Checking and securing understanding of solving with simple algebraic fractions | Maths

Starter quiz

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

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

$7x \times 7 = 8\times 7$

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

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

$7x \times 8 = 8\times 8$

$7x \times {1\over 8} = 8\times {1\over 8}$
Match each number to its reciprocal.

$2$

⇔

$1\over 2$ ✓

$1\over 2$

⇔

$2$ ✓

$3\over 2$

⇔

$2\over 3$ ✓

$-{1\over 2}$

⇔

$-2$ ✓

$-{2\over 3}$

⇔

$-{3\over 2}$ ✓

$1\over 6$

⇔

$6$ ✓
The solution to the equation $4x + 8 = 12$ is when $x =$ ______.

'1' ✓
What is the value of $\frac{x-10}{5}$ when $x = 20$ ?

'2' ✓
Match each expression containing brackets to its expanded form.

$2(3x-6)$

⇔

$6x-12$ ✓

$6(x-1)$

⇔

$6x-6$ ✓

$2(x-6)$

⇔

$2x-12$ ✓

$-6(-2-x)$

⇔

$6x+12$ ✓

$3(2x-6)$

⇔

$6x-18$ ✓

$6(3-x)$

⇔

$-6x+18$ ✓

Exit quiz

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

'18' ✓
Match each equation to its solution.

${1\over 4}a + 3 = 10$

⇔

$a = 28$ ✓

${1\over 4}(a + 3)=10$

⇔

$a = 37$ ✓

${4\over 7} a = 1$

⇔

$a = {7\over 4}$ ✓

${7\over 4}a=14$

⇔

$a = 8$ ✓

$\frac{a+3}{7} = 2$

⇔

$a = 11$ ✓
Match each expression to an equivalent expression.

${2\over 3}x$

⇔

$2x\over 3$ ✓

$2\over 3x$

⇔

$2({1\over 3x})$ ✓

${2\over 3}\times {1\over 3x}$

⇔

$2\over 9x$ ✓

$2x \times {1\over 9}$

⇔

$2x\over 9$ ✓

${3\over 2}\times {1\over x}$

⇔

$3\over 2x$ ✓
The solution to the equation ${6\over a}=2$ is when $a =$ ______.

'3' ✓
Which of these is the solution to the equation ${4\over 5a}+2 = 8$ ?

$3\over 10$

$2\over 15$ ✓

$2\over 25$

$15\over 2$

$25\over 2$
Which of these is the solution to the equation $\frac{20}{a+3}=6$ ?

$-{27\over 10}$

$-{3\over 10}$

$1\over 3$ ✓

$17\over 6$

$20\over 3$

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Lesson Details

Key learning points

The product of a number and its reciprocal is 1
The product of a term and its reciprocal is 1
Equivalence can be maintained by multiplying the connected statements by the same reciprocal.
This step can help you simplify an equation so you can solve it.

Common misconception

When solving equations with fractional coefficients, pupils may divide by the reciprocal rather than multiply. E.g. $\\frac{1}{2}x = 8$ pupils may just halve $8$

Start with integer coefficients, and get pupils used to the idea of multiplying by the reciprocal (not just dividing by the coefficient). This step should be written as part of the working. Answers can be checked by substitution.

Keywords

Solution - A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.
Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1