Order of operations
Apply the order of operations (BODMAS) to evaluate expressions involving integers.
Worked examples
Two operations, no brackets
Straightforward
Problem
Calculate .
1
Identify the operations present: subtraction and division.
2
Division is performed before subtraction (BODMAS: D before S).
3
Now perform the subtraction.
Answer
Brackets and exponents
Moderate
Problem
Calculate .
1
Identify the operations: exponent, multiplication, subtraction. Apply BODMAS order.
2
Evaluate the exponent first (O in BODMAS).
3
Perform multiplication next (M before S).
4
Finally, perform the subtraction.
Answer
Nested brackets with exponent
Challenging
Problem
Calculate .
1
Work inside the brackets first. Inside, there is an exponent and addition.
2
Inside the brackets, evaluate the exponent before adding.
3
Complete the addition inside the brackets.
4
Multiply by the value outside the brackets.
Answer
Practise
Q1·Straightforward
Calculate .
Explanation
Perform multiplication first, then addition:
Q2·Straightforward
Calculate .
Explanation
Perform division first, then subtraction:
Q3·Straightforward
Calculate .
Explanation
Perform multiplication first, then addition:
Q4·Straightforward
Calculate .
Explanation
Perform division first, then addition:
Q5·Moderate
Calculate .
Explanation
Evaluate brackets first, then multiply:
Q6·Moderate
Calculate .
Explanation
Evaluate the exponent first:
Q7·Moderate
Calculate .
Explanation
Evaluate brackets first, then multiply:
Q8·Moderate
Calculate .
Explanation
Exponents first, then multiplication, then subtraction:
Q9·Challenging
Calculate .
Explanation
Brackets, then exponent, then division:
Q10·Challenging
Calculate .
Explanation
Exponent inside brackets first, then the bracket sum, then multiply:
Q11·Challenging
Calculate .
Explanation
Evaluate both sets of brackets, then divide:
Q12·Challenging
Calculate .
Explanation
Brackets, then exponent, then multiplication, then subtraction: