Mathematical Mischief (2012)
BODMAS
So, what’s the first thing that comes to mind, when you hear that word?
Crickets chirping? Static? Absolute confusion?
Don’t worry, this tutorial is here to help. Today, we’re going to learn about BODMAS, which
is how we apply the order of operations.
Wait, what’s that?
The order of operations is the way that we operate in maths. It works on a few principles,
and it helps us to get standardized answers across all forms of math.
Let’s see an example.
Example 1: Jack and Jill went up the hill to fetch a pail of water. On the way, they stopped
at a fence, with an equation on it.
5+6×5=?
Jack, thinking for a second, decided that the answer would be 55.
Jill, on the other hand, was determined that the answer was 35.
Who is right?
If we think about it, without the order of operations or BODMAS, can we really say that
there’s only one answer? Both of their logic processes are sound.
Except one thing. The order of operations hasn’t been applied to either format. (yet)
The order of operations is a special thing, that allows us to complete equations in a way
that makes the solution the same for everyone. It means, that when we go around the
world, one question doesn’t have fifty answers, it just has one.
What does BODMAS stand for?
BODMAS stands for this:
Brackets (anything that’s in brackets goes first)
Of (powers and percentages)
Division
Multiplication
Addition
Subtraction
Mathematical Mischief (2012)
When we are following through equations, we must always follow the order of
BODMAS. This is fairly straightforward.
Let’s try Example 1 again.
5+6×5=?
By identifying that the first thing we have to do (in this case) is multiplication, we
multiply 6 by 5. Then, we add 5, yielding us the following answer.
5+6×5=?
5 + 30 = ?
5 + 30 = 35
So, this time, Jill is right.
Let’s try a harder example.
Example 2: Find the values of:
(i) 3 − 4 ÷ 2
(ii) 6 × 4 − 5
(iii) (3 + 7) × 5
(iv) 9 ÷ (6 − 3)
2
(v) (6 − 4) + 4 − 2 × 3 ÷ 2
i) 3 − 4 ÷ 2
3− 4 ÷ 2
3− 2
Step 1: Define the equation.
Step 2: Apply D - Division.
Step 3: Apply S - Subtraction.
1
ii) 6 × 4 − 5
6×4−5
24 − 5
Step 1: Define the equation.
Step 2: Apply M - Multiplication.
Step 3: Apply S - Subtraction.
19
Mathematical Mischief (2012)
iii) (3 + 7) × 5
Step 1: Define the equation.
(3 + 7) × 5
(10) × 5
Step 2: Apply B - Brackets. Repeat all steps of BODMAS inside the brackets.
Step 3: Apply M - Multiplication.
50
iv) 9 ÷ (6 − 3)
Step 1: Define the equation.
9 ÷ (6 − 3)
Step 2: Apply B - Brackets. Repeat all steps of BODMAS inside the brackets.
9 ÷ (3)
Step 3: Apply D - Division.
3
2
v) (6 − 4) + 4 − 2 × 3 ÷ 2
Step 1: Define the equation.
(6 − 4) + 4 − 2 × 3 ÷ 2
2
Step 2: Apply B - Brackets. Repeat all steps of BODMAS inside the brackets.
(2) + 4 − 2 × 3 ÷ 2
2
4 + 4 − 2 × 3÷ 2
Step 3: Apply O - Of (in this case, powers).
Step 4: Apply D - Division.
3
4+4−2×
2
4+4−3
8−3
Step 5: Apply M - Multiplication.
Step 6: Apply A - Addition.
Step 7: Apply S - Subtraction.
5