Simplifying algebraic fractions | Maths | Quizalize & Oak National Academy

Starter quiz

Which fractions simplify to $4\over 5$ ?

$8\over 12$

$24\over 30$ ✓

$36\over 40$

$404\over 515$

$720\over 900$ ✓
Which of these is the highest common factor of $12a^2b$ and $6a^3b^2$ ?

$3a^2b^2$

$6ab$

$6a^2b$ ✓

$12a^2b$

$12a^3b^2$
Which of these is equivalent to $a^6 \div a^3$ ?

$a$

$a^2$

$a^3$ ✓

$a^9$

$a^{18}$
Fully factorise $12x^2 + 18x$ .

$2x(6x+9)$

$6(x^2+3x)$

$6x(2x+3)$ ✓

$12x(x+3)$

$12x(x^2+6)$
Factorise $x^2 + 5x -6$

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

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

$(x+6)(x-1)$ ✓

$(x+1)(x-6)$
Factorise $6x^2-5x -4$

$(2x+1)(3x-4)$ ✓

$(2x-1)(3x+4)$

$(6x+1)(x-4)$

$(6x-4)(x+1)$

Exit quiz

What is the simplest form of the fraction $18x^2y^6\over 12x^5y^2$ ?

$3y^3\over 4x$

${3\over 2}x^3y^4$

${3y^4\over 2x^3}$ ✓

${3xy^5\over 2x^4y}$

${9xy^3\over 6x^3}$
Simplify fully $4a+8\over 6a+2$ .

$1\over 2$

$2$

$a+2\over 3a+1$

$2a+4\over 3a+1$ ✓

$4a+8\over 6a+2$
Write the fraction $8a + 24\over 4a + 12$ in its simplest form.

'2' ✓
Simplify $3x^2 -6x\over x^2 - 7x + 10$ .

$3\over x-5$

$3x\over x-2$

$x+3\over x-2$

$3x\over x-5$ ✓

$3\over x+10$
Simplify $x^2 -16\over x^2 - x - 12$ .

$16\over x+12$

$x\over x-3$

$x-4\over x-3$

$x+4\over x+3$ ✓
Simplify $3x^2 +17x + 10\over 6x^2 + 25x + 14$ .

$x+5\over 2x+7$ ✓

$x+10\over 3x+2$

$3x+2\over 2x+5$

$3x+5\over 6x+7$

Worksheet

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Video

Lesson Details

Key learning points

An algebraic fraction can have more than one term in the denominator.
Your equivalent fraction knowledge can be used to simplify the fraction.

Common misconception

Simplifying $\\frac{(x+4)}{(x+5)}$ by crossing out the $x$ terms and getting $\\frac{4}{5}$

Refrain from crossing out factors. Instead pupils should write the numerator and denominator as products of the hightest common factor and see that HCF/HCF = 1.

Keywords

Simplify - To simplify an expression is to write it in a more efficient form without affecting the value of the original expression. Fully simplifying means the expression cannot be simplified further.
Factorise - To factorise is to express a term as the product of its factors.