Understanding Fraction Rules in Maths

Fractions are the mathematical way of representing part of something whole. They are in the form of numerator and denominator. We call the upper part (or the part which represents how much part of something whole we are considering) as the numerator and the lower part (which represents how many equal parts we have done of something whole) is called the denominator.

Fraction = Numerator/Denominator

Parts of Fraction

The parts of a fraction are:

1. Numerator: The numerator is the number, which is on the top. It shows how many equal parts of the whole or collection is considered.

2. Denominator: The number which is below the line is the denominator. It shows the total equal parts which we did of the whole.

For example, consider we have a watermelon and we did 8 equal parts of it then 8 will be in the denominator of the fractions. Now if we want to represent five parts out of them then the fraction will be ⅝. If we want to represent only one part out of them then the fraction will be ⅛. As shown in the following figure.

Fraction Rules

We have learnt many mathematical operations like addition, subtraction, division and multiplication also we have got a new way of representing objects that are fractions. Can we perform those mathematical operations to fractions also? The answer is yes. In this section, we'll do different mathematical operations with Fraction rules.

1. Fraction Rule of Addition

How can we add two fractions together? There are some rules which we need to keep in our mind while adding two fractions.

• Fractions with different denominators can’t be added.

• To add fractions, first of all, we need to equate the denominator by taking the least common multiple that is LCM of the numbers present in the denominator.

• After making the denominator the same, accordingly, numerators will also get changed.

• Now, add these new numerators to get the desired result.

For Example: Suppose we want to add ¼ with ¼. Then observe that the denominator is already the same and even if we take the least common multiple of the denominator then it also is 4 only. Now we can add numerators 1 + 1 = 2. Hence the required result will be 2/4. Also, observe that 4 is a common multiple of 2 and 4. So it can be cancelled. So after simplifying we get ½.

We can also understand this with the help of the following diagram:

2. Fraction Rule of Subtraction

Subtraction is almost the same as addition. Instead of adding numerators, we’ll subtract them. There are some rules which we need to keep in our mind while subtracting two fractions.

• Fractions with different denominators can’t be subtracted.

• To subtract fractions, first of all, we need to equate the denominator by taking the least common multiple that is LCM of the numbers present in the denominator.

• After making the denominator the same, accordingly, numerators will also get changed.

• Now, subtract these new numerators to get the desired result.

For Example: Suppose we want to subtract ¼ from ¾. Then observe that the denominator is already the same and even if we take the least common multiple of the denominator then it also is 4 only. Now we can subtract numerators, 3-1=2. Hence the required result will be 2/4. Also, observe that 4 is a common multiple of 2 and 4. So it can be cancelled. So after simplifying we get ½.

We can also understand this with the help of following diagram:

3. Fraction Rule of Multiplication

How can we multiply two fractions? Will it be the same as addition or subtraction where we have to make denominators the same? The answer is No. In multiplication, we don’t need to do so. There are some rules which we need to keep in our mind while multiplying two fractions.

• Fractions with different denominators can be multiplied.

• Numerator can only be multiplied by numerator and denominator will only be multiplied by denominator.

• We can’t multiply numerators with denominators however they can be divided.

For example: Let us suppose we want to multiply ⅔ with 3/15. We know that numerator will only get multiplied with the numerator. So, 2 × 3 = 6. Hence, 6 will be the numerator of our desired result. For denominators, 3 × 15 = 45. Hence, 45 will be the denominator of our desired fraction.

So the multiplication of ⅔ with 3/15 will be 6/45. Also, observe that they can be further simplified. After simplifying we get it as 2/15.

Refer to the following:

⅔ × 3/15

= 2 × 3/3 × 15

= 6/45

= 2/15

4. Fraction Rule of Division

To perform division of fractions we need to remember certain rules and follow multiple steps. We have to multiply the first fraction with the reciprocal of the second. Division involves some steps to be followed-

1. Change the division sign (÷) into multiplication (×).

2. If we change the sign of division into multiplication, then we have to write the reciprocal of the second term or fraction.

3. In the end, we simply multiply them to get the required answer.

Here, is an example of the Division of fractions:

Suppose we have to divide 3/2 by 5/4.

3/2 ÷ 5/4

Step 1: Changing the sign to multiplication from division and writing the reciprocal of the second term [÷5/4 =× 4/5].

 = 3/2 × 4/5

Step 2: Multiplying the first with the reciprocal of the second fraction.

 = (3 × 4)/(2 × 5)

= (3 × 2)/ (1 × 5)

= 6/5

Step 3: Getting the simplified result of the expression.

Division of fractions is the multiplication of fractions by just changing the second fraction to its reciprocal.

Did You Know?

There is one more way of representing fractions that is decimals. They are interchangeable to each other. Decimals can be divided further into terminating and non-terminating ones. If they are non-terminating then further divided into recurring and non-recurring decimals. The definition of rational numbers and irrational numbers comes from here only. If they are either terminating or non-terminating and recurring then we call them rational numbers. If they are non-terminating and non-recurring then we call them irrational numbers.