11+ Maths Solved Topic Wise Questions

1. Introduction:

When we subtract two numbers, the greater number from which we subtract another number is called a minuend.

The smaller number which we subtract from the greater number is called a subtrahend.

After subtraction what we get, as a result, is called the difference.

Example: Find the difference of £19 and £4?

£19 - £4 = £15, where 19 is minuend, 4 is subtrahend and 15 is a difference.

1.1. Subtract numbers without borrowing

Steps:

• Place the numbers on top of each other, by lining up the hundreds, tens and ones.
• Subtract them column-wise from right to left. (first, subtract the ones, then the tens, then the hundreds and so on).
• After subtraction the result is the difference.

1.2. Subtract numbers with borrowing

Steps:

• Place the numbers on top of each other, by lining up the hundreds, tens and ones.
• Subtract them column-wise from right to left. (first, subtract the ones, then the tens, then the hundreds and so on).
• When the digits being subtracted is greater than the digit being subtracted from, borrow from the top number from the next column to the left.
• Since a number is borrowed from the next place, the number reduces.
• Subtract the last number to get the final difference.

For example: Subtract 186 from 479.

2. Subtraction:

2.1 Subtraction of decimals

Steps:

• Arrange the numbers under each other, with the decimal points lined up.
• Put in zeros on empty places.
• Include decimal in the final result.

Example:

Subtract 17.38 from 44.86

Arrange the numbers under each other along with the decimals.

Start subtracting from right to left.

Include decimal in the final answer.

2.2 Subtraction of fractions

Steps:

• Check the denominators of the fractions.
• If denominators are the same, we can directly subtract the numerators, keeping the denominators the same.
• If denominators are not the same, make the denominators the same, by finding the LCM of denominators and rationalizing them.
• Now, subtract the numerators, keeping the denominators the same.
• Hence, reduce the fraction to get the final difference.

Example: Subtract fractions 7/9 - 3/9

Since the denominators of these fractions are the same, these given fractions are like fractions.

Now, subtract the numerators by keeping the denominators same and get the difference.

7/9 - 3/9 = 6/9 = 2/3

Example: Subtract fractions 2/3 - 1/6

Let us consider 1 as a denominator of 4.

LCM of 3 and 6 is 6.

Rewrite both the fractions as equivalent fractions with 6 as the denominator and then subtract fractions.

4/6 - 1/6 = 3/6 = 1/2