epotli

BODMAS practice

Brackets first, then powers, then divide and multiply, then add and subtract. The ladder starts with one bracket and ends with brackets inside brackets, powers, and negative numbers in the same line.

Which class?

20 questions. No timer, no score, nothing to lose.

What this practice is

Brackets, Orders, Divide, Multiply, Add, Subtract. Orders means powers and roots. The practice starts with a single bracket and climbs to brackets inside brackets, powers, and negative numbers in the same line, and the class you choose decides which of those are allowed to appear at all.

BODMAS is the name most Indian classrooms and parents use, which is why it is the name on this page. It is worth knowing that the current NCERT Ganita Prakash books for classes 6 to 8 do not print the acronym: class 7, Part 1, Chapter 2, Arithmetic Expressions teaches the same order and builds it out of brackets and the idea of terms instead. If your child says their teacher never used the word, both things can be true.

  • A single bracket, where ignoring it changes the answer completely.
  • A bracket plus the rest of the line, which is where most marks are actually lost.
  • Subtracting a bracket, where every sign inside it flips.
  • Two brackets, brackets inside brackets, powers, and negatives in a multi-step line.

Why children find it hard

The acronym is six letters in a row, which suggests six steps in that order. Two of them are not steps at all. Divide and multiply rank together and are settled left to right, and so do add and subtract. A child reading the letters literally will do every multiplication before any division, which changes nothing at all until a division turns up first in the line. Then it gives 24 ÷ 6 × 3 as 24 ÷ 18 instead of 12.

Then there is the bracket that gets subtracted. In 20 − (8 − 3) the minus reaches everything inside, so the 3 is being added back rather than taken away. Children who can resolve the bracket perfectly still write 9 here, because the sign is doing something a step ahead of where they are looking.

The third one to watch for is what a power covers. −2² and (−2)² look almost identical on a page and give −4 and 4. The tell is a child who answers immediately, because reading the two as the same thing feels obvious right up until it is marked.

What each step fixes

  1. Step 1 · Brackets first

    (7 + 3) × 4

    Walking straight past the bracket, so the answer comes out as 19 rather than 40.

  2. Step 2 · Bracket, then the rest

    6 + 3 × (9 − 5)

    Opening the bracket correctly and then combining what is left in the wrong order. This is where the marks usually go.

  3. Step 3 · Minus a bracket

    20 − (8 − 3)

    The sign flip. Reading it as 20 − 8 − 3 and landing on 9 instead of 15.

  4. Step 4 · What is being divided

    24 ÷ (6 × 3) vs 24 ÷ 6 × 3

    What is actually being divided. Same digits either way, and a different answer depending on whether the bracket is there.

  5. Step 5 · Two brackets

    (8 − 3) × (2 + 4)

    Two independent brackets, where one gets resolved and the other quietly gets forgotten.

  6. Step 6 · Powers before multiplying

    3 + 2² × 5

    Reading a power as a multiplication — 2³ taken as 2 × 3 — and reaching the × before the power is settled.

  7. Step 7 · What the power covers

    (3 + 2)² vs 3 + 2²; −2² vs (−2)²

    What the power covers. −2² is −4 and (−2)² is 4, and one pair of brackets is the whole difference.

  8. Step 8 · Bracket inside a bracket

    48 ÷ [2 × (7 − 3)] + 5

    Inner before outer, and the whole bracket being what the 48 is divided by rather than just the 2.

  9. Step 9 · Negatives in the line

    −3 + 5 × (2 − 6)

    A negative number sitting in a line with several operations, where the answer itself finishes below zero.

  10. Step 10 · Everything at once

    full synthesis, per class layer

    Everything at once, drawn only from what the chosen class has actually met.

How to practise it

Do not start by asking for the answer. Ask which part goes first and why, and let them point at it. A child who can name the first step is usually fine from there, and a child who cannot will guess at the whole line no matter how many times the acronym is repeated.

Keep the sessions short and keep the class setting honest. Choosing a higher class to stretch your child mostly produces questions built out of entities they have not been taught yet, which teaches them that maths is a thing that arrives without warning. The steps on a wrong answer are the part that does the work here, so let them read the working before moving on.

Worked examples

  1. (7 + 3) × 4 = 40

    1. Brackets first7 + 3 = 10→ 10 × 4
    2. Multiply last10 × 4 = 40→ 40

    Skip the bracket and you get 19 instead.

  2. 20 − (8 − 3) = 15

    1. Brackets first8 − 3 = 5→ 20 − 5
    2. Subtract last20 − 5 = 15→ 15

    Subtracting a bracket flips the sign inside it.

  3. 12 + 3 × (4 − 1) = 21

    1. Brackets first4 − 1 = 3→ 12 + 3 × 3
    2. Multiply before adding3 × 3 = 9→ 12 + 9
    3. Add last12 + 9 = 21→ 21

    A bracket and a priority step in one line.

  4. 3 + 2² × 5 = 23

    1. Powers before multiplying2² = 4→ 3 + 4 × 5
    2. Multiply before adding4 × 5 = 20→ 3 + 20
    3. Add last3 + 20 = 23→ 23

    The power goes before the multiplication, not after.

Those steps are not written by hand. They come out of the same evaluator the practice screen uses, which is how every generated question can be explained.

By class

Common questions

What does BODMAS stand for?

Brackets, Orders, Divide, Multiply, Add, Subtract. Orders means powers and roots. Divide and multiply rank equally and are worked left to right, and so do add and subtract.

Is BODMAS in the NCERT textbooks?

The acronym is not printed in the current NCERT Ganita Prakash books for classes 6 to 8. Those books teach the same order without naming it — class 7 Part 1, Chapter 2, Arithmetic Expressions builds it from brackets and the idea of terms. BODMAS is what most Indian classrooms and parents call it, which is why we use the word here.

Which class is this for?

Classes 6 to 8, broadly. Order of operations sits in class 7 in the Ganita Prakash books, class 6 brings in negative numbers and simple brackets, and exponents wait until class 8.

Is it free, and does my child need an account?

It is free and there is no account. Nothing is typed in except answers, progress stays on the device you practise on, and no gameplay is recorded.

Is there a timer or a score?

Neither. A countdown is the last thing a child who already dreads maths needs, and a score turns practice into a test. A session is 20 questions, and a wrong answer adds two more of the same kind rather than taking anything away.

What happens when my child gets one wrong?

The ring turns amber, never red. Then the screen asks which part of the sum comes first, and once that is settled it folds the expression down one line at a time until the answer is left standing.

Other topics