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Explainer Video

Tutor: Meera

Summary

Rearranging formulae

In a nutshell

Rearranging or changing the subject means moving the terms in an equation around. The aim is usually to get a variable in a formula by itself on one side of the equation, with all other terms and numbers on the other side of the equation. The equation or formula is the same, it is just displayed in a different way. Rearranging for a particular variable makes it easier to calculate its value.

Rearrange a formula

To rearrange an equation for a particular variable, you must take the other variables over to the other side of the equation. This is so that the variable you want to calculate is by itself on one side of the equation, and all other variables or numbers are on the other side. Whatever you do to one side of the equation, do the same to the other. In the formula

$x+y=z$

to rearrange for $x$ , decide which variables to move to the other side, in this case $y$ . Think about what operation $y$ is doing, here it is $+y$ . The formula has $+y$ , so do the inverse operation and $-y$ to both sides of the equation.

$\begin {aligned}\qquad x+y&=z \\-y \qquad & \qquad -y\\\qquad x&=\underline{z-y}\end {aligned}$

Inverse operations

Inverse operations perform the opposite function. For example, addition is opposite to subtraction, or multiplication is opposite to division.

$+$	$-$
$\times$	$\div$
$x^2$	$\sqrt{x}$

Example 1

$F=ma$

Rearrange for $a$ and calculate $a$ if $F=250$ and $m=80$

First rearrange for $a$ . To get $a$ by itself, move $m$ to the other side. As $m$ is multiplying $a$ , perform the inverse operation and divide by $m$ to both sides.

$\begin {aligned}\qquad F&=ma \\\div m \qquad& \qquad \div m \\\qquad \frac F m &=a \\ \end {aligned}\\\quad \underline{a= \frac F m}$

Now substitute numbers

$\qquad a= \frac {250} {80} = \underline{3.125}$

Example 2

Rearrange $v=u+at$ for $t$

To get $t$ by itself, on one side of the equation, you need to move $u$ and $a$ . To work out which variable to move first, think about what order you would perform a calculation, if you were given numbers to substitute in. If you were given a value for $t$ , you would multiply by $a$ first, then add $u$ . So when rearranging, reverse this process and move $u$ first, then $a$ .

$\begin {aligned}v&=u+at \\-u \qquad &\qquad -u \\v-u &= at \\\div a \qquad &\qquad \div a \\\frac {v-u} a &= t \\ \end {aligned}\\\quad \underline { t = \dfrac {v-u} a }$

Example 3

Rearrange $y = \frac {x+1} {x-2}$ for $x$

When there are fractions, it is always best to multiply the formula up by the denoinator, to eliminate fractions first, then multiply out and rearrange.

$\begin {aligned}y &= \frac {x+1} {x-2} \\&& \times (x-2) \\y(x-2) &= x+1 \\xy -2y &= x+1 \\&& -x \\xy-2y-x &= 1 \\&& +2y \\xy-x &=1+2y \\x(y-1) &= 1+2y \\x &= \underline{\frac {1+2y}{y-1}} \\\end {aligned}$

Learn with Basics

Length:

Unit 1

Solving equations

Unit 2

Rearranging formulae

Jump Ahead

Optional

Unit 3

Rearranging formulae

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What does rearrange mean in maths?

Rearranging means we are moving the terms in an equation around to help us find the answer. It is a different way of displaying an equation.

What are inverse operations?

Inverse operations perform the opposite function. For example, addition is opposite to subtraction, or multiplication is opposite to division.

Why do we rearrange in algebra?

We rearrange an equation to display the equation in a different way. We rearrange equations and formulae to make one variable the subject, to make it easier to calculate its value.

Home

Maths

Algebra

Rearranging formulae

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Summary

Exercises

Select Lesson

Exam Board

Select an option

Statistics

Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability

Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry

Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

3D Pythagoras - Higher

3D Trigonometry - Higher

Vectors

Vectors - Higher

Angles and geometry

Angles: types, notation and measuring

Basic angle rules

Angles in parallel lines

Circle theorems - Higher

Constructing triangles: SSS, SAS, ASA

Construction: angle and perpendicular bisectors

Construction: Loci

Bearings

Maps and scale drawings

Shapes and area

Properties of 2D shapes

Congruence: conditions for congruent triangles

Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change

Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

Graphs

Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra

Number

Explainer Video

Tutor: Meera

Summary

Rearranging formulae

In a nutshell

Rearrange a formula

$x+y=z$

$\begin {aligned}\qquad x+y&=z \\-y \qquad & \qquad -y\\\qquad x&=\underline{z-y}\end {aligned}$

Inverse operations

Inverse operations perform the opposite function. For example, addition is opposite to subtraction, or multiplication is opposite to division.

$+$	$-$
$\times$	$\div$
$x^2$	$\sqrt{x}$

Example 1

$F=ma$

Rearrange for $a$ and calculate $a$ if $F=250$ and $m=80$

First rearrange for $a$ . To get $a$ by itself, move $m$ to the other side. As $m$ is multiplying $a$ , perform the inverse operation and divide by $m$ to both sides.

$\begin {aligned}\qquad F&=ma \\\div m \qquad& \qquad \div m \\\qquad \frac F m &=a \\ \end {aligned}\\\quad \underline{a= \frac F m}$

Now substitute numbers

$\qquad a= \frac {250} {80} = \underline{3.125}$

Example 2

Rearrange $v=u+at$ for $t$

$\begin {aligned}v&=u+at \\-u \qquad &\qquad -u \\v-u &= at \\\div a \qquad &\qquad \div a \\\frac {v-u} a &= t \\ \end {aligned}\\\quad \underline { t = \dfrac {v-u} a }$

Example 3

Rearrange $y = \frac {x+1} {x-2}$ for $x$

When there are fractions, it is always best to multiply the formula up by the denoinator, to eliminate fractions first, then multiply out and rearrange.

Learn with Basics

Length:

Unit 1

Solving equations

Unit 2

Rearranging formulae

Jump Ahead

Optional

Unit 3

Rearranging formulae

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What does rearrange mean in maths?

Rearranging means we are moving the terms in an equation around to help us find the answer. It is a different way of displaying an equation.

What are inverse operations?

Inverse operations perform the opposite function. For example, addition is opposite to subtraction, or multiplication is opposite to division.

Why do we rearrange in algebra?

We rearrange an equation to display the equation in a different way. We rearrange equations and formulae to make one variable the subject, to make it easier to calculate its value.