# Unit Fraction

## Define Unit Fraction

Unit fraction definition states that Unit Fraction is a rational number which is written as a fraction where the unity is the numerator and any positive integer is the denominator.

Consequently, a Unit Fraction means that it is an inverse of a positive integer.

Ex: 1/10, 1/25, 1/33, 1/47, etc are Unit fractions.

Whereas 5/10, 7/25, -4/33 are not Unit fractions even though they are rational numbers.

### Division of Fractions with Whole Numbers

Dividing Unit Fractions by whole numbers will result in a Unit Fraction. When a Unit fraction say 1/3 is divided by a whole number 4 then the whole number will get multiplied with the Denominator so the numerator remains the same.

1/3 ÷ 4 = 1/16 which is still a Unit fraction.

### Dividing Unit Fractions by Rational Numbers

Dividing a Unit fraction by a rational number will not give us a Unit fraction. When a Unit fraction say 1/5 is divided by a rational number 2/5 then the resulting fraction will not be a unit fraction because the denominator of the rational number will get multiplied with the numerator of the unit fraction.

1/5 ÷ 2/5 = 5/10 which is not a Unit fraction.

### Finding Volume with Cubes with Fraction Lengths

Unit fractions can be used to find the volume of a rectangular prism by finding the volume of the unit cube. Consider a rectangular prism made of a unit cube of fraction length, width, and depth. Let the fraction length, width, and depth be 1/4. So the volume of a unit cube will be,

V = Length* Width* Depth

V = l*b*d

V = (1/4)*(1/4)*(1/4) =1/64 which is a Unit fraction.

Now, let us consider the Rectangular Prism is broken into 32 Unit cubes. So the total Volume of the Rectangular Prism will be equal to the volume of each unit cube multiplied by the total number of unit cubes in a rectangular prism.

The volume of rectangular prism = 32* 1/64 = 1/2 which is a Unit fraction.

The Volume of a rectangular prism satisfies the Unit Fraction Meaning.

### Properties of Unit Fractions:

• The unit fraction will always have the numerator as unity whereas the denominator can be any positive integer.

• Multiplication of a unit fraction from a whole number will always not give us a Unit fraction, but dividing Unit Fractions by whole numbers will give us Unit Fraction.

Ex: 1/6 * 3 = 3/6 = 1/2 is a Unit fraction.

1/6 * 4 = 4/6 = 2/3 is not a Unit fraction.

• Multiplication of two unit fractions will give us a unit fraction.

Ex: 1/5 * 1/5 = 1/25

1/9 * 1/9 = 1/81

• Dividing Unit fractions by a Rational number will not give us a Unit fraction.

### Problems on Unit Fractions

1) In the given list of fractions circle the Unit Fraction and list them out.

1/4, 3/5, 7/8, 1/14, 1/2, 5/8, 1/22, 5/22.

Ans: Here in the given list of fractions 1/4, 1/14, 1/2, 1/22 satisfies the Unit Fraction definition. Therefore 1/4, 1/14, 1/2, 1/22 are the unit fractions in the given list.

2) By Comparing Unit Fractions in the given list arrange them in ascending order.

1/4, 1/14, 1/2, 1/22, 1/5.

Ans: First let us find the value of the Unit Fractions given here:

1/4 = 0.25

1/14 = 0.07

1/2 = 0.5

1/22 = 0.04

1/5 = 0.2

Here we have to note that as the number in the denominator is higher then the Unit fraction will have the least value.

So 0.04 <  0.07 < 0.2 < 0.25 < 0.5

Ascending order means from smallest to largest. Therefore the ascending order of the given list is 0.04, 0.07, 0.2, 0.25, 0.5.

### Conclusion

The Unit fraction is equal to one part out of the total number of parts equal to the entire unit. It is important that students know what unit they work with. Mathematics as a language indicates that students would have an easier time grasping the definition if they know what unit they are dealing with.