What does mod mean in math?

Mod is short for modulo, and a mod b means the remainder when a is divided by b. You read 23 mod 4 as “23 modulo 4”, and it equals 3, because 4 × 5 = 20. Many programming languages write the same operation with %, so 23 % 4 also gives 3. Clocks use it too: 15 o’clock shows as 3, since 15 mod 12 = 3.

How do you find a remainder with a calculator?

A calculator shows a decimal instead of a remainder, so it takes three steps. For 250 mod 12, divide first: 250 ÷ 12 = 20.83… Keep only the whole part, 20, and multiply it back: 20 × 12 = 240. Then subtract, and 250 − 240 = 10 is the remainder. Without a calculator, the same three steps work in your head.

At what age do children learn division with remainders?

In many school systems, children first divide with remainders at about age 8 or 9, once they know their times tables. Dividing by two-digit numbers usually follows a year or two later. The levels here are aimed at ages 9 to 11. The word modulo and its short form, mod, often come later, in secondary school or a first coding class.

Why does my child get remainders wrong?

Most wrong remainders come from typing the other part of the division. In 29 ÷ 4, seven 4s fit and 1 is left over, so a child who answers 7 has given the number of groups, not the remainder. Saying the whole result aloud helps: “29 is seven 4s and 1 more.” Multiplying back checks it, since 7 × 4 + 1 = 29.

Is the remainder game free for schools, and how would a teacher use it?

Both levels are free for any class and run in a browser tab, with no install or logins. For modular arithmetic practice, write 1 to 24 on the board in rows of six. Pupils notice that each column shares one remainder after dividing by 6, then predict where 50 would land: under the 2, since 50 mod 6 = 2. Then everyone fights on tablets. The schools plan, billed per student, adds a teacher dashboard of who is improving.

Math practice · reimagined

Modulo Game

This modulo fighting game asks for remainders only: first of numbers up to 100 divided by 2 to 9, then of three-digit numbers divided by 10 to 19. Spot the leftover before your rival does, and your fighter turns that head start into a hit.

Ages 4–99+ · no download · plays in your browser · 23 languages

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What does modulo mean?

Modulo is the operation that gives the remainder of a division: what is left when no more equal groups fit. It is written mod, so 26 mod 4 = 2. Picture 26 apples packed into bags of 4. Six bags fill up with 24 apples, and 2 apples stay out.

Every level of Modulo

Example: what is 54 mod 8?

Read 54 mod 8 as a question: what is left of 54 once every possible 8 is taken out?
Climb the 8 times table: 8 × 6 = 48 still fits, but 8 × 7 = 56 is more than 54.
Take the 48 away: 54 − 48 = 6, and 6 is less than 8, so no other 8 fits.
The remainder is 6, so you type 6 on the keypad.

Learn it step by step

Modulo is just the leftover after dividing — the part that won't split evenly.

17 mod 5 asks: share 17 into groups of 5 — you get 3 groups (15) with 2 left over. So 17 mod 5 = 2. It's the remainder you'd write at the end of a division.

Divide as far as whole groups go, and type what's left.

Tips and common mistakes

Dividing by 10 always leaves the last digit, so 537 mod 10 = 7. Dividing by 2 leaves 1 for every odd number, as in 75 mod 2 = 1.
The remainder must stay below the number you divide by. A 9 for 57 mod 8 means another 8 fits: seven 8s make 56, leaving 1.
Ask what day comes 30 days after a Monday. Four weeks use 28 of them and 30 mod 7 = 2, so it is Wednesday.

How to play

Each round shows a problem written with mod, such as 43 mod 5, and you type just the leftover on the keypad: 3, not the eight fives that fit. No problem here divides evenly, so 0 is never the answer. Get the right remainder in before your rival and Carrot attacks, with a heavier blow the quicker you were.

— Quick answers —

Modulo: the short FAQ

What does mod mean in math?: Mod is short for modulo, and a mod b means the remainder when a is divided by b. You read 23 mod 4 as “23 modulo 4”, and it equals 3, because 4 × 5 = 20. Many programming languages write the same operation with %, so 23 % 4 also gives 3. Clocks use it too: 15 o’clock shows as 3, since 15 mod 12 = 3.
How do you find a remainder with a calculator?: A calculator shows a decimal instead of a remainder, so it takes three steps. For 250 mod 12, divide first: 250 ÷ 12 = 20.83… Keep only the whole part, 20, and multiply it back: 20 × 12 = 240. Then subtract, and 250 − 240 = 10 is the remainder. Without a calculator, the same three steps work in your head.
At what age do children learn division with remainders?: In many school systems, children first divide with remainders at about age 8 or 9, once they know their times tables. Dividing by two-digit numbers usually follows a year or two later. The levels here are aimed at ages 9 to 11. The word modulo and its short form, mod, often come later, in secondary school or a first coding class.
Why does my child get remainders wrong?: Most wrong remainders come from typing the other part of the division. In 29 ÷ 4, seven 4s fit and 1 is left over, so a child who answers 7 has given the number of groups, not the remainder. Saying the whole result aloud helps: “29 is seven 4s and 1 more.” Multiplying back checks it, since 7 × 4 + 1 = 29.
Is the remainder game free for schools, and how would a teacher use it?: Both levels are free for any class and run in a browser tab, with no install or logins. For modular arithmetic practice, write 1 to 24 on the board in rows of six. Pupils notice that each column shares one remainder after dividing by 6, then predict where 50 would land: under the 2, since 50 mod 6 = 2. Then everyone fights on tablets. The schools plan, billed per student, adds a teacher dashboard of who is improving.

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