# NCERT Solutions Practice Questions

## Convert Mixed Fraction to Decimal

**Convert Mixed Fraction to Decimal – Example 1**

**Solution**

Whenever, we have a mixed fraction, it would consist of two parts.

Whole Number Part = 5

Fraction Part = 3/5

The Whole Number Part would remain the same.

The Fraction Part should be converted into decimal

When we convert 3/5 into decimal we would get 0.6

The Decimal value of the given fraction = Whole Number Part . Decimal value of Fraction Part

The Decimal value of the given fraction = 5.6

**Convert Mixed Fraction to Decimal – Example 2**

**Solution**

Whenever, we have a mixed fraction, it would consist of two parts.

Whole Number Part = 6

Fraction Part = 4/5

The Whole Number Part would remain the same.

The Fraction Part should be converted into decimal

When we convert 4/5 into decimal we would get 0.8

The Decimal value of the given fraction = Whole Number Part . Decimal value of Fraction Part

The Decimal value of the given fraction = 6.8

## Convert Decimal to Fraction

**To Convert Decimal to Fraction we have to follow the following steps.**

**Step 1:** Write the given Decimal without the Decimal point as the numerator of the fraction.

**Step 2:** In the Denominator, write 1 followed by as many zeroes, as there are Decimal places in the given Decimal.

**Step 3:** Convert the fraction into simplest form.

### Convert Decimal to Fraction

**Convert Decimal to Fraction – Example 1**

Convert 0.8 into a fraction in its Simplest form?

**Solution**

Step 1: Write the given Decimal without the Decimal point as the numerator of the fraction 8

Step 2: Write 1 followed by as many zeroes, as there are Decimal places in the given Decimal 10 (Since there was 1 decimal place in the given number, we have added 1 zero at the end of 1 )

= 8/10

Step 3: Convert the fraction 8/10 into simplest form

HCF of 8 and 10 is 2

To simplify this we have to divide both the numerator and denominator of the fraction by their HCF i.e,

8 and 10 by 2

Hence, 0.8 = 4/5

**Convert Decimal to Fraction – Example 2**

Convert 0.55 into a fraction in its Simplest form?

**Solution**

Step 1: Write the given Decimal without the Decimal point as the numerator of the fraction 55

Step 2: Write 1 followed by as many zeroes, as there are Decimal places in the given Decimal 100 (Since there was 2 decimal place in the given number, we have added 2 zero at the end of 1 )

= 55/100

Step 3: Convert the fraction 55/100 into simplest form

HCF of 55 and 100 is 5

To simplify this we have to divide both the numerator and denominator of the fraction by their HCF i.e,

55 and 100 by 5

Hence, 0.55 = 11/20

## Dividing Fractions

### Dividing Whole numbers by Fractions:

- When a whole number is divided by a fraction, whole number is to be multiplied by the reciprocal of that fraction.
- In generalise form, for any whole number ‘a’ and fraction b/c

- Reciprocal of a fraction, fraction are said to be reciprocal when we simply reverse the fraction i.e numerator becomes denominator and denominator becomes numerator. Two fractions are said to be reciprocal of each other if their product is 1.
- In generalise form, for any fraction a/b

**Example **

Divide 40 by 6/4

**Solution**

We have, 40 ÷ 6/4

In order to divide a whole number by a Fraction, we need to multiply the whole number with the reciprocal of that Fraction.

We have to multiply Whole number by Reciprocal of that Fraction

40 x 4/6 (Since, Reciprocal of 6/4 is 4/6)

Simplifying the given Fraction,

HCF of 160 and 6 is 2

__Dividing Fraction by Whole Number:__

- When a fraction is divided by a whole number, fraction is to be multiplied by the reciprocal of that whole number.
- In generalise form, for any fraction a/b and whole number ‘c’

**Example**

Divide 3/7 by 6

**Solution**

We have, 3/7 ÷ 6

In order to divide a Fraction by a whole number

We have to multiply Fraction with Reciprocal of that whole number

__Dividing Fraction by Fractions__

- When a fraction is divided by another fraction, the first fraction is multiplied by the reciprocal of second fraction.

**Example**

In order to divide a Fraction by another Fraction

We have to multiply First Fraction with Reciprocal of the second Fraction

### Division of Mixed Fraction by Improper or Proper Fractions

- When a mixed fraction is divide by a proper or improper fraction, convert mixed fraction into improper fraction and then divide them.

**Example**

In order to divide a Fraction by another Fraction

We have to multiply First Fraction with Reciprocal of the second Fraction

### Learn More..

## Types of Fraction | Proper | Improper | Mixed Fraction

Types of Fraction:

- Proper Fraction
- Improper Fraction
- Mixed Fraction

– Convert Improper Fraction To Mixed Fraction

– Convert Mixed Fraction To Improper Fraction

## Fraction:

- A fraction is a part of the whole number.
- In generalising form for any two natural numbers ‘a’ and ‘b’ fraction is:
- a/b

### Where,

- a = Numerator
- b = Denominator

### Example 1

Write down the Numerator and Denominator of the Fraction:

4/3

### Explanation

The numerator is the upper part (Number on Top) of the Fraction

So, the Numerator of 4/3 is 4

The denominator is the lower number ( Number at Bottom) of the Fraction

So, the Denominator of 4/3 is 3

### Example 2

Write down the Numerator and Denominator of the Fraction:

5/6

### Explanation

The numerator is the upper part (Number on Top) of the Fraction

So, the Numerator of 5/6 is 5

The denominator is the lower number ( Number at Bottom) of the Fraction

So, the Denominator of 5/6 is 6

### TYPES OF FRACTION

### Types of Fraction – Proper Fraction

- A proper fraction is a fraction which represents the part of the whole number. In a proper fraction, the numerator is always less than its denominator.
- In generalising form for any two integers ‘a’ and ‘b’
- a/b where (a < b)
- i.e Numerator < Denominator

### Example 1

Is 2/3 is a proper fraction?

### Explanation

A proper fraction is a fraction which represents the part of the whole number. In a proper fraction, the numerator is always less than its denominator.

- In generalise form for any two integer ‘a’ and ‘b’
- a/b where (a < b)
- i.e Numerator < Denominator
- Numerator = 2
- Denominator = 3
- Here 2 < 3
- i.e, Numerator < Denominator
- Hence, 2/3 is a proper fraction

### Example 2

Is 7/5 is a proper fraction?

### Explanation

A proper fraction is a fraction which represents the part of the whole number. In a proper fraction, the numerator is always less than its denominator.

- In generalising form for any two integers ‘a’ and ‘b’
- a/b where (a < b)
- i.e Numerator < Denominator
- Numerator = 7
- Denominator = 5
- Here 7 > 5
- i.e, Numerator > Denominator
- Hence, 7/5 is not a proper fraction

### Types of Fraction – Improper Fraction

Improper fractions are the combination of a whole number and a proper fraction. An improper fraction is opposite of proper fraction since in improper fraction numerator is greater than its denominator

- In generalising form for any two integers ‘a’ and ‘b’
- a/b where (a > b)
- i.e Numerator > Denominator

### Example 1

Is 17/9 is an improper fraction?

### Explanation

Improper fractions are the combination of a whole number and a proper fraction. An improper fraction is opposite of proper fraction since in improper fraction numerator is greater than its denominator

- In generalising form for any two integers ‘a’ and ‘b’
- a/b where (a > b)
- i.e Numerator > Denominator
- Numerator = 17
- Denominator = 9
- Here, 17 > 9
- i.e, Numerator > Denominator
- Hence, 17/9 is an improper fraction.

### Example 2

Is 7/10 is an improper fraction?

### Explanation

Improper fractions are the combination of a whole number and a proper fraction. An improper fraction is opposite of proper fraction since in improper fraction numerator is greater than its denominator

- In generalising form for any two integers ‘a’ and ‘b’
- a/b where (a > b)
- i.e Numerator > Denominator
- Numerator = 7
- Denominator = 10
- Here, 7 < 10
- i.e, Numerator < Denominator
- Hence, 7/10 is not an improper fraction.

### Types of Fraction – Mixed Fraction

Mixed Fraction is a sum of a whole number and a proper fraction. An improper fraction can be converted into a mixed fraction and mixed fraction can be converted into an improper fraction with the help of simple multiplication, division and addition.

### Convert Improper Fraction to Mixed Fraction

To Convert Improper Fraction into Mixed Fraction, we follow the steps given below:-

**Step I**: Divide the Numerator by the Denominator.

**Example 1**

Convert 3/2 into Mixed Fraction.

**Explanation**

Given Fraction:

- 3/2
- Divide the Numerator by the Denominator
- On dividing 3 by 2
- We get Quotient = 1
- Remainder = 1

### Example 2

Convert 5/3 into Mixed Fraction.

### Explanation

Given Fraction:

- 5/3
- Divide the Numerator by the Denominator
- On dividing 5 by 3
- We get Quotient = 1
- Remainder = 2

### Convert Mixed Fraction to Improper Fraction

To Convert Mixed Fraction into Improper Fraction, we follow the steps given below:-

**Step 1**: Multiply the Whole Number Part and Denominator of the Mixed Fraction

**Step 2**: Add the Numerator to the product obtained in Step 1

**Step 3**: Write the sum as the numerator and denominator would remain the same, as in the Mixed Fraction.

### Example 1

### Explanation

A combination of Whole Number and a Proper Fraction is called a Mixed Fraction Here,

- Whole Number Part = 2
- Numerator = 2
- Denominator = 3
- Step 1: Multiply the Whole Number Part and Denominator of the Mixed Fraction
- 2 x 3 = 6
- Step 2: Add the Numerator to the product obtained in Step 1
- 2 + 6 = 8
- Write the sum as the numerator and denominator would remain the same, as in the Mixed Fraction.

8/3

### Example 2

### Explanation

A combination of Whole Number and a Proper Fraction is called a Mixed Fraction Here

- Whole Number Part = 3
- Numerator = 1
- Denominator = 2
- Step 1: Multiply the Whole Number Part and Denominator of the Mixed Fraction
- 3 x 2 = 6
- Step 2: Add the Numerator to the product obtained in Step 1
- 1 + 6 = 7
- Write the sum as the numerator and denominator would remain the same, as in the Mixed Fraction.
- 7/2

### Learn More..

- Types of Fractions | Proper | Improper | Mixed Fraction
- Equivalent Fractions Examples
- Fraction in Simplest Form
- Like Fractions and Unlike Fractions
- Comparing Fractions
- Adding Fractions
- Subtracting Fractions
- Multiplying Fraction
- Dividing Fractions