BODMAS (OCR GCSE Maths): Revision Notes

Example Problem: Question: What is $3+2×4?$

• Step 1: According to BODMAS, multiplication should be done before addition.
• Step 2: First, solve the multiplication part of the expression: $2×4=8.$
• Step 3: Then, add the result to $3$: $3+8=11$ So, the correct answer is 11.

Common Mistake: If you were to add first and then multiply, you might do this:

                                                                  $(3+2)×4=5×4=20$

This gives an incorrect answer of 20.

B: Brackets:

• Solve anything inside brackets first.

O or I: Order or Indices

• Order refers to powers or indices, such as $2³$.
• Always solve powers before moving on to multiplication or division.

D: Division

• Division comes next, and it can appear in different forms:
• $÷$ as in $8÷2$
• Fraction form like $\frac{4}{9}$

M: Multiplication

• Multiplication follows division, and like division, it is performed from left to right.

A: Addition

• After handling any multiplication or division, move on to addition.

S: Subtraction

• Finally, perform subtraction, after all other operations have been completed.

Problem: Solve the following expression using BODMAS:

                                               $20−(3+2)×3$

Solution:

Step 1: Solve Brackets First

• According to BODMAS, we need to handle any brackets first.
• Inside the brackets, we have $3+2$, which equals $5$.
• So, the expression simplifies to: $20−5×3$

Step 2: Multiplication Next

• There are no powers or indices, so we move on to multiplication.
• Multiply $5$ by $3$ to get $15$.
• The expression now becomes: $20−15$

Step 3: Final Operation - Subtraction

• Now, perform the subtraction.
• Subtract $15$ from $20$, which gives us: $5$

Answer:

The final answer is 5.

Problem: Solve the following expression using BODMAS:

                                               $3+(2×3²−3)÷5$

Step 1: Solve Brackets First

• Just like in the previous example, we start by solving everything inside the brackets.
• The expression inside the brackets is $2×3²−3$.

Step 2: Deal with the Power (Order)

• According to BODMAS, within the brackets, powers come before multiplication.
• Calculate $3²=9$.
• Now, the expression inside the brackets is: $2×9−3$

Step 3: Perform Multiplication Next

• Next, multiply $2×9=18$.
• The expression inside the brackets now simplifies to: $18−3$

Step 4: Complete the Subtraction in the Brackets

• Subtract $3$ from $18$: $18−3=15$

Step 5: Return to the Original Expression

• Now that the brackets are simplified, substitute back into the original expression: $3+15÷5$

Step 6: Perform Division Next

• Division is next according to BODMAS: $15÷5=3$

Step 7: Complete the Final Addition

• Now, add the result to $3$: $3+3=6$

Answer:

The final answer is 6.

Problem: Solve the following expression using BODMAS:

Step 1: Recognising Hidden Brackets

• Even though there are no explicit brackets, the division line acts as a bracket. You need to treat the entire top and bottom of the fraction separately, as if they were enclosed in brackets.

Step 2: Simplify the Top of the Fraction

• Start by solving the top part: $10+2×3$.

• According to BODMAS, multiplication comes before addition, so: $2×3=6$

• Now add: $10+6=16$

• The top part simplifies to $16$.

Step 3: Simplify the Bottom of the Fraction

• Now, move to the bottom part of the fraction: $10−2³$.

• According to BODMAS, powers come before subtraction. So, calculate $23$: $2³=8$

• Now subtract: $10−8=2$

• The bottom part simplifies to $2$.

Step 4: Perform the Division

• Now, divide the simplified top by the simplified bottom:

Answer:

The final answer is 8.