The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

To factorise is to express a term as the product of its factors.

Operations with algebraic fractions

Maths

Checking and securing understanding of solving with simple algebraic fractions

Simplifying algebraic fractions

Solving equations with algebraic fractions

Checking and securing understanding of changing the subject with simple algebraic fractions

Changing the subject with multiple algebraic fractions

Changing the subject where the variable appears in multiple terms

Problem solving with advanced algebraic fractions

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

In the prior unit, pupils explored various ways to manipulate and solve various equations and formulae. In this unit, pupils apply these skills to algebraic fractions in order to change the subject and manipulate the algebraic fraction.

In this unit, pupils apply skills in manupulating and solving various equations and formulae to algebraic fractions in order to change the subject and manipulate them.

Algebraic fractions

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

Simplify $${2\over a}\div {3a\over 4}$$. 

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

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

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

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

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

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

Which of these is the fully factorised form of $$24-36x$$?

What is the simplest form of the fraction $$14x^3y^6\over 15x^4y^3$$?

Starter Quiz

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