   x = y12

    Yes

  4. y = 5x   so   x = 5y

    No: x = y5

  5. y = x + 10   so   x = y + 10

    No: x = y − 10

  1. Make x the subject of y = 2x + 1.

    x = y − 12

  2. A taxi costs £3 a mile. C = 3m. A journey costs £24. Make m the subject. How many miles is it?

    m = C3, 8 miles

  3. Make x the subject of y = 3x − 2.

    x = y + 23

  1. Make x the subject of y = x + 7. The machine is + 7.

    x = y − 7

  2. Make x the subject of y = 9x.

    x = y9

  3. Make x the subject of y = x − 2. Show your steps.

    x = y + 2
Exit tickets to print