What you need to know

Things to remember:

  • We can work through the BIDMAS acronym, starting with brackets and working down to addition and subtraction.

Previously we have heard the term “BIDMAS”, which tells us in what order we do our operations:

Brackets
I
ndices
D
ivision
M
ultiplication
A
ddition
S
ubtraction

This tells us that when we are using mathematical operations, we start with brackets, then indices (powers), then division, then multiplication, and finally addition and subtraction. If we work through BIDMAS, it gives us a five step process for finding the value of our expressions.

What is the value of (5-3)^3+20\div4-2

 

Step 1: Do what’s in the brackets.

(5-3)^3+20\div4-2=2^3+20\div4-2

Step 2: Evaluate the indices (find the value of them)

  2^3+20\div4-2=8+20\div4-2

 

Step 3: Perform the divisions.

  8+20\div4-2=8+5-2

Step 4: Perform the multiplications.

 

There aren’t any multiplications, so we can move on to the next step.

 

Hint: As we have seen with the additions and subtractions, we can do them in any order, so can do them at the same time.

Step 5: Performs the additions and subtractions.

8+5-2=13-2=11

(5-3)^3+20\div4-2=11

What is the value of 4\times(15\div3)^2+20\times5-7

 

Step 1: Do what’s in the brackets.

4\times(15\div3)^2+20\times5 -7=4\times5^2+20\times5-7

Step 2: Evaluate the indices (find the value of them)

 4\times5^2+20\times5-7=4\times25+20\times5-7

 

Step 3: Perform the divisions.

There aren’t any divisions, so we can move on to the next step.

Step 4: Perform the multiplications.

 

4\times25+20\times5-7 =100+100-7

 

Step 5: Performs the additions and subtractions.

100+100-7=200-7=193

 4\times(15\div3)^2+20\times5-7=193

Example Questions

Step 1: Do what’s in the brackets.

 

Hint: Remember, when there is a number in front of a bracket, it means “multiply”.

 

 

6^2(6-4)+(7+2)^2=6^2\times2+9^2

 

Step 2: Evaluate the indices (find the value of them)

 

6^2\times2+9^2=36\times2+81

 

 

Step 3: Perform the divisions.

 

There aren’t any divisions, so we can move on to the next step.

 

Step 4: Perform the multiplications.

 

 

36\times2+81 =72+81

 

 

Step 5: Performs the additions and subtractions.

 

72+81=153

 

 6^2(6-4)+(7+2)^2 =153

Step 1: Do what’s in the brackets.

 

Hint: Remember, when there is a number in front of a bracket, it means “multiply”.

 

 

(5+6)^2-16\div4-7^2+2 =11^2-16\div4-7^2+2

 

Step 2: Evaluate the indices (find the value of them)

 

11^2-16\div4-7^2+2 =121-16\div4-49+2

 

 

Step 3: Perform the divisions.

 

121-16\div4-49+2=121-4-49+2

 

Step 4: Perform the multiplications.

 

 

There aren’t any multiplications, so we can move on to the next step.

 

 

Step 5: Performs the additions and subtractions.

 

121-4-49+2=70

 

 (5+6)^2-16\div4-7^2+2 =70

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