Define the term subject in the context of formulas.

The subject is the variable that is by itself on one side of the formula. You can find its value if you substitute in the values for all the variables on the other side of the formula. Rearranging a formula to get a different variable by itself on one side is known as ' changing the subject '.

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Rearranging Formulas (Cambridge (CIE) IGCSE Maths)

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Define the term subject in the context of formulas.

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Define the term subject in the context of formulas.
The subject is the variable that is by itself on one side of the formula.
You can find its value if you substitute in the values for all the variables on the other side of the formula.
Rearranging a formula to get a different variable by itself on one side is known as 'changing the subject'.
True or false?
The methods for changing the subject of a formula are the same as the methods for solving an equation.
True.
The methods for changing the subject of a formula are the same as the methods for solving an equation.
For example, if you want to make $a$ the subject of a formula, 'solve' the formula for $a .$
The only difference is that the 'answer' will be another formula, not a number.
True or False?
If a formula contains the power n, e.g. $x^{5} = y + 3$ ,you can use the nth root to reverse this operation.
True.
If a formula contains the power n, you can use the nth root to reverse this operation.
E.g.
$x^{5} = y + 3 x = \sqrt[5]{y + 3}$
Just be careful if n is an even number as you need a $\pm$ sign, for example if $x^{2} = . . .$ then $x = \pm \sqrt{. . .}$
True or False?
To rearrange a formula with fractions, e.g. $\frac{2 a}{7} + b = c$ , you should first multiply both sides of the equation by the denominator(s).
True.
To rearrange a formula with fractions, you should first multiply both sides of the equation by the denominator(s).
This gets rid of the fractions and makes the formula easier to rearrange.
E.g.
$\begin{array}{rcl} \frac{2 a}{7} + b & = & c \\ 2 a + 7 b & = & 7 c \end{array}$
True or False?
If the letter you want to make the subject appears twice in a formula,
e.g. $b = \frac{2 a}{c - a}$ , you will not need to factorise to change the subject.
False.
If the letter you want to make the subject appears twice in a formula, you will often need to factorise to change the subject.
For example, to make $a$ the subject of $b = \frac{2 a}{c - a}$ :
- Multiply both sides by $c - a$ : $b (c - a) = 2 a$
- Expand the brackets: $b c - a b = 2 a$
- Get the terms with $a$ onto one side: $b c = 2 a + a b$
- Factorise the right-hand side: $b c = a (2 + b)$
- Divide both sides by $2 + b$ : $\frac{b c}{2 + b} = a$

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