Mixed operations practice
Several operations in one line, and nothing to tell your child which one goes first. This is the DMAS half of the order of operations — everything except brackets and powers.
Which class?
20 questions. No timer, no score, nothing to lose.
What this practice is
Several operations in one line and no brackets to point at the one that goes first. Divide and multiply are settled before add and subtract, and within each of those pairs the work runs left to right. Indian classrooms call this DMAS, and it is usually taught before brackets arrive, which is why it has a page of its own here rather than being folded into BODMAS.
Splitting the two also makes a hidden problem visible. A bracket tells a child where to start, so a child who is quietly working left to right still lands on the right answer often enough to look fine. Take the brackets away and there is nowhere for that habit to hide.
- Addition and subtraction together, left to right, where a plus does not outrank a minus.
- Multiplication and division together, where a divide does not wait its turn behind a times.
- One multiplication inside a longer sum, then two, then three at once.
- The same shapes with unfamiliar numbers, so the answer has to be worked out rather than remembered.
Why children find it hard
Everything else your child reads runs left to right, and for years every sum they were given ran that way too. A line like 7 + 3 × 4 asks them to read it in one direction and evaluate it in another, and the answer they produce by reading straight through is 40 rather than 19. There is nothing careless about that number. It is what the rule they are actually using produces.
The second difficulty is the minus sign, which does not stay where it is put. In 30 − 4 × 6 + 3 the minus belongs to the product and nothing else, and a child who reads it as belonging to everything that follows gets 3 for an answer instead of 9. The order was followed correctly and the answer is still wrong, which is why it is worth its own rung.
What each step fixes
Step 1 · Minus then plus
18 − 7 + 4
Thinking a plus outranks a minus, and losing the minus sign on the way past it.
Step 2 · Divide then multiply
24 ÷ 6 × 3
Reading the M of DMAS as an instruction to multiply first, whatever the line says.
Step 3 · Multiply before adding
7 + 3 × 4
Working straight along the line, which gives 40 here instead of 19.
Step 4 · Divide before subtracting
20 − 12 ÷ 3
Separating an order mistake from a division mistake, so you can tell which one to sit down and explain.
Step 5 · Two priority chunks
4 × 5 + 18 ÷ 3
Doing one priority step correctly, then sliding back into left to right for the rest of the line.
Step 6 · Keep hold of the minus
30 − 4 × 6 + 3
Sign loss: reading it as 30 − (24 + 3) and taking the 3 away as well.
Step 7 · Traps that change nothing
5 + 7 × 0, 12 ÷ 1 − 3
Traps that change nothing. A × 0 quietly wipes out a whole term, a ÷ 1 leaves everything as it was, and both still get computed.
Step 8 · Three chunks at once
2 × 3 + 4 × 5 − 6 ÷ 2
Holding three priority chunks at once, where the order is understood and the working memory runs out.
Step 9 · Same shapes, bigger numbers
same shapes, larger numbers
Fluency. The shape is already familiar, so what is being tested is whether the arithmetic holds up underneath it.
Step 10 · Shapes you have not seen
mixed shapes, unseen order
Transfer. Doing it without recognising the shape from the previous question.
How to practise it
Before they calculate anything, ask which part of the line is one lump. In 4 × 5 + 18 ÷ 3 there are two lumps and one plus holding them together, and a child who can point at the lumps has already done the hard half. The arithmetic after that is work they can already do.
When an answer comes out wrong, look at the number itself before saying anything. If it is 40 on 7 + 3 × 4 then the method was left to right, and that is a five-minute conversation. If it is 19 with a slip somewhere else, it is a different conversation entirely, and the parent report separates the two for you.
Worked examples
18 − 7 + 4 = 15
- Left to right18 − 7 = 11→ 11 + 4
- Add last11 + 4 = 15→ 15
Same strength, so it really is left to right.
7 + 3 × 4 = 19
- Multiply before adding3 × 4 = 12→ 7 + 12
- Add last7 + 12 = 19→ 19
The classic — 40 is the left-to-right answer.
30 − 4 × 6 + 3 = 9
- Multiply before adding4 × 6 = 24→ 30 − 24 + 3
- Left to right30 − 24 = 6→ 6 + 3
- Add last6 + 3 = 9→ 9
The minus applies to the product only, not to what follows.
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.
Common questions
What is DMAS?
Divide, Multiply, Add, Subtract — the order teachers use once brackets are out of the picture. Divide and multiply are equal in strength and are worked left to right, and so are add and subtract.
Why practise this separately from BODMAS?
Because Indian classrooms teach it in that order, and because a bracket can hide the problem. A child who works left to right will get the right answer often enough on bracketed sums to look fine, and only come apart on a line with no brackets in it.
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.