A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.

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

Checking and securing understanding of solving with simple algebraic fractions

Maths

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.

Algebraic fractions

The solution to the equation $${1\over 3}a = 6$$ is when $$a =$${{}}.

Match each expression to an equivalent expression.

The solution to the equation $${6\over a}=2$$ is when $$a = $${{}}.

Which of these is the solution to the equation $${4\over 5a}+2 = 8$$?

Which of these is the solution to the equation $$\frac{20}{a+3}=6$$?

Any non-zero number multiplied by its {{}} is equal to 1

$$7x \times {1\over 7} = 8\times {1\over 7}$$

$$7x \times {1\over 8} = 8\times {1\over 8}$$

What is the correct calculation to solve $$7x=8$$ in one step?

The solution to the equation $$4x + 8 = 12$$ is when $$x = $${{}}.

What is the value of $$\frac{x-10}{5}$$ when $$x = 20$$?

Match each expression containing brackets to its expanded form.

Starter Quiz