New
New
Year 9

# Changing the subject with more complex formula

I can apply an understanding of inverse operations to a complex formula in order to make a specific variable the subject.

New
New
Year 9

# Changing the subject with more complex formula

I can apply an understanding of inverse operations to a complex formula in order to make a specific variable the subject.

## Slide deck

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## Lesson details

### Key learning points

1. With more complex formula, it is important to apply the inverse operations in the right order.
2. The subject can be thought of as the unknown you are trying to find the value of.
3. Instead of finding a value though, you will find an expression that the unknown is equal to.

### Common misconception

The subject of a formula is just the first term in the formula.

Draw attention to the variety of equations and formulae used in the lesson.

### Keywords

• Subject of an equation/formula - The subject of an equation/a formula is a variable that is expressed in terms of other variables. It should have an exponent of 1 and a coefficient of 1.

It will help pupils if they can link this skill back to solving equations. Pupils will need to be confident in forming expressions correctly so this can be an important skill to practise before this lesson.
Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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## Worksheet

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## Starter quiz

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### 6 Questions

Q1.
The subject of a formula is a variable expressed in terms of the other __________.
equations
values
Correct answer: variables
variants
Q2.
$$x^2$$ is not the subject of the equation $$x^2=9-y^2$$. Why not?
Because the coefficient is not $$1$$.
Correct answer: Because the exponent of $$x$$ is not $$1$$.
Because $$y^2$$ is the subject.
That's incorrect. $$x^2$$ is the subject of the equation.
Q3.
Which of these are rearrangements of the equation $$5e-7=2d$$ ?
$$7-5e=2d$$
Correct answer: $$5e-2d=7$$
Correct answer: $$5e=7+2d$$
Correct answer: $$2d+7=5e$$
$$2d+5e=7$$
Q4.
Which two inverse operations should you perform to both sides to solve the equation $$6x+7=49$$?
$$-49$$
$$+7$$
Correct answer: $$-7$$
$$\times 6$$
Correct answer: $$\div 6$$
Q5.
Select the expressions that are equivalent to $${1\over3}(y-5)$$.
$${1\over3}y-5$$
$${y\over3}-5$$
Correct answer: $${y\over3}-{5\over3}$$
Correct answer: $${{y-5}\over3}$$
$$y-{5\over3}$$
Q6.
Match each expression to its description.
Correct Answer:$$5d+2$$,$$d \text{ }$$ multiplied by $$5$$ then add $$2$$

$$d \text{ }$$ multiplied by $$5$$ then add $$2$$

Correct Answer:$${d\over5}+2$$,$$d\text{ }$$ divided by $$5$$ then add $$2$$

$$d\text{ }$$ divided by $$5$$ then add $$2$$

Correct Answer:$${{d+5}\over2}$$,$$d\text{ }$$ add $$5$$ then divided by $$2$$

$$d\text{ }$$ add $$5$$ then divided by $$2$$

Correct Answer:$$2d+5$$,$$d\text{ }$$ multiplied by $$2$$ then add $$5$$

$$d\text{ }$$ multiplied by $$2$$ then add $$5$$

Correct Answer:$$5(d+2)$$,$$d\text{ }$$ add $$2$$ then multiplied by $$5$$

$$d\text{ }$$ add $$2$$ then multiplied by $$5$$

Correct Answer:$${1\over5}(d+2)$$,$$d\text{ }$$ add $$2$$ then divided by $$5$$

$$d\text{ }$$ add $$2$$ then divided by $$5$$

## Exit quiz

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### 6 Questions

Q1.
Performing the inverse operation $$\div7$$ would make $$x$$ the __________ of the equation $$7x=y.$$
expression
solution
Correct answer: subject
value
Q2.
Some Oak pupils are rearranging the equation $$5e-f=14$$ to make $$e$$ the subject. Who has a correct rearrangement?
Laura: $$5e=14+f$$
Correct answer: Andeep: $$e={{1\over5}(14+f)}$$
Jun: $$e=14-{f\over5}$$
Correct answer: Aisha: $$e={14\over5}-{f\over5}$$
Alex: $$e=5(14+f)$$
Q3.
Match each formula to the correct rearrangement with $$d$$ the subject.
Correct Answer:$${{d+6}\over8}=e$$,$$d=8e-6$$

$$d=8e-6$$

Correct Answer:$$8d+6=e$$,$${{e-6}\over8}=d$$

$${{e-6}\over8}=d$$

Correct Answer:$${{d-6}\over8}=e$$,$$d=8e+6$$

$$d=8e+6$$

Correct Answer:$$8(d+6)=e$$,$${e\over8}-6=d$$

$${e\over8}-6=d$$

Correct Answer:$${d\over8}-6=e$$,$$d=8(e+6)$$

$$d=8(e+6)$$

Q4.
Make $$x$$ the subject of the equation $$y=7x^2$$.
$${y\over7}=x^2$$
$$({y\over7})^2=x$$
Correct answer: $$\sqrt{{y\over7}}=x$$
$${\sqrt{y}\over7}=x$$
Q5.
Make $$x$$ the subject of the equation $$y={7\over{x^2}}$$.
$$x^2={7\over{y}}$$
Correct answer: $$x=\sqrt{7\over{y}}$$
$$x={7\over\sqrt{y}}$$
$$x={7\over{y^2}}$$
$$x={7\times{y^2}}$$
Q6.
Match each formula to the correct rearrangement with $$x$$ the subject.
Correct Answer:$$2x=\sqrt{y}$$,$$x={\sqrt{y}\over2}$$

$$x={\sqrt{y}\over2}$$

Correct Answer:$$2\sqrt{x}=y$$,$$x=({y\over2})^2$$

$$x=({y\over2})^2$$

Correct Answer:$$\sqrt{2x}=y$$,$$x={y^2\over2}$$

$$x={y^2\over2}$$

Correct Answer:$$2x^2=y$$,$$x=\sqrt{y\over2}$$

$$x=\sqrt{y\over2}$$

Correct Answer:$$(2x)^2=y$$,$$x={{\sqrt{y}}\over2}$$

$$x={{\sqrt{y}}\over2}$$