Changing the subject with multiple algebraic fractions | Maths

Starter quiz

What is the solution to the equation ${8\over a}=6$ ?

$a=\frac{3}{4}$

$a=\frac{4}{3}$ ✓

$a=1.5$

$a=2$

$a=48$
Make $x$ the subject of ${2\over 5x} = 3y$ .

$x = {2\over 3}y$

$x = {3y\over 10}$

$x = {6y\over 5}$

$x = {2\over 15y}$ ✓

$x = {6\over 5y}$
Make $a$ the subject of $x=\frac{y+5}{a-b}$ .

$a=\frac{y+5}{x} + b$ ✓

$a=\frac{y+5}{-bx}$

$a=\frac{y+5+b}{x}$

$a=\frac{y+5-bx}{x}$

$a=5x+xy+b$
Factorise $x^2-5x-6$ .

$(x-5)(x-6)$

$(x-5)(x-1)$

$(x-3)(x-2)$

$(x-1)(x+6)$

$(x+1)(x-6)$ ✓
Which of these is equivalent to ${3x^2-12x\over x^2-9x+20}$ ?

$3\over x$

$3x\over x-4$

$3x\over x-5$ ✓

$x^2-2x\over 10$

$x^2 -4x\over x^2-3x+20$
Which of these is the simplest form of ${3\over 2x+4}+{7\over 5x+10}$ ?

$100x+74$

$29\over 10x+20$ ✓

$58\over 5x+10$

$10x+20\over 7x+14$

$29x+58\over (2x+4)(5x+10)$

Exit quiz

In which of these is $a$ the subject?

${1\over a}=bc + 2$

$a = {bc+2 \over 4a}$

$a^2 = bc + 2$

$a={5b-2\over 2c+3b}$ ✓

${1\over 3}a = b^2+c + 2$
Make $a$ the subject of $5=\frac{b+2a}{a+4}$ .

$a=\frac{b-4}{3}$

$a = 4 - \frac{b}{5}$

$a=\frac{b-20}{3}$ ✓

$a=\frac{b+2a}{5}-4$

$a=\frac{5a+4-b}{2}$
Which of these is equivalent to $4+b=\frac{3a-4}{2b+1}$ ?

$a=\frac{10b}{3}+3$

$a=\frac{2b^2+8}{3}$

$a=\frac{b(2b+9)}{3}$

$a=\frac{2b^2+8b + 5}{3}$

$a=\frac{2b^2+9b + 8}{3}$ ✓
Make $a$ the subject of $\frac{a}{4} + \frac{3}{b}= \frac{c+2}{5}$ .

$a=\frac{4bc+8b}{15}$

$a=\frac{4bc-52}{5b}$

$a=\frac{4bc-58}{5b}$

$a=\frac{4bc+8b-60}{5b}$ ✓

$a=\frac{bc+2b+4c}{5}+1$
Make $a$ the subject of $\frac{6b+3}{c}=\frac{4b+2}{a}$ .

$a = {2c\over 3}$ ✓

$a ={3\over 2}c$

$a={c\over 6b+3}$

$a = {4bc-3\over 6}$

$a = {2b+1\over c}$
Make $a$ the subject of $\frac{2}{c} = \frac{2}{b} - \frac{2}{a}$ .

$a = b-c$

$a = c+b$

$a = \frac{bc}{c-b}$ ✓

$a = \frac{b-c}{4}$

$a = \frac{bc+c}{2b}$

Worksheet

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Lesson Details

Key learning points

It is important to identify which variable is to become the subject.
Like terms containing the new subject should be collected.
You should be prepared to utilise any of your algebraic manipulation skills.

Common misconception

Pupils may think that the reciprocal of $\\frac{1}{a} + \\frac{1}{b}$ is $a + b$

$\\frac{1}{2} + \\frac{1}{4} = \\frac{3}{4}$ which is not the reciprocal of 2 + 4 = 6. To find the reciprocal, it helps for the expression to be written as a single fraction.

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