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1Long Multiplication at Scale2Long Division with Bigger Numbers3What to Do With the Remainder4Multi-Step Problems with Large Numbers5BODMAS6Brackets7Orders8Operator Families9Word Problems

Concept 8 of 9

Operator Families: D and M Go Together, A and S Go Together

1

Today's big idea

Division and multiplication rank equal, and so do addition and subtraction.

Whichever sign in a family stands further left is the one you do first.

2

How it works

👀 What's going on?

BODMAS looks like six separate steps in a queue. It is really four, because two pairs of letters share a place in that queue.

💡 Here's the trick

Same family? Left to right.÷ M FAMILY24 ÷ 8 × 5 → 3 × 5 = 15+ S FAMILY12 − 4 + 2 → 8 + 2 = 10⚠️ Common trapDon't do all × then all ÷ — read LEFT to RIGHT.

Look at the families above. Division and multiplication sit on one level, and addition and subtraction sit on another. Inside a level you go left to right, so whichever sign you meet first is the one you do first.

🪄 How to do it

  1. 1.Clear brackets and powers, then sort the signs into the families above.
  2. 2.Sweep left to right doing every division and multiplication.
  3. 3.Sweep left to right again doing every addition and subtraction.

✍️ Try it

What is 60 ÷ 6 × 3? Then: what is 18 − 9 + 4?

Left to right gives 60 ÷ 6 = 10, then 10 × 3 = 30. The second gives 18 − 9 = 9, then 9 + 4 = 13.

⚠️ Watch out

You might be thinking the A in BODMAS means every addition happens before any subtraction. It does not. In 100 − 40 + 20 the subtraction comes first, and the answer is 80 rather than 40.

🌟 Why this matters

Doubling a recipe and then taking out a portion gives one answer, and swapping those two jobs gives another. Order changes the result, so the sweep direction matters.
Exam tip: Draw a small arrow left to right above each family before you start.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Solve: 24 ÷ 8 × 5”

  1. 1

    Same family check

    ÷ and × are the same level. 👯

  2. 2

    Read LEFT to RIGHT

    Do whichever comes first. 24 ÷ 8 is on the left.

  3. 3

    Divide first

    24 ÷ 8 = 3

  4. 4

    Then multiply ✓

    3 × 5 = 15

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Same family? Solve LEFT to RIGHT. Tap the leftmost ÷/× first, then the leftmost +/−.

LEFT TO RIGHT · ROUND 1 OF 3

36 ÷ 6 × 2

D = MA = S
5

Quick check

✅ VERIFICATION

What is the value of 72 ÷ 6 ÷ 3?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Word Problems

Read the question. Keep only what it needs.

Concept 9 of 9 →