Unit Fraction

Unit fractions are those whose numerator is 1 and the denominator is any natural number. It is of the form 1/x, where x∈N. Few examples of unit fractions are 1/2, 1/5, 1/34, etc.

All the fractions with 1 as the numerator are known as unit fractions. In these fractions, we take only one part of the whole which is divided equally into a finite number of parts. Unit denotes one. Therefore, they are known as unit fractions. For example, if a pizza is divided into 8 equal parts and Joseph is eating one part of it, then it will be represented as 1/8 which is a unit fraction.

In the image below, 1/2, 1/4, and 1/7 are unit fractions.

Any fraction with a numerator other than 1 is a non-unit fraction. For example, 3/4, 3/8, 2/3, etc are all non-unit fractions. Here, it is important to understand that fractions that can be reduced to 1 in the numerator are also non-unit fractions that can be expressed as a unit fraction after simplification. For example, 2/4 is a non-unit fraction, which can be expressed as a unit fraction with a different denominator 1/2. The idea behind unit fractions is that we are taking 1 part out of a whole, so if we have taken 2 parts out of 4, that is surely not what we are asked for. But yes, if we consider that whole divided into 2 parts, then we can say that we are considering 1 part out of 2, which is a unit fraction.

Dividing unit fractions by whole numbers is done by multiplying the whole number with the denominator of the given fraction. Follow the steps given below to understand the division of a unit fraction by the whole number in detail:

• Step 1: Find the reciprocal of the whole number.
• Step 2: Change the division fact to multiplication by changing the sign and multiplying the reciprocal with the unit fraction.
• Step 3: Find the product and write the answer.

Let us take an example of dividing 1/7 by 8.

Step 1: The reciprocal of 8 is 1/8.

Step 2: 1/7 ÷ 8 = 1/7 × 1/8

Step 3: 1/7 × 1/8 = 1/56.

Therefore, dividing 1/7 by 8 gives us 1/56. If you observe carefully, we are just multiplying the given whole number to the denominator of the fraction. It's easy, isn't it? Now, let us learn about dividing a whole number by a unit fraction. To do that, we will just have to multiply the whole number with the denominator of the fraction. It will always give us a whole number as the answer. For example, 5 ÷ 1/6 can be written as 5 × 6, which is 30. So, 5 ÷ 1/6 = 30.

Unit Fraction Related Articles

Check these interesting articles related to the concept of the unit fraction.

• Fractions
• Types of Fractions
• Multiplication of Fractions
• Improper Fractions

What are a Unit Fraction and a Non-unit Fraction?

A unit fraction is a fraction with 1 as the numerator. While a non-unit fraction has a numerator other than 1. Examples of unit fractions are 1/2, 1/3, 1/4, etc. Examples of non-unit fractions are 2/3, 4/9, 12/15, etc.

Why is it called a Unit Fraction?

Unit fractions mean we are considering one part out of the total parts of the whole. Unit means one. Therefore, it is called a unit fraction.

What is a Product of a Whole Number and a Unit Fraction?

The product of a whole number 'a' and a unit fraction '1/b' is 'a/b'. For example, 3 × 1/5 = 3/5.

How to Divide a Whole Number by a Unit Fraction?

To divide a whole number by a unit fraction, we just have to multiply it by the denominator of the fraction. It always results in a whole number. For example, 10 ÷ 1/4 = 10 × 4 = 40.

How to Decompose a Fraction into Unit Fractions?

To write a fraction as a sum of unit fractions, we write it in the form of the addition of two unit fractions with two unknown integers in the denominators. For example, 7/10 = 1/A + 1/B. This implies, 7/10 = (A+B)/AB. Now, we can simply equate numerators and denominators separately. So, A+B=7, and AB=10. Solving these two equations, we get A= 2 or 5, and B = 5 or 2. Therefore, 7/10 can be decomposed as the sum of two unit fractions 1/2 and 1/5.

Is Unit Fraction a Proper Fraction?

Unit fractions are always proper fractions except 1/1 (which is an improper fraction). This is because, for unit fractions, the numerator is always 1 which is the smallest natural number. So, any natural number in the denominator greater than 1 forms a proper fraction.

Is 1 a Unit Fraction?

Yes, 1 is a unit fraction as it can be represented as 1/1. And we know that any fraction with 1 as the numerator is a unit fraction.

What is a Multiple of a Unit Fraction?

We can write any fraction as a multiple of a unit fraction. For example, 7/8 is 7 × 1/8. So it is the seventh multiple of 1/8.