Informative line

# Representation of Fraction

• A fraction consists of two numbers.
• Both numbers are separated by a line known as fraction bar.
• One number is written at the top of the fraction bar.
• Another number is written at the bottom of the fraction bar.

For example:

$$\dfrac{1}{2}, \; \dfrac{2}{3}, \;\dfrac{5}{6}, \; \dfrac{1}{3}$$ etc are fractions.

#### Which one of the following options represents a fraction?

A $$2.5$$

B $$10$$

C $$\dfrac{3}{2}$$

D 4

×

A fraction has two numbers, separated by a line known as fraction bar.

In option (C), i.e., $$\dfrac{3}{2}$$

$$3$$ and $$2$$ are separated by a line.

$$\therefore$$ $$\dfrac{3}{2}$$ is a fraction.

Hence, option (C) is correct.

### Which one of the following options represents a fraction?

A

$$2.5$$

.

B

$$10$$

C

$$\dfrac{3}{2}$$

D

4

Option C is Correct

# Numerator of a Fraction

• A fraction consists of two numbers.
• Both numbers are separated by a line known as fraction bar.
• The number at the top of the fraction bar is called numerator.

For example:

In fraction $$\dfrac{1}{2},$$ $$1$$ is the numerator of the fraction.  #### Which one of the following fractions has $$5$$ as the numerator?

A $$\dfrac{1}{2}$$

B $$\dfrac{5}{3}$$

C $$\dfrac{1}{6}$$

D $$\dfrac{3}{5}$$

×

In a fraction, the number at the top of the fraction bar is called numerator.

Thus, in option (B), i.e., $$\dfrac{5}{3}$$

Numerator = $$5$$

Hence, option (B) is correct.

### Which one of the following fractions has $$5$$ as the numerator?

A

$$\dfrac{1}{2}$$

.

B

$$\dfrac{5}{3}$$

C

$$\dfrac{1}{6}$$

D

$$\dfrac{3}{5}$$

Option B is Correct

# Fraction as a Part of a Whole

•  A fraction is a part of a whole thing.
• If $$\dfrac{1}{b}$$ is a fraction where $$b\neq 0$$, then it shows that the whole thing is divided into $$b$$ equal parts and we have $$1$$ part of it.

Here, $$1$$= numerator, represents number of parts we have, i.e., $$1$$

$$b$$ = denominator, represents whole is divided into $$b$$ equal parts

• A fraction also represents some parts of a figure.
• To understand it easily, let us consider an example:
• Two friends, Ronnie and Robin ordered a pizza which is cut into $$8$$ equal slices.
• Let Ronnie and Robin ate $$3$$ and $$5$$ slices respectively.  Finding their shares in fraction form.

Ronnie's share :

• From the figure,

Total number of slices  = $$8 \leftarrow$$ denominator

Number of slices Ronnie ate $$= 3 \leftarrow$$ numerator

$$\therefore$$ Ronnie's share in fraction from = $$\dfrac{3}{8}$$  Robin's share :

• From the figure,

Total number of slices $$= 8 \leftarrow$$ denominator

Number of slices Robin ate $$= 5 \leftarrow$$ numerator

$$\therefore$$ Robin's share in fraction form $$= \dfrac {5}{8}$$  #### What fraction of the square is shaded?

A $$\dfrac{4}{9}$$

B $$\dfrac{5}{9}$$

C $$\dfrac{1}{9}$$

D $$\dfrac{7}{9}$$

×

Total number of parts = $$9 \leftarrow$$ denominator

Number of shaded parts = $$4 \leftarrow$$ numerator

Fraction of the shaded part = $$\dfrac{4}{9}$$ Hence, option (A) is correct. ### What fraction of the square is shaded? A

$$\dfrac{4}{9}$$

.

B

$$\dfrac{5}{9}$$

C

$$\dfrac{1}{9}$$

D

$$\dfrac{7}{9}$$

Option A is Correct

# Fraction as a Part of a Whole

•  A fraction is a part of a whole thing.
• If $$\dfrac{1}{b}$$ is a fraction where $$b\neq 0$$, then it shows that the whole thing is divided into $$b$$ equal parts and we have $$1$$ part of it.

Here, $$1$$= numerator, represents number of parts we have, i.e., $$1$$

$$b$$ = denominator, represents whole is divided into $$b$$ equal parts

• A fraction also represents some parts of a figure.
• To understand it easily, let us consider an example:
• Ana buys a chocolate cake to celebrate Sara's birthday.
• Sara cuts the cake into $$4$$ equal slices, as shown in the figure.
• Let Sara and Ana ate $$1$$ and $$3$$ slices respectively.  Finding their shares in fraction form,

Sara's share in cake:

Here, number of slices Sara ate $$= 1$$

Total number of slices $$= 4$$

$$\therefore$$ Sara's share in fraction form $$=\dfrac{1}{4}$$  Ana's share in cake:

Here, number of slices Ana ate $$= 3$$

Total number of slices $$= 4$$

$$\therefore$$ Ana's share in fraction form $$=\dfrac{3}{4}$$  #### Which one of the following figures' shaded parts represents the fraction $$\dfrac{2}{5}$$?

A B C D ×

Given fraction $$= \dfrac{2}{5}$$

The fraction $$\dfrac{2}{5}$$ represents

Shaded parts $$= 2$$

Total parts $$= 5$$

In option (A),

Number of shaded parts $$= 2$$

Total number of parts $$= 4$$

$$\therefore$$ Fraction $$= \dfrac{2}{4}$$

Hence, option (A) is incorrect. In option (B),

Number of shaded parts $$= 1$$

Total number of parts $$= 4$$

$$\therefore$$ Fraction $$= \dfrac{1}{4}$$

Hence, option (B) is incorrect. In option (C),

Number of shaded parts $$= 2$$

Total number of parts $$= 5$$

$$\therefore$$ Fraction $$= \dfrac{2}{5}$$

Hence, option (C) is correct. In option (D),

Number of shaded part $$= 1$$

Total number of parts $$= 8$$

$$\therefore$$ Fraction $$= \dfrac{1}{8}$$

Hence, option (D) is incorrect. ### Which one of the following figures' shaded parts represents the fraction $$\dfrac{2}{5}$$?

A B C D Option C is Correct

# Denominator of a Fraction

• A fraction consists of two numbers.
• Both numbers are separated by a line known as fraction bar.
• The number at the bottom of the fraction bar is called denominator.

For example:

In fraction $$\dfrac{1}{2}$$$$2$$ is the denominator.  #### Which one of the following fractions has $$8$$ as the denominator?

A $$\dfrac{8}{2}$$

B $$\dfrac{1}{5}$$

C $$\dfrac{2}{7}$$

D $$\dfrac{9}{8}$$

×

In a fraction, the number at the bottom of the fraction bar is called denominator.

Thus, in option (D), i.e., $$\dfrac{9}{8}$$

Denominator $$= 8$$

Hence, option (D) is correct.

### Which one of the following fractions has $$8$$ as the denominator?

A

$$\dfrac{8}{2}$$

.

B

$$\dfrac{1}{5}$$

C

$$\dfrac{2}{7}$$

D

$$\dfrac{9}{8}$$

Option D is Correct

# Fraction as a Part of a Group

• A fraction also represents a part of a group of things.
• To understand it easily, let us consider an example:
• Tara and Alia, go to the market. They buy a packet of muffins from Uncle John's bakery. There are total $$7$$ muffins in the packet.
• Tara takes $$3$$ muffins and gives $$4$$ muffins to Alia.
• The figure shows a packet of $$7$$ muffins.
• Tara's share in muffins $$= 3$$
• Alia's share in muffins $$= 4$$
• Total muffins $$= 7$$  Finding their shares in fraction form,

Tara's share in fraction form:

Tara has $$3$$ muffins out of $$7$$.

$$\therefore$$ Fraction $$= \dfrac{3}{7}$$

Alia's share in fraction form:

Alia has $$4$$ muffins out of $$7$$.

$$\therefore$$ Fraction $$= \dfrac{4}{7}$$

#### A basket contains two different shapes of chocolates – triangular and round. Determine the fraction of the triangular shaped chocolates.

A $$\dfrac{6}{13}$$

B $$\dfrac{7}{6}$$

C $$\dfrac{6}{7}$$

D $$\dfrac{7}{13}$$

×

In the given figure,

Triangular shaped chocolates $$= 7$$

Round shaped chocolates $$= 6$$

Total chocolates $$= 13$$ Thus, fraction for the triangular shaped chocolates $$= \dfrac{7}{13}$$ Hence, option (D) is correct. ### A basket contains two different shapes of chocolates – triangular and round. Determine the fraction of the triangular shaped chocolates. A

$$\dfrac{6}{13}$$

.

B

$$\dfrac{7}{6}$$

C

$$\dfrac{6}{7}$$

D

$$\dfrac{7}{13}$$

Option D is Correct

# Fraction as a Part of a Group

• A fraction can also be represented by a part of a group of things.
• To understand it easily, let us consider an example:
• Cherri and Monica are plucking tea leaves from a tea garden. They have plucked  $$11$$ green tea leaves. There are $$5$$ long leaves and $$6$$ short leaves.
• Cherri takes long leaves while Monica takes short ones.
• The figure shows a basket of leaves.
• Number of long leaves = $$5$$
• Number of short leaves = $$6$$
• Total leaves = $$11$$  Finding their shares in fraction form,

Cherri's share of leaves in fraction form:

Here, Cherri takes $$5$$ out of $$11$$ leaves.

$$\therefore$$ Cherri's share in fraction form = $$\dfrac{5}{11}$$

[As shown in figure]  Monica's share of leaves in fraction form:

Here, Monica takes $$6$$ out of $$11$$ leaves.

$$\therefore$$ Monica's share in fraction from = $$\dfrac{6}{11}$$

[As shown in figure]  #### Consider the given four baskets of fruits. Which one of them represents mangoes as $$2/9$$?

A B C D ×

For mangoes' fraction to be $$2/ 9$$:

Number of mangoes should be $$2$$, while total number of fruits in the basket should be $$9$$.

In option (A),

Mangoes = $$2$$

Total fruits = $$10$$

Thus, the fraction of mangoes = $$\dfrac{2}{10}$$

Hence, option (A) is incorrect. In option (B),

Mangoes = $$2$$

Total fruits = $$9$$

Thus, the fraction of mangoes = $$\dfrac{2}{9}$$

Hence, option (B) is correct. For option (C),

Mangoes = $$3$$

Total fruits = $$8$$

Thus, the fraction of mangoes = $$\dfrac{3}{8}$$

Hence, option (C) is incorrect. For option (D),

Mangoes = $$2$$

Total fruits = $$8$$

Thus, the fraction of mangoes = $$\dfrac{2}{8}$$

Hence, option (D) is incorrect. ### Consider the given four baskets of fruits. Which one of them represents mangoes as $$2/9$$?

A B C D Option B is Correct