Operations with Fractions

In these revision notes for Operations with Fractions, we cover the following key points:

• How to add or subtract two fractions with the same denominator?
• How to add or subtract two fractions with different denominators.
• How to multiply two fractions?
• How to multiply mixed numbers with fractions or whole numbers?
• How to divide fractions or mixed numbers?
• How to raise a fraction in a given power?
• How to use the BEDMAS Rule in fractions?
• What are some applications of fractions in daily life?

Operations with Fractions Revision Notes

For addition and subtraction of fractions with the same denominator, numerators are added while the denominator does not change. Symbolically, we can write

For addition and subtraction of fractions with different denominators, first we find a common denominator, and after arranging the fractions accordingly, the method of addition or subtraction of fractions with the same denominator is applied. Symbolically, we can write

When mixed numbers or integers are involved in the addition or subtraction of fractions, it is better to have them written as fractions and then we do the operations as usual.

For multiplication of fractions, we multiply numerators with each other and denominators with each other too. The result obtained is the product of multiplication. Symbolically, we can write

For division of fractions, we use the same method as in multiplication; the only difference is that the second fraction is inverted down, since division is the inverse operation of multiplication. Symbolically, we can write

Since power is a kind of recurrent multiplication by the same factor, we obtain the following rule for power of fractions:

We can use the PEMDAS Rule in expressions containing fractions in the same way as we have used it in expressions with whole numbers.

There are many applications of operations with fractions in practice where a number of operations are involved.