🔢 Division Basics

What is Division?
Division means splitting a number into equal groups. It is the opposite of multiplication (putting equal groups together). The division sign is ÷.
Two ways to think about division
1. Sharing equally. "Share 12 sweets among 3 children" how many does each get? Deal them out one by one until none are left: each child gets 4. So 12÷3=4.
2. Making equal groups. "How many groups of 3 are in 12?" Take groups of 3 away: 12→9→6→3→0, that is 4 groups. So 12÷3=4 again.
The words we use
WordMeaningIn 12÷3=4Dividendthe number being shared12Divisorhow many groups (or group size)3Quotientthe answer4Division is repeated subtraction. 12÷3 asks how many times you can take 3 away from 12. You can do it 4 times, so the answer is 4.
Special division facts:
• Any number ÷ 1 is itself: 7÷1=7.
• Any number ÷ itself is 1: 7÷7=1.
• 0 shared into any group is 0: 0÷5=0.

Real…

Multiplication and division are opposites. One undoes the other. If you multiply 3 by 4 to get 12, then dividing 12 by 4 takes you back to 3. Because of this, every multiplication fact gives you matching division facts.
Fact families. Three numbers that multiply and divide together make a fact family. For 3, 4 and 12:
MultiplicationDivision3×4=1212÷3=44×3=1212÷4=3Use your times tables to divide. To work out 42÷7, just ask: "7 times what is 42?" Since 7×6=42, the answer is 42÷7=6. So learning the tables well makes division quick.
Check your division by multiplying back. To check 36÷6=6, multiply: 6×6=36 correct! This is the easiest way to be sure a division answer is right.
Why it helps: you do not need to learn division facts separately they come free with the multiplication facts you already know.
Common mistake: getting the family the wrong way round. From 5×6=30…

Sometimes a number cannot be shared into equal groups exactly a little is left over. The amount left over is called the remainder.
Example. Share 13 sweets among 4 children. Each child gets 3 (that uses 12 sweets), and 1 sweet is left over. We write this as:
13÷4 = 3 remainder 1(short: 3 r 1)
Here 3 is the quotient (how many each got) and 1 is the remainder (what was left).
The most important rule: the remainder is always smaller than the divisor. If the remainder were as big as the divisor, you could give out one more to each group.
How to check your answer. Use:
quotient×divisor+remainder=dividend
For 13÷4=3 r 1: 3×4+1=13 correct!
When the remainder is 0. If nothing is left over, the number divides exactly. For example 12÷4=3 with remainder 0.
Common mistakes to avoid:
• Leaving a remainder that is equal to or bigger than the divisor (it must be smaller).
•…