➗Division

24 candies shared equally among 6 friends — how many each? $24 \div 6 = 4$. Multiplication packs equal groups; division unpacks them by asking: how many such groups fit inside?

Sharing fairly vs grouping

$12 \div 3$ tells two different stories:

• Sharing fairly: 12 candies split among 3 people, 4 each — how big is one share?
• Grouping: bags hold 3 candies each, so 12 candies fill 4 bags — how many bags?

Same expression, different question. Learn the names of the parts too: in $624 \div 5$, the 624 is the dividend, the 5 is the divisor, and the result is the quotient.

Division undoes multiplication

Because $6 \times 4 = 24$, we get $24 \div 6 = 4$ and $24 \div 4 = 6$. Solid times tables make division mental math. A few special cases deserve instant answers:

• Dividing by 1 changes nothing: $7 \div 1 = 7$;
• Dividing a number by itself gives 1: $7 \div 7 = 1$;
• 0 divided by any nonzero number is 0: $0 \div 5 = 0$.

Like subtraction, division is not commutative: $8 \div 2 = 4$ but $2 \div 8 = 0.25$ — entirely different. And there is one red line: 0 can never be a divisor — "share 6 candies equally among 0 people" simply makes no sense.

18 ÷ 3 = ?

✓

🔥 0 · ★ 0

Long division, one digit at a time

Big divisions go step by step. Compute $624 \div 5$:

1. Look at the hundreds: $6 \div 5$ gives quotient 1, remainder $6 - 5 = 1$;
2. Bring down the 2 from the tens: $12 \div 5$ gives 2, remainder 2;
3. Bring down the 4 from the ones: $24 \div 5$ gives 4, remainder 4.

The quotient is 124 with remainder 4, written $624 \div 5 = 124 \cdots\cdots 4$.

What remainders really mean

A remainder is not garbage — how you use it depends on the story:

• 17 children and 5-seat minibuses: $17 \div 5 = 3 \cdots\cdots 2$, but the 2 leftover children also need a ride, so you need 4 buses;
• 30 dollars and pens costing 8 each: $30 \div 8 = 3 \cdots\cdots 6$, so you can buy only 3 pens; the last 6 dollars will not stretch.

The same remainder, rounded up in one story and dropped in the other — always ask what the question is really asking.

Check yourself

✅

Quick quiz

↺ Try again

1. 1. What are the quotient and remainder of 624 ÷ 5?

   124 remainder 4123 remainder 9134 remainder 4

2. 2. 17 children need rides in 5-seat minibuses. How many buses at least?

   3 buses4 buses5 buses

3. 3. Which expression is the problem?

   7 ÷ 1 = 77 ÷ 7 = 17 ÷ 0 = 0