Order of Operations Reinforcement Questions

1.

Calculate the answer to this equation:

begin mathsize 14px style 7 space plus space 7 space divided by space 7 space plus space 7 space cross times space 7 space minus space 7 space equals space ? end style

We have no parenthesis or exponents, so we start with multiplication and division:

begin mathsize 14px style 7 space plus space 7 space divided by space 7 space plus space 7 space cross times space 7 space minus space 7 space equals space ? end style

begin mathsize 14px style 7 space plus space 1 space plus space 49 space minus space 7 space equals space ? end style

We then move to addition and subtraction working from left to right:

begin mathsize 14px style 8 space plus space 49 space minus space 7 space equals space ? end style

begin mathsize 14px style 57 space minus space 7 space equals space 50 end style

2.

What is the answer to the equation below?

begin mathsize 14px style left parenthesis 24 space divided by space 3 space minus space 2 space minus space 4 right parenthesis cubed space plus space left parenthesis 7 space plus space 5 space divided by space 5 right parenthesis squared space equals space ? end style

We begin with the operations in brackets following the order of division, multiplication, addition, and subtraction:

begin mathsize 14px style left parenthesis 24 space divided by space 3 space minus space 2 space minus space 4 right parenthesis cubed space plus space left parenthesis 7 space plus space 5 space divided by space 5 right parenthesis squared space equals space ? end style

begin mathsize 14px style left parenthesis 8 space minus space 2 space minus space 4 right parenthesis cubed space plus space left parenthesis 7 space plus space 1 right parenthesis squared space equals space ? end style

begin mathsize 14px style left parenthesis 2 right parenthesis cubed space plus space left parenthesis 8 right parenthesis squared space equals space ? end style

Now with the brackets sorted, we move to the exponents:

begin mathsize 14px style 8 space plus space 64 space equals space 72 end style

3.

What is the outcome of this equation?

begin mathsize 14px style 15 space minus space 9 space divided by space 3 space plus space left square bracket left parenthesis 5 space plus space 1 right parenthesis space minus space 3 right square bracket squared space cross times space 2 space equals space ? end style

This equation has every element of PEMDAS. Following the correct order, we begin with the bits in the brackets.

begin mathsize 14px style 15 space minus space 9 space divided by space 3 space plus space left square bracket left parenthesis 5 space plus space 1 right parenthesis space minus space 3 right square bracket squared space cross times space 2 space equals space ? end style

begin mathsize 14px style 15 space minus space 9 space divided by space 3 space plus space left square bracket left parenthesis 6 right parenthesis space minus space 3 right square bracket squared space cross times space 2 space equals space ? end style

And then the calculation in the next set of brackets:

begin mathsize 14px style 15 space minus space 9 space divided by space 3 space plus space left square bracket left parenthesis 6 right parenthesis space minus space 3 right square bracket squared space cross times space 2 space equals space ? end style

begin mathsize 14px style 15 space minus space 9 space divided by space 3 space plus space left square bracket 3 right square bracket squared space cross times space 2 space equals space ? end style

With that complete, we then move on to the exponents:

begin mathsize 14px style 15 space minus space 9 space divided by space 3 space plus space left square bracket 3 right square bracket squared space cross times space 2 space equals space ? end style

begin mathsize 14px style 15 space minus space 9 space divided by space 3 space plus space 9 space cross times space 2 space equals space ? end style

Then, we address the division and multiplication:

size 14px 15 size 14px space size 14px minus size 14px space size 14px 9 size 14px space size 14px divided by size 14px space size 14px 3 size 14px space size 14px plus size 14px space size 14px 9 size 14px space size 14px cross times size 14px space size 14px 2 size 14px space size 14px equals size 14px space size 14px ?

begin mathsize 14px style 15 space minus space 3 space plus space 18 space equals space ? end style

Finally, we do the addition and subtraction working from left to right:

size 14px 15 size 14px space size 14px minus size 14px space size 14px 3 size 14px space size 14px plus size 14px space size 14px 18 size 14px space size 14px equals size 14px space size 14px ?

begin mathsize 14px style 12 space plus space 18 space equals space 30 end style

4.

What is the value of x in the equation below?

begin mathsize 14px style 10 space plus space fraction numerator left parenthesis 6 minus 3 right parenthesis over denominator 2 squared end fraction space cross times space 4 space minus space 1 space equals space x end style

As always, we start with the calculations in the brackets:

size 14px 10 size 14px space size 14px plus size 14px space size 14px 3 over 2 squared size 14px space size 14px cross times size 14px space size 14px 4 size 14px space size 14px minus size 14px space size 14px 1 size 14px space size 14px equals size 14px space size 14px x

Then exponents:

size 14px 10 size 14px space size 14px plus size 14px space size 14px 3 over 4 size 14px space size 14px cross times size 14px space size 14px 4 size 14px space size 14px minus size 14px space size 14px 1 size 14px space size 14px equals size 14px space size 14px x

Then multiplication:

size 14px 10 size 14px space size 14px plus size 14px space size 14px 0 size 14px. size 14px 75 size 14px space size 14px cross times size 14px space size 14px 4 size 14px space size 14px minus size 14px space size 14px 1 size 14px space size 14px equals size 14px space size 14px x

Next division:

begin mathsize 14px style 10 space plus space 3 space minus space 1 space equals space x end style

Finally, addition and subtraction:

begin mathsize 14px style x space equals space 12 end style

5.

Complete the calculation below to find the value of a.

begin mathsize 14px style a space equals space 3 space plus space fraction numerator open square brackets 6 space cross times space left parenthesis 11 space plus space 1 space minus space 4 right parenthesis close square brackets over denominator 8 end fraction space cross times space 2 end style

So it's parenthesis first:

size 14px a size 14px space size 14px equals size 14px space size 14px 3 size 14px space size 14px plus size 14px space fraction numerator begin mathsize 14px style left square bracket 6 space cross times space left parenthesis 8 right parenthesis right square bracket end style over denominator size 14px 8 end fraction size 14px space size 14px cross times size 14px space size 14px 2

Then we resolve the next set of parentheses (brackets):

size 14px a size 14px space size 14px equals size 14px space size 14px 3 size 14px space size 14px plus size 14px space fraction numerator begin mathsize 14px style 48 end style over denominator size 14px 8 end fraction size 14px space size 14px cross times size 14px space size 14px 2

Then the division as that’s closest to the left:

size 14px a size 14px space size 14px equals size 14px space size 14px 3 size 14px space size 14px plus size 14px space size 14px 6 size 14px space size 14px cross times size 14px space size 14px 2

Then multiplication:

size 14px a size 14px space size 14px equals size 14px space size 14px 3 size 14px space size 14px plus size 14px space size 14px 12

Finally addition:

size 14px a size 14px space size 14px equals size 14px space size 14px 3 size 14px space size 14px plus size 14px space size 14px 12

size 14px a size 14px space size 14px equals size 14px space size 14px 15

Now it’s time for everyone’s favourite part of maths, equations!

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