Times and divide before plus and minus

Who calculates first when a bracket is missing

Last time you saw that 2 + 3 × 4 gives 14, and I promised you an explanation. Here it is.

When there is no bracket in a question, a worldwide agreement holds: times and divide are worked out before plus and minus.

So 2 + 3 × 4 you read like this: first 3 × 4 = 12, then 2 + 12 = 14. Multiplying took priority, even though it stood after the adding.

Why like that? Remember that multiplying is a shortcut for adding piles. The write-up 2 + 3 × 4 means “two things and on top of that three piles of four”. You have to unpack the piles first (12 things), then add those two. If you added first, you would mix things with piles.

Plus and minus have no priority among themselves — they are just worked out from left to right. Same for times and divide among themselves: from left to right.

Jonáš is doing homework and calls from the table: “Mum, how much is 20 minus 12 divided by 4?” Mum from the cooker answers: “Seventeen.” Jonáš blinks: “I thought two! Twenty minus twelve is eight, divided by four…” Mum shakes her head: “Divided goes first. Twelve divided by four is three, twenty minus three is seventeen.” Jonáš writes it down and underlines the division with a wavy line, so he can see what he worked out first. From then on, in every question he first underlines times and divide — and only then picks up the pencil.

💡

Before you start calculating, underline every times and divide in the question. The underlined bits you work out first, the rest then from left to right.

Order step by step

The full order for this level:

Brackets (last lesson).
Times and divide, from left to right.
Plus and minus, from left to right.

Method for a question with no brackets, say 20 − 12 ÷ 4 + 5:

Step 1: underline times and divide. Here there is only 12 ÷ 4.

Step 2: work out the underlined and rewrite the question.

20 − 12 ÷ 4 + 5

= 20 − 3 + 5

Step 3: the rest from left to right.

20 − 3 = 17, then 17 + 5 = 22.

Watch “from left to right” with minus: 20 − 3 + 5 is not 20 − 8! Minus belongs only to the three, not to everything after it. That is why you go in order: first 20 − 3, then + 5.

And what are brackets for then? For moments when you want to break the order. If you want to add before you multiply, you have to wrap the adding in a bracket: (2 + 3) × 4. A bracket is the only way to beat priority.

Times is worked out first

Example: 2 + 3 × 4.

Step 1: I underline: 3 × 4.

Step 2: I work it out and rewrite:

2 + 3 × 4

= 2 + 12

Step 3: I finish: 14.

As a story: I have 2 stickers in my hand and 3 packs of 4 stickers. First I unpack the packs (12), then I add the ones from my hand: 14. If I “added” the hand with the packs (2 + 3 = 5) and multiplied, I would count as if the hand were a pack too. It is not.

Divide in the middle of a question

Example: 20 − 12 ÷ 4.

Step 1: I underline 12 ÷ 4.

Step 2: I rewrite:

20 − 12 ÷ 4

= 20 − 3

Step 3: I finish: 17.

A common wrong path: from the left 20 − 12 = 8, then 8 ÷ 4 = 2. It looks honest, but it breaks the agreement — divide has priority. Whoever really wants to subtract first must write (20 − 12) ÷ 4.

Two times at once

Example: 5 × 6 − 4 × 5.

Step 1: I underline both times: 5 × 6 and 4 × 5.

Step 2: I work out both and rewrite:

5 × 6 − 4 × 5

= 30 − 20

Step 3: I finish: 10.

As a story: five packs of six cards I have, four packs of five I give to my brother. I am left with 30 − 20 = 10 cards.

⚠️

Do not calculate blindly from left to right across all the signs. 2 + 3 × 4 is not 5 × 4. From left to right you go only inside the same priority — among pluses and minuses, or among times and divide. But first the priority: times and divide first.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Start with ten. When it goes well, add more.

Underline times and divide, work them out first, the rest from left to right.

Practise the questions

On paper

For each question first underline what goes first. Only then calculate.

Work out with underlining and middle steps: 4 + 2 × 7, 30 − 15 ÷ 3, 6 × 3 + 8 ÷ 2.
Decide without calculating what is worked out first, and circle it: 8 + 4 × 5, 40 ÷ 8 − 2, 7 × 2 + 9.
Compare the trio: 12 − 6 ÷ 2, (12 − 6) ÷ 2 and 12 ÷ 6 − 2. Work out all three and write the results next to each other.
Find the mistake: a friend calculated 5 + 5 × 5 = 50. Write where they broke the order, and fix it to the right result.

Now you 💪

You can say the order: brackets, then times and divide, then plus and minus.
You work out 20 − 12 ÷ 4 correctly (17) and you can say why not 2.
You know what brackets are for: they are the only way to beat priority.

✅

Done when: In a question with no brackets you automatically work out times and divide first and you do the rest from left to right.

What to take from this lesson

Order: 1. brackets, 2. times and divide, 3. plus and minus.
Inside the same priority you calculate from left to right.
Before calculating, underline times and divide — first job for the pencil.
Multiplying has priority because piles have to be unpacked before you add them.
Want a different order? Write a bracket. Otherwise the agreement holds.