In division we will see the relationship between the dividend, divisor, quotient and remainder. The number which we divide is called the dividend. The number by which we divide is called the divisor. The result obtained is called the quotient. The number left over is called the remainder.

55 ÷ 9 = 6 and 1

** Dividend Divisor**** **** Quotient**** Remainder**

**For example: **

(i) Divide 217 by 4

(ii) Divide 5679 by 7

Remainder, 55 ÷ 9 can also write as 9) 55 ( or 9) 55**Note: **dividend = divisor × quotient + remainder

**Understanding Remainder: **

We know divisor means to split a large group of objects into small equal groups. The large group is called the dividend. The number of smaller equal groups is called the divisor and the number of objects in each smaller group is called the quotient.

Let us Divide 12 cupcakes among 3 children.

Now, let us Divide 9 pencils into 2 equal groups.

When we cannot make equal groups or share equally all the objects, the number which is left undivided is called the remainder. Remainder is always less than the divisor.

So, Dividend = Divisor × Quotient + Remainder

In the above example = 9 × 2 + 1

The dividend, divisor, quotient and remainder will help us to verify the answer of division. Add remainder (if any) with the product of divisor and quotient. The sum we get should be equal to the dividend.

**Let us consider some examples to verify the answer of division.**

**1. Divide 38468 by 17 and verify the answer.**

Now let us verify the answer; dividend = divisor × quotient + remainder 38468 = 17 × 2262 + 14 = 38454 + 14 = 38468 So, the answer is correct. |

The quotient is 2262 and the remainder is 14.

**2. Divide 58791 by 36 and verify the answer.**

Now let us verify the answer; dividend = divisor × quotient + remainder 58791 = 36 × 1633 + 3 = 58788 + 3 = 58791 So, the answer is correct. |

The quotient is 1633 and the remainder is 3.

**3. Divide 94 by 3 and verify the answer.**

We know that 3 × 3 = 9 Write 3 in the quotient and 9 below 9. Subtract 9 from 9.
Write 1 in the quotient and subtract 3 from 4. |
Thus, quotient = 31 and remainder = 1 |

**Check:** To check answer, we use the following relationship:

Dividend = Divisor × Quotient + Remainder

94 = 3 × 31 + 1

94 = 93 + 1

94 = 94

Hence, division is correct.

**4. Divide 654 by 7 and verify the answer.**

Write the quotient 3 and subtract 321 from 24. |
Thus, quotient = 93 and remainder = 3 |

**Check:** To check answer, we use the following relationship:

Dividend = Divisor × Quotient + Remainder

654 = 7 × 93 + 3

654 = 651 + 3

654 = 654

Hence, division is correct.

Therefore, to check a division sum, add the remainder to help product of divisor and quotient. The result should be equal to the dividend.

Properties
of division:

When zero is divided by a number the quotient is zero.

**For example:**

(i) 0 ÷ 4 = 0

(ii) 0 ÷ 12 = 0

(iii) 0 ÷ 25 = 0

(iv) 0 ÷ 314 = 0

(v) 0 ÷ 225 = 0

(vi) 0 ÷ 7135 = 0

Division of a number by zero is not possible.

**For example**, we
cannot divide 74 by 0.

If we divide any number by 1, the quotient is the number itself.

**For example: **

(i) 28 ÷ 1 = 28

(ii) 4558 ÷ 1 = 4558

(iii) 335 ÷ 1 = 335

(iv) 9387 ÷ 1 = 9387

If we divide a non-zero number by itself, the quotient is 1.

**For example: **

(i) 45 ÷ 45 = 1

(ii) 98 ÷ 98 = 1

(iii) 1371 ÷ 1371 = 1

(iv) 5138 ÷ 5138 = 1

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