11+ Maths Solved Topic Wise Questions

1. Introduction

It is a process of dividing an amount into equal parts. It is one of the basic arithmetic operations. The division is the opposite of multiplication.

For example, A boy gives 16 bananas to 4 monkeys. How many bananas will each get?

Each will get = 16 ÷ 4 = 4 bananas.

1.1 What are dividend, divisor, quotient and remainder?

• In division, the number that is being divided by another number is called the dividend.
• The number by which we divide is called a divisor.
• The number which we get as a result is called the quotient.
• The value left after division is called the remainder.

For example: Divide 26 by 5.

 1.2 How to divide?

Steps to divide a number:

• First, divide the first digit of the dividend by the divisor.
• Multiply the digit of the quotient by the divisor.
• Subtract the result from the dividend.
• Now, write down the second digit of the dividend.
• Repeat the same process uptill the last digit of the dividend.

For example: Divide 621 by 3.

2. Division:

2.1 Divide a Number by 10, 100 and 1000: 

• To divide a number by 10, the quotient is obtained by removing the unit's digit from the number and the remainder is the one's digit of the number.

For example: Work out 1998 ÷ 10

On dividing 1998 by 10, we get:

Quotient = 199 and remainder = 8.

• To divide a number by 100, the quotient is obtained by removing the last two digits from the number and the last two digits is the remainder.

For example: work out 1237 ÷ 100

On dividing 1237 by 100, we get

Quotient = 12 and remainder = 37

• To divide a number by 1000, the quotient is obtained by removing the last three digits from the number and the last three digits is the remainder.

For example: work out 7880 ÷ 1000

On dividing 7880 by 1000, we get

Quotient = 7 and remainder = 880

2.2 Divide positive and negative numbers: 

• Division of a positive number with another positive number always gives a positive result. Example: 8 ÷ 4 = 2
• Division of a negative number with a positive number always gives a negative result
• Example: -6 ÷ 2 = -3
• Division of a negative number with another negative number always gives a positive result. Example: - 40 ÷ -4 = 10

2.3 Dividing Decimals: 

• Convert the divisor to a whole number by moving the decimal to the right.
• Similarly, move the dividend’s decimal to the right up to the same number of places.
• Now, divide the numbers using the usual method.

Example: Divide 3.6 by 0.6.

Let us move decimals for both numbers.

36 ÷ 6 = 6

So, the answer is 6.

Example: Divide 0.336 by 0.8.

First, we need to move the decimal at the right side to make 0.8 into a whole number.

So it will be 3.36 ÷ 8

Now, ignore the decimal in the dividend and divide them without the decimal.

Now put the decimal before the last two digits in the answer.

The answer is 0.42

2.4 Division of fractions:

To divide the fractions, multiply the first fraction by the reciprocal (reverse the numerator and denominator) of the second fraction and then reduce the fraction.

Example: 4⁄6 ÷ 3⁄5 = 4⁄6 × 5⁄3

= 2⁄3 × 5⁄3 = 10⁄9