Learn division in simple steps

Meaning of division

Division is breaking a number up into an equal number of parts.

Example:

40 divided by 4 = ?

40 = 10 + 10 + 10 + 10

If you take 40 things and put them into four equal sized groups, there will be 10 things in each group. The answer is 10.

OR

40 divided by 4 = 10.

Signs for Division ÷ and /

There are a number of signs that you may use to indicate division. The most common one is ÷, but the backslash / is also used.

Sometimes you can write one number on top of another with a line between them. This is also called a fraction.

Example signs for “a divided by b”:

a ÷ b
a/b
a
b

Definition for Dividend, Divisor, Quotient and Remainder

Each part of a division equation has a name. The three main names are the dividend, the divisor, and the quotient.

  • Dividend – The dividend is the number you are dividing up
  • Divisor – The divisor is the number you are dividing by
  • Quotient – The quotient is the answer
  • Remainder – If the answer to a division problem is not a whole number, the “leftovers” are called the remainder.

Dividend ÷ Divisor = Quotient

Example:

In the problem 40 ÷ 4 = 10

Dividend = 40
Divisor = 4
Quotient = 10

Special Cases

There are three special cases to consider when dividing.

1) Dividing by 1: When dividing something by 1, the answer is the original number. In other words, if the divisor is 1 then the quotient equals the dividend.

Examples:

10 ÷ 1 = 10
12.9 ÷ 1 = 12.9

2) Dividing by 0: You cannot divide a number by 0. The answer to this question is undefined.

3) Dividend equals Divisor: If the dividend and the divisor are the same number (and not 0), then the answer is always 1.

Examples:

10 ÷ 10 = 1
12.9 ÷ 12.9 = 1

Remainder

If the answer to a division problem is not a whole number, the “leftovers” are called the remainder.

For example, if you were to try and divide 40 by 3 you would discover that 3 does not divide evenly into 40. The closest numbers to 40 that 3 can divide into are 39 and 42. You pick the closest number that 3 divides into that is smaller than 40. That is 39.

39 divided by 3 = 13, but there are still some leftovers. 40 -39 = 1. There are 1 remaining.

We write the remainder after an “r” in the answer.

40 ÷ 3 = 13 r 1

Examples:

12 ÷ 5 = 2 r 2
23 ÷ 4 = 5 r 3
18 ÷ 7 = 2 r 4

Division is the Opposite of Multiplication

Another way to think of division is as the opposite of multiplication. Taking the first example on this page:

40 ÷ 4 = 10

You can do the reverse, replacing the = with a x sign and the ÷ with an equal sign:

10 x 4 = 40

Examples:

12 ÷ 4 = 3
3 x 4 = 12

21 ÷ 3 = 7
7 x 3 = 21

Dividing multiple digit numbers

you need to divide the nearest highest number and carryover the reminders until the reminder is lesser then the divisor. As you can see in the below example. 10 x 8 =80 which is nearest to 84 and lesser then 10 x 9 = 90 . next 10 x 4 = 40 is nearest to 47 and is lesser then 10 x 5 = 50 . At last the left over is 7 which is again lesser then the divisor which is 10, so here 7 is the remainder.

Dividend = 8470
Divisor = 10
Quotient = 84
Remainder = 7

This concept will be helpful to you to divide any bigger number , there will be no of scenarios based question on division concept like if ram has 40 candy with him and he gave equal no of candy to his 13 friends . How much will be left with him for his sister.? you can easily solve these type of question with the concept of division.