How To Rearrange An Equation
Rearranging Equations
Here is everything you lot need to know most rearranging equations for GCSE maths (Edexcel, AQA and OCR). You lot'll learn what rearranging equations ways and how to change the subject area of the formula.
Look out for the rearranging equations worksheets and exam questions at the terminate.
What is rearranging equations?
Rearranging equations changes the form of the equation to brandish it in a different way. This is sometimes called irresolute the subject.
How to rearrange equations step past step:
- Identify the variable yous need to brand the discipline.
- Isolate the variable by: removing any fractions by multiplying by the denominator/s, dividing by the coefficient of the variable, and past square rooting or squaring both sides of the equation
- Perform inverse operations so that each term that needs to exist made the subject is on one side of the equation.
What does rearranging equations mean?
When nosotros rearrange an equation we change the course of the equation to brandish it in a dissimilar style.
For example, the below three equations are rearranged forms of exactly the same equation.
\[\begin{aligned} a-b &=2 \\ a &=b+2 \\ a-2 &=b \stop{aligned}\]
Typically we rearrange equations and formulas past using inverse operations to make 1 variable the subject field of the formula. The subject field of the formula is the unmarried variable that is equal to everything else. i.east. the term by itself on one side of the equal sign.
Hither are some example where
\[south=iv+a \qquad\qquad southward=5 f-vi c+viii \qquad s=\frac{5+t}{y-8}\]
To do this nosotros movement variables and constants (numbers) to the other side of the equation from the variable we are trying to brand the subject field of the formula.
Rearranging Equations worksheets
Go your free rearranging equations worksheet of xx+ questions and answers. Includes reasoning and applied questions.
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Rearranging Equations worksheets
Go your free rearranging equations worksheet of 20+ questions and answers. Includes reasoning and practical questions.
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How to rearrange formula to alter the subject of the formula
In guild to do rearrange formula to alter the subject of the formula, I need to follow the steps:
- Place the variable y'all need to make the field of study of the formula.
- Isolate the variable – this step may look slightly different depending on the format of the question.
– Remove any fractions by multiplying past the denominator/s
– Divide past the coefficient of the variable
– Square root or foursquare both sides of the equation
*not ever required* - Rearrange the equation so each term containing the term you want to be the subject area is on ane side of the equation – normally the left-manus side.
- Factorisation may be needed if you have multiple different terms containing your subject e.g. factorise
2x + 3xy tox(2 + 3y)
*not ever required* - Perform an operation to ensure just the unmarried variable is left as the subject area.
Rearranging equations examples
Instance ane: multiple footstep just with single variable
p = 2(ten − 3)
- Identify the variable to be fabricated the subject area.
\[p = two(10 − 3)\]
In this question it is
ii Divide each side of the equation by 2
3 Add together 3 to each side of the equation
Answer:
\[\frac{p}{2}+3= x\]
Fully worked out respond:
Example ii: questions involving tentwo
\[y=x^{2}-4\]
Place the variable to be made the subject.
\[y=x^{2}-4\]
In this question information technology is
Add 4 to each side of the equation.
Square root each side. Recollect: the square root can be a + or -.
Answer:
\[\pm\sqrt{y+four}=x\]
Fully worked out answer:
Example 3: questions involving √x
\[y=\sqrt{iii x}+n\]
Identify the variable to exist fabricated the subject.
\[y=\sqrt{three ten}+n\]
In this question it is
Subtract 'n' from each side of the equation.
The inverse functioning of 'square root' is to 'square' each side.
Divide each side by the equation by the 'coefficient of ten'. Here the coefficient is 3. Note in this question step 4 was not required.
Reply:
\[\frac{(y-northward)^{2}}{3}=x\]
Fully worked out reply:
Example 4: factorisation of the variable is required
\[y=\frac{2 x z}{10-five}\]
Identify the variable to exist made the subject.
\[y=\frac{2 x z}{10-5}\]
In this question it is
Multiply each side of the equation by the denominator.
Expand the bracket on the left hand side of the equation. This will assistance us become all terms with 10 onto one side of the equation.
If we factorise the left side of the equation we will be left with only one of the variable x.
Divide past (y - 2z). This will leave x as the discipline of the equation.
Reply:
\[x =\frac{five y}{y-two z}\]
Fully worked out answer:
Example five: factorisation of the variable is required
\[\frac{a}{three}=\frac{2-seven x}{10-5}\]
Identify the variable to be made the subject area.
\[\frac{a}{three}=\frac{2-vii x}{x-v}\]
In this question it is
Equally in the previous example, we are multiplying the equation by the denominator. In this example we take denominators on both sides we multiply by both.
Expand the bracket on the LHS and RHS of the equation. This volition help to get all terms with x onto one side of the equation.
If we factorise the left side of the equation we will be left with but one of the variable x.
Now divide by (a+21). This volition go out x as the field of study of the equation.
Reply:
\[x =\frac{six+five a}{a+21}\]
Fully worked out respond:
Common misconceptions
- When nosotros perform an operation to 1 side of the equation nosotros have to practise to the other.
- Incorrect use of the inverse operation.
- Incorrectly following the order of operations.
- All variables of the subject area need to be on i side of the equal sign.
\[E.g. x = 2x+2\]
- When nosotros foursquare root a number/variable the reply tin be positive or negative.
\[East.yard. \sqrt{4}=\pm{2}\]
√x should exist written every bit ± √x
- Not factorising when we take the subject in more than i term.
E.m. Make x the subject
\[\begin{aligned} 2x+3xy&=3y\\ x(two+3y)&=3y\\ x&=\frac{3y}{ii+3y} \end{aligned}\]
Exercise rearranging equations questions
h=three(a+7)
Split both sides by 3
\frac{h}{3}=a+7
Subtract 7 from both sides
\frac{h}{3}-7=a
p=b^{ii}-9k
Add together 9k to both sides
p+9k=b^{two}
Foursquare root both sides
\pm \sqrt{p+9 one thousand}=b
g=\sqrt{5 c-r}
Square both sides
yard^{2}=5c-r
Add together r to both sides
one thousand^{two}+r=5c
Split up both sides by five
\frac{g^{2}+r}{5}=c
y=\frac{3d+1}{4d}
Multiply both sides by 4d
4dy=3d+1
Subtract 3d from both sides
4dy-3d=one
Factorise the left hand side
d(4y-iii)=one
Split both sides by 4y-three
d=\frac{1}{4y-3}
\frac{q}{iii} = \frac{6-2e}{eastward+one}
Multiply both sides past 3(east+one)
qe+q=18-6e
Decrease q , and add 6e to both sides
qe+6e=xviii-q
Factorise the left manus side
due east(q+6)=18-q
Divide both sides by q+half dozen
e=\frac{18-q}{q+6}
f=\frac{20 l+9 l^{3}}{2 l^{3}+15}
f=\frac{20 l-nine l^{3}}{ii l^{3}+xv}
f=\frac{20 fifty-nine fifty^{iii}}{2 l^{3}-fifteen}
f=\frac{20 l+9 50^{3}}{ii l^{3}-xv}
\frac{l^{3}}{5} = \frac{4l-3f}{2f+9}
Multiply both sides by 5(2f+ix)
2fl^{3}+9l^{3}=20l-15f
Add 15f , and subtract 9l^3 , from both sides
2fl^{3}+15f=20l-9l^{3}
Factorise the left hand side
f(2l^{iii}+15)=20l-9l^{three}
Divide both sides past 2l^3+15
f=\frac{20 l-ix l^{3}}{2 fifty^{3}+15}
Rearranging equations GCSE questions
ane. Make x the subject area of the formula
\[y=2x+4\]
Show reply
\[y-4=2x\]
(− 4) to make iix the subject (1)
\[\frac{y-iv}{two}=x\]
(÷ 2) to make ten the subject (1)
(2 marks)
2. Make s the discipline of
\[v^{two}=u^{two}+2as\]
Show answer
\[v^{2}-u^{2}=2as\]
(− u 2) to make iias the subject (1)
\[\frac{five^{2}-u^{2}}{2a}=s\]
(÷ 2a) to brand s the subject field (1)
(two marks)
3. Make g the subject of the formula
\[y=\sqrt{\frac{g+6}{v}}\]
Show answer
\[y^{2}=\frac{1000+six}{5}\]
Square each side or 'y2' seen (one)
\[5y^{two}=g+6\]
Multiply by denominator, 'x5′ (1)
\[5y^{2}-6=g\]
Subtract 6 from both sides (i)
(iii marks)
Learning checklist
- Understand and use standard mathematical formulae
- Rearrange formulae to alter the subject
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How To Rearrange An Equation,
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