LESSON 5
DIVISION
Splitting Numbers Into Equal Groups
What is Division?
Division is the process of splitting a number into equal groups. It is the inverse (opposite) of multiplication and one of the four basic arithmetic operations.
The symbol for division is the division sign (÷) or a forward slash (/). When we write 12 ÷ 4 = 3, we are saying that 12 split into 4 equal groups gives 3 in each group. The number being divided is the dividend, the number we divide by is the divisor, and the result is the quotient.
Basic Division
Basic division asks: how many times does one number fit into another? If you have 15 apples to share equally among 3 people, you ask how many times 3 fits into 15. The answer is 5 — each person gets 5 apples.
Remainders
Sometimes a number cannot be divided evenly. The amount left over after dividing as far as possible is called the remainder. For example, 13 ÷ 4 = 3 remainder 1, because 4 goes into 13 three times (12), with 1 left over.
Long Division
Long division is a method for dividing large numbers step by step. We divide, multiply, subtract, and bring down — repeating until there are no digits left. It breaks a big problem into a series of smaller, manageable steps.
Checking with Multiplication
You can always check a division answer by multiplying the quotient by the divisor. If you get the dividend back, your answer is correct. If there is a remainder, add it back after multiplying.
Key Facts
Division by zero is undefined — it has no answer in mathematics. You can never divide any number by zero.
The division sign (÷) is called an obelus. It was first used as a division symbol by Johann Rahn in 1659.
Division is NOT commutative — 12 ÷ 4 is not the same as 4 ÷ 12.
Any number divided by 1 equals itself, and any number divided by itself equals 1 (except zero).