Operations with algebraic fractions | Maths | Quizalize & Oak National Academy

Starter quiz

Calculate ${3\over 5} \times {2\over 3}$ .

$2\over 5$ ✓

$3\over 4$

$5\over 8$

$7\over 15$

$6$
Calculate ${9\over 10} \div {12\over 5}$ .

$1\over 2$

$1\over 3$

$3\over 2$

$3\over 8$ ✓

$54\over 25$
Calculate ${3\over 8}-{1\over 6}$ .

$5\over 24$ ✓

$13\over 24$

$2\over 48$

$11\over 48$
Which of these is the fully factorised form of $24-36x$ ?

$2(-18x+12)$

$4(-9x+6)$

$6(-6x+4)$

$12(-3x+2)$ ✓

$24(1-3x)$
Factorise $x^2 - 2x -24$ .

$(x-3)(x+8)$

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

$(x-6)(x+4)$ ✓

$(x-8)(x+3)$

$(x-12)(x+2)$
What is the simplest form of the fraction $14x^3y^6\over 15x^4y^3$ ?

$14y^2\over 15x$

$14y^2\over 15x^3$

$14xy^3\over 15$

$14x^3\over 15y^3$

$14y^3\over 15x$ ✓

Exit quiz

Simplify ${5x\over 6x}\times {4x\over 3x}$ .

$5\over 2$

$10\over 9$ ✓

$9x\over 10$

$20x^2\over 18x$

$20x^2\over 21x^2$
Simplify ${2\over a}\div {3a\over 4}$ .

$2\over 3$

$3\over 2$

$8\over 3a$

$2\over 3a^2$

$8\over 3a^2$ ✓
Write ${3\over a}+{2a\over 5}$ in its simplest form.

$6\over 5$

$15\over2a^2$

$3 + 2a\over 5a$

$2a + 15\over 10a$

$2a^2 + 15\over 5a$ ✓
Which of these are equivalent to ${2x+10\over 5}\times {x\over x^2 +8x + 15}$ ?

$2\over x+3$

$x\over 5x+10$

$2x\over 5x+15$ ✓

$2x\over 5x+50$

$4x+2\over 8x+15$
Which of these are equivalent to ${x^2-x -6\over 2x}\div {x^2+x-12\over x}$ ?

$x+2\over x+4$

$x-3\over x-4$

$x+2\over 2x+8$ ✓

$x^2+6x+8\over 2x^2$
Write ${5\over 3x+12}+{x\over 5x+20}$ in its simplest form.

$x+5\over 8x+32$

$28x\over 5x+20$

$13x+40\over 5x+20$

$3x+25\over 15x+60$ ✓

$5x+15\over 15x+60$

Worksheet

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Lesson Details

Key learning points

When multiplying/dividing, it can be easier to fully factorise every expression first.
When dividing by an expression, it is equivalent to multiplying by the reciprocal of that expression.
When adding/subtracting with algebraic fractions, a common denominator is required.

Common misconception

Trying to simplify a division calculation by identifying common factors before calculating.

Pupils need to understand why this works with multiplication questions to understand why this does not work with division. Encourage pupils to write their division as a multiplication of the reciprocal before identifying common factors.

Keywords

Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1
Factorise - To factorise is to express a term as the product of its factors.