# NCERT Solutions Practice Questions

## Convert Mixed Fraction to Decimal

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

Express into Decimal.

**Solution**

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

Whole Number Part = 5

Fraction Part =

The Whole Number Part would remain the same.

The Fraction Part should be converted into decimal

When we convert 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**

Express into Decimal.

**Solution**

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

Whole Number Part = 6

Fraction Part =

The Whole Number Part would remain the same.

The Fraction Part should be converted into decimal

When we convert 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

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## 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 )

=

Step 3: Convert the fraction 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

In other words = =

Hence, 0.8 =

**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 )

=

Step 3: Convert the fraction 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

In other words = =

Hence, 0.55 =

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## 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

a ÷ = =

- 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

Reciprocal of = ; = 1

**Example **

Divide 40 by

**Solution**

We have, 40 ÷

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 (Since, Reciprocal of )

=

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 and whole number ‘c’

÷ c ==

**Example**

Divide by 6

**Solution**

We have, ÷ 6

In order to divide a Fraction by a whole number

We have to multiply Fraction with Reciprocal of that whole number

(Since, Reciprocal of

=

Simplifying the given Fraction,

HCF of 3 and 42 is 3

= =

__Dividing Fraction by Fractions__

- When a fraction is divided by another fraction, the first fraction is multiplied by the reciprocal of second fraction.
- In generalise form, for any two fractions and

÷==

**Example**

Divide ÷

**Solution**

We have, ÷

In order to divide a Fraction by another Fraction

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

We have ÷

= (Since, Reciprocal of )

=

Simplifying the given Fraction,

HCF of 20 and 180 is 20

= =

### 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**

Divide ÷

**Solution**

We have, ÷

Simplifying, the above equation, we get ÷

In order to divide a Fraction by another Fraction

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

(Since, Reciprocal of )

=

Simplifying the given Fraction,

HCF of 45 and 60 is 15

= =

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## 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:__

- Fraction is a part of whole number.
- In generalise form for any two natural numbers ‘a’ and ‘b’ fraction is:

Where,

a = Numerator

b = Denominator

**Example 1**

Write down the Numerator and Denominator of the Fraction:

**Explanation**

Numerator is the upper part (Number on Top) of the Fraction

So, the Numerator of is 4

Denominator is the lower number ( Number at Bottom) of the Fraction

So, the Denominator of is 3

**Example 2**

Write down the Numerator and Denominator of the Fraction:

**Explanation**

Numerator is the upper part (Number on Top) of the Fraction

So, the Numerator of is 5

Denominator is the lower number ( Number at Bottom) of the Fraction

So, the Denominator of is 6

## TYPES OF FRACTION

## Types of Fraction – Proper Fraction

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

In generalise form for any two integer ‘a’ and ‘b’

where (a < b)

i.e Numerator < Denominator

**Example 1**

Is is a proper fraction?

**Explanation**

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

In generalise form for any two integer ‘a’ and ‘b’

where (a < b)

i.e Numerator < Denominator

Numerator = 2

Denominator = 3

Here 2 < 3

i.e, Numerator < Denominator

Hence, is a proper fraction

**Example 2**

Is is a proper fraction?

**Explanation**

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

In generalise form for any two integer ‘a’ and ‘b’

where (a < b)

i.e Numerator < Denominator

Numerator = 7

Denominator = 5

Here 7 > 5

i.e, Numerator > Denominator

Hence, is not a proper fraction

## Types of Fraction – Improper Fraction

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

In generalise form for any two integer ‘a’ and ‘b’

where (a > b)

i.e Numerator > Denominator

**Example 1**

Is is a improper fraction?

**Explanation**

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

In generalise form for any two integer ‘a’ and ‘b’

where (a > b)

i.e Numerator > Denominator

Numerator = 17

Denominator = 9

Here, 17 > 9

i.e, Numerator > Denominator

Hence, is an improper fraction.

**Example 2**

Is is a improper fraction?

**Explanation**

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

In generalise form for any two integer ‘a’ and ‘b’

where (a > b)

i.e Numerator > Denominator

Numerator = 7

Denominator = 10

Here, 7 < 10

i.e, Numerator < Denominator

Hence, is not an improper fraction.

## Types of Fraction – Mixed Fraction

Mixed Fraction is a sum of whole number and proper fraction. Improper fraction can be converted into mixed fraction and mixed fraction can be converted into 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.

**Step II**: Write the Mixed Fraction as: ( Quotient + )

**Example 1**

Convert into Mixed Fraction.

**Explanation**

Given Fraction:

Divide the Numerator by the Denominator

On dividing 3 by 2

We get Quotient = 1

Remainder = 1

For a Mixed Fraction we have to write ( Quotient + )

So, the Mixed Fraction is ( 1 + ) =

**Example 2**

Convert into Mixed Fraction.

**Explanation**

Given Fraction:

Divide the Numerator by the Denominator

On dividing 5 by 3

We get Quotient = 1

Remainder = 2

For a Mixed Fraction we have to write ( Quotient + )

So, the Mixed Fraction is ( 1 + ) =

### 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**

Convert the Fraction into an Improper Fraction

**Explanation**

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

Here,

Mixed Fraction =

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.

Hence, =

**Example 2**

Convert the Fraction into an Improper Fraction

**Explanation**

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

Here,

Mixed Fraction =

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.

Hence, =

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**Equivalent Fractions Examples****Fraction in Simplest Form****Like Fractions and Unlike Fractions****Comparing Fractions****Adding Fractions****Subtracting Fractions****Multiplying Fraction****Dividing Fractions**