GCSE Priority of operations Practice Questions

Multiply before adding

BIDMAS says multiplication comes before addition, so do the $4\times 2$ first.

Do the multiplication

$4 \times 2 = 8$.

Now add

Add the $3$ to get $11$.

Power before multiplying

Indices come before multiplication, so square the $2$ first.

Work out the power

$2^{2} = 4$.

Multiply

$3 \times 4 = 12$.

Read the equation

3x means $3$ times $x$.

The inverse of times $3$

To undo '$\times 3$' we divide by $3$.

Do the same to both sides

Divide both sides by $3$.

Work it out

$21 \div 3 = 7$.

So

The value of $x$ is $7$.

Check

Putting $x=7$ back in gives $21$, which matches.

See what is done to $x$

First $5$ is added to $x$, then the bracket is multiplied by $2$.

Undo in reverse order

Reverse the last operation first: undo the $\times 2$.

Divide both sides by $2$

The inverse of $\times 2$ is $\div 2$.

Work it out

$26 \div 2 = 13$.

Now undo the $+5$

The inverse of $+5$ is $-5$.

Subtract $5$

Subtract $5$ from both sides.

So

$13 - 5 = 8$.

Check: add $5$

Put $x=8$ back: $8+5 = 13$.

Check: times $2$

$2 \times 13 = 26$, which matches.

State the answer

So $x = 8$.

Look at the answer given

The student claims the answer is $5$. Let us see where $5$ could come from.

Where $5$ comes from

$5$ is what you get if you add first: $(4+6)\div 2$.

Check that

$10 \div 2 = 5$, so the student added before dividing.

But there are no brackets

The original has no brackets, so we cannot add first.

Recall the rule

BIDMAS says division comes before addition.

Do the division first

So work out $6\div 2$ first.

Evaluate it

$6 \div 2 = 3$.

Now add

Add the $4$ to the result.

Evaluate

$4+3 = 7$.

So the correct answer is

The right answer is $7$, not $5$.

State the mistake

The student's error was doing the addition before the division.

What would justify their working

Only brackets around $4+6$ would make adding first correct.

But those brackets are not there

Without brackets, division must come first.

Confirm the correct value

Dividing first then adding gives $7$.

State the answer

So the mistake was adding before dividing, and the correct answer is $7$.