Concepts · Mathematical operations

BODMAS

A line of numbers and signs needs an agreed order. This is the order that decides the answer.

Riya meets this in a mock test:

20 + 12 ÷ 4 × 3 − 5 = ?

She does what reading has taught her: left to right. 20 + 12 is 32. Divided by 4 is 8. Times 3 is 24. Minus 5 is 19. The options include 19, so she ticks it, pleased with how fast that was.

The shop counter

After the test she buys a pen for ₹10 and two notebooks at ₹30 each. She hands over ₹70 without a thought.

On the walk home with Kabir, she writes the bill on the back of the receipt the way the mock wrote its line: 10 + 2 × 30. Then she reads it left to right, as she did in the test. 10 + 2 is 12, times 30 is 360.

“Left to right, this bill comes to ₹360,” she says. “For a pen and two notebooks?”
Kabir laughs. “That’s some pen.”

She stops. At the counter she had multiplied first without thinking: two notebooks, ₹60, before the pen joined the bill. So 10 + 2 × 30 is 70, and her mock answer was done in the wrong order.

The rule

Brackets first. Then Order: powers and roots. Then division and multiplication, together, from left to right. Then addition and subtraction, together, from left to right.

The letters: B for Brackets, O for Order, D and M for Division and Multiplication, A and S for Addition and Subtraction. O stands for powers and roots, such as 3² or √16. A power sticks to its own number before anything else touches it, so 2 × 3² is 2 × 9 = 18, not 6² = 36.

Some books read O as “of”. If a question writes “of”, as in 48 ÷ 4 of 3, treat it as × and do it before the other ÷ and ×: 4 of 3 = 12, and 48 ÷ 12 = 4. Read left to right, you would get 36, the wrong answer.

Riya’s question, again

1. No brackets, no powers or roots.
2. ÷ and ×, left to right: 12 ÷ 4 = 3, then 3 × 3 = 9. The line is now 20 + 9 − 5.
3. + and −, left to right: 20 + 9 = 29, then 29 − 5 = 24.

19 is exactly what left to right gives, so it is the option to distrust.

The ladder trap

Then, for a day, Riya takes the letters too literally. A comes before S in BODMAS, so in 20 − 5 + 3 she adds first: 5 + 3 = 8, and 20 − 8 = 12.

Then she tries it on her own purse. She has ₹20, spends ₹5 on a pen, and a friend pays her back ₹3. She has ₹18, not ₹12. The letters are not a ladder of six steps: addition and subtraction share a rung, so you go left to right, 20 − 5 = 15, then 15 + 3 = 18. Division and multiplication share a rung too: 36 ÷ 6 × 2 is 6 × 2 = 12. Multiplying first (36 ÷ 12 = 3) is the mistake there.

Why it helps in the paper

Watch for options that match the two mistakes: left to right all the way, or a shared rung done right to left instead of left to right. Some questions also disguise the signs, as letters or swapped for each other. Write the whole line in true signs first, then apply the order once, starting with the innermost bracket.

Try three

Next mock

A week later: 30 − 18 ÷ 3 × 2 + 1 = ? Riya circles the ÷ and the × together. 18 ÷ 3 is 6, times 2 is 12. Then 30 − 12 + 1. She writes 19, and this time it is right.