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Rearranging formulae

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Rearranging formulae

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Writing indices and index laws

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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.

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

Inverse operations

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

Example 1

$F=ma$

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

Answer

First rearrange for $a$

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

Now substitute numbers

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

Example 2

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

Answer

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

Learn with Basics

Length:

Unit 1

Inverse operations to check calculations

Unit 2

Solving equations

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

Formulae and equations

Rearranging formulae

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Summary

Exercises

Select Lesson

Statistics

Qualitative and quantitative data

Representing data: Graphs and charts

Mean, median, mode and range

Frequency tables

Averages from frequency tables

Averages from grouped frequency tables

Scatter graphs

Probability

Calculating probability

Equal and unequal probabilities

Relative frequency

Listing outcomes

Venn diagrams

Trigonometry

Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

Lines and angles

Types of angles

Angle rules

Interior and exterior angles

Parallel lines

Measures

Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

Volume of prisms

Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

Similar shapes

Nets and surface area

Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

Circles: Area and circumference

3D shapes: Identification and properties

Rates of change

Percentage change

Conversion factors

Imperial units

Solving best buy problems

Reading timetables

Maps and scale drawings

Speed: Formula and units

Density: Formula and units

Proportion

Ratio

Other graphs

Interpreting graphs

Solving simultaneous equations using graphs

Quadratic graphs

Travel graphs: Distance-time graphs

Conversion graphs

Straight line graphs

X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Meera

Summary

Rearranging formulae

In a nutshell

Rearrange a formula

$x+y=z$

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

Inverse operations

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

Example 1

$F=ma$

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

Answer

First rearrange for $a$

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

Now substitute numbers

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

Example 2

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

Answer

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

Learn with Basics

Length:

Unit 1

Inverse operations to check calculations

Unit 2

Solving equations

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.