Informative line

Concept Of Fraction And Its Representation

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.

Illustration Questions

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.

Illustration Questions

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 \(= \dfrac {5}{8}\)

Illustration Questions

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 = \(\dfrac{4}{9}\)

 

image

Hence, option (A) is correct.

image

What fraction of the square is shaded?

image
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 \( =\dfrac{3}{4}\)

Illustration Questions

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.

image

In option (B),

Number of shaded parts \(= 1\)

Total number of parts \(= 4\)

\(\therefore\) Fraction \(= \dfrac{1}{4}\)

Hence, option (B) is incorrect.

image

In option (C),

Number of shaded parts \(= 2\)

Total number of parts \(= 5\)

\(\therefore\) Fraction \(= \dfrac{2}{5}\)

Hence, option (C) is correct.

image

In option (D),

Number of shaded part \(= 1\)

Total number of parts \(= 8\)

\(\therefore\) Fraction \(= \dfrac{1}{8}\)

Hence, option (D) is incorrect.

image

Which one of the following figures' shaded parts represents the fraction \(\dfrac{2}{5}\)?

A image
B image
C image
D image

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.

Illustration Questions

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 \(= \dfrac{4}{7}\)

Illustration Questions

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 \( = 13\)

image

Thus, fraction for the triangular shaped chocolates \( = \dfrac{7}{13}\)

image

Hence, option (D) is correct.

image

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

image
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]

Illustration Questions

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.

image

In option (B),

Mangoes = \(2\)

Total fruits = \(9\)

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

Hence, option (B) is correct.

image

For option (C),

Mangoes = \(3\)

Total fruits = \(8\)

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

Hence, option (C) is incorrect.

image

For option (D),

Mangoes = \(2\)

Total fruits = \(8\)

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

Hence, option (D) is incorrect.

image

Consider the given four baskets of fruits. Which one of them represents mangoes as \(2/9\)?

A image
B image
C image
D image

Option B is Correct

Practice Now