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# BIDMAS

### BIDMAS

When a calculation involves multiple operations, we must decide which order to perform our operations

The order we carry out calculations like $+$ , $-$ , $\times$ or $\div$ affects the final answer. What is the correct order to carry them out?

BIDMAS tells us the order of operations

Brackets come first, while addition and subtraction come last.

Always follow this order when answering a question

This is true of all calculations.

Would you do multiplication *before* or *after* addition?

Let's try this example together: $6 + 5 \times 3$

We will walk through this step by step

Don't forget that BIDMAS gives us the order of operations

We have two operations here: addition $+$ and multiplication $\times$ Using BIDMAS, which one do we calculate first?

What is $5 \times 3$?

Now we use the value we've just found

The calculation is now $6 + 15$

What is $6 + 15$?

Good work!

The final answer is $21$

Division and Multiplication are equal (as they are opposite operations). If they appear in the same question, go from left to right.

This also applies to **Addition and Subtraction**.

There is one tricky thing about BIDMAS when it comes to addition and subtraction.

When it is just addition and subtraction, we **must** work from left to right.

The correct answer is found by working from left to right. What is $24-10+4$?

But what happens if we do the addition first?

We know that $10+4=14$.

What is the final answer now?

It's not possible for both of these answers to be correct!

Remember when it is just addition and subtraction, work from left to right.

Now let's try working out this one: $7^2 - 3 \times 8 + 2$

This one has a few more operations

And we will walk through it step by step

We have four operations here

Indices $7^2$
subtraction $7^2-3$,
multiplication $3 \times 8$,

addition $8+2$

Which operation do we do first?

So what is $7^2$?

Multiplication is the next step. What is $3\times8$?

Let's put these into our calculation

It now looks like $49-24+2$

What happens next?

Addition and subtraction are equal in order, so we perform from left to right.

What is $49-24+2$?

Nice! 👍

The final answer is $27$

Here is a quick test before we move on.

What is $2 + 3 \times 4$?

And how about $5 \times 3^2$?

This is a slightly harder one!

This exercise will use all of the operations

Let's walk through it step by step....

Tackle the brackets in the numerator first

**B** is the first letter in **BIDMAS**

Which operation do we do first?

What is $8 \times 2$?

Subtract $4$ from $16$

$16-4=12$

Now we can tackle the set of brackets in the denominator. Do the indices first

$1^2=1$

Finish the calculation in the bracket by adding the numbers together

$1+3=4$

Divide the numerator by the denominator

$\dfrac{12}{4}=3$

Nice!

The final answer is $3$

Find $\dfrac{(7-2^2)}{(4^2-15)}$.

Feel free to take your time working this one out. You may need to write your workings down.

Summary! BIDMAS tells us the order of operations

Brackets come first, while addition and subtraction come last.

If we only have addition and subtraction we must work from left to right.

Do the calculation as if you were reading it