Informative line

Like And Unlike Fractions

Like Fractions as Parts of One Whole

  • Two or more fractions having the same denominators are called like fractions.

For example:

\(\dfrac{1}{5}\) and \(\dfrac{3}{5}\) are like fractions because they have same denominators \((5)\).

  • Like fractions are parts of one whole.

  • To understand it easily, let us consider an example:
  • Jack ordered a cheese pizza.
  • Let the number of slices he ate = \(3\)
  • Number of slices remaining = \(5\)
  • \(\therefore\) In fraction form
  • Pizza slices eaten = \(\dfrac{3}{8}\)
  • Pizza slices remaining = \(\dfrac{5}{8}\)
  • Here, both the fractions have the same denominators and these are parts of one whole.
  • Thus,  \(\dfrac{3}{8}\) and \(\dfrac{5}{8}\) are like fractions.
  • Therefore, if two or more fractions are parts of one whole then those fractions are like fractions.

Illustration Questions

Which one of the following options shaded parts DOES NOT represent the like fraction of the given figure?

A

B

C

D

×

Given:

Number of equal parts \(=6\)

Number of shaded parts \(=4\)

Fraction of shaded parts \(=\dfrac{4}{6}\)

Option (A):

image

Number of equal parts \(=6\)

Number of shaded parts \(=5\)

Fraction of shaded parts \(=\dfrac{5}{6}\)

\(\because\) The denominator of both the fractions \(\left(\dfrac{4}{6}\;\text{and}\;\dfrac{5}{6}\right)\) are same and they are also the parts of the same whole

\(\therefore\;\dfrac{4}{6}\) and \(\dfrac{5}{6}\) are like fractions.

Hence, option (A) is incorrect.

Option (B):

image

Number of equal parts \(=6\)

Number of shaded parts \(=3\)

Fraction of shaded parts \(=\dfrac{3}{6}\)

\(\because\) The denominator of both the fractions \(\left(\dfrac{4}{6}\;\text{and}\;\dfrac{3}{6}\right)\)  are same and they are also the parts of the same whole

\(\therefore\;\dfrac{4}{6}\) and \(\dfrac{3}{6}\)  are like fractions.

Hence, option (B) is incorrect.

Option (C):

image

Number of equal parts \(=4\)

Number of shaded parts \(=1\)

Fraction of shaded parts \(=\dfrac{1}{4}\)

\(\because\) The denominator of both the fractions \(\left(\dfrac{4}{6}\;\text{and}\;\dfrac{1}{4}\right)\)  are different and they are also not the parts of the same whole

\(\therefore\;\dfrac{4}{6}\) and \(\dfrac{1}{4}\) are not like fractions.

Hence, option (C) is correct.

Option (D):

image

Number of equal parts \(=6\)

Number of shaded parts \(=1\)

Fraction of shaded parts \(=\dfrac{1}{6}\)

\(\because\) The denominator of both the fractions \(\left(\dfrac{4}{6}\;\text{and}\;\dfrac{1}{6}\right)\) are same and they are also the parts of the same whole

\(\therefore\;\dfrac{4}{6}\) and \(\dfrac{1}{6}\) are like fractions.

Hence, option (D) is incorrect.

Which one of the following options shaded parts DOES NOT represent the like fraction of the given figure?

image
A image
B image
C image
D image

Option C is Correct

Like Fractions as Parts of Different Wholes

  • Two or more fractions having the same denominators are called like fractions.

For example: \(\dfrac{1}{2}, \dfrac{3}{2}, \dfrac{5}{2},\dfrac{7}{2}\) are like fractions.

  • Like fractions are also parts of different wholes, which have equal number of parts.
  • To understand it easily, let us consider an example:
  • A fruit seller, Mr. James has \(12\) apples and \(12\) bananas to sell.
  • If he sells,

   Bananas = \(7\)

   Apples = \(5\)

Then,

   Number of bananas sold in fraction form = \(\dfrac{7}{12}\)

   Number of apples sold in fraction form = \(\dfrac{5}{12}\)

\( \dfrac{7}{12}\) and \(\dfrac{5}{12}\) have same denominators.

Thus, these are like fractions.

Note:- In the above example, bananas and apples are different wholes.

Illustration Questions

Which one of the following options represents the like fractions?

A \(3\) cars out of \(5\) and \(1\) pencil out of \(5\)

B \(4\) dusters out of \(5\) and \(4\) sharpeners out of \(7\)

C \(2\) mugs out of \(3\) and \(1\) page out of \(2\)

D \(9 \) bags out of \(20\) and \(6\) slices out of \(29\)

×

If two or more fractions are parts of different wholes and each whole has same number of equal parts, then the fractions are like fractions.

In option (A),

\(3\) cars out of \(5 = \dfrac{3}{5}\)

\(1\) pencil out of \(5 = \dfrac{1}{5}\)

Both the fractions have same denominators.

Thus,  \(\dfrac{3}{5}\) and \(\dfrac{1}{5}\) are like fractions. 

Hence, option (A) is correct.

In option (B),

\(4\) dusters out of \(5 = \dfrac{4}{5}\)

\(4\) sharpeners out of \(7 = \dfrac{4}{7}\)

Both the fractions do not have same denominators.

Thus, \(\dfrac{4}{5}\) and \(\dfrac{4}{7}\) are not like fractions. 

Hence, option (B) is incorrect.

In option (C),

\(2\) mugs out of \(3 = \dfrac{2}{3}\)

One page out of \(2 = \dfrac{1}{2}\)

Both the fractions do not have same denominators.

Thus, \(\dfrac{2}{3}\) and \(\dfrac{1}{2}\) are not like fractions. 

Hence, option (C) is incorrect.

In option (D),

\(9\) bags out of \(20 = \dfrac{9}{20}\)

\(6\) slices out of \(29 = \dfrac{6}{29}\)

Both the fractions do not have same denominators.

Thus,  \(\dfrac{9}{20}\) and \(\dfrac{6}{29}\) are not like fractions. 

Hence, option (D) is incorrect.

Which one of the following options represents the like fractions?

A

\(3\) cars out of \(5\) and \(1\) pencil out of \(5\)

.

B

\(4\) dusters out of \(5\) and \(4\) sharpeners out of \(7\)

C

\(2\) mugs out of \(3\) and \(1\) page out of \(2\)

D

\(9 \) bags out of \(20\) and \(6\) slices out of \(29\)

Option A is Correct

Like Fractions as Parts of Different Wholes

  • Two or more fractions having the same denominators are called like fractions.

For example: \(\dfrac{1}{2}, \dfrac{3}{2}, \dfrac{5}{2},\dfrac{7}{2}\) are like fractions.

  • Like fractions are also parts of different wholes, which have equal number of parts.

  • To understand it easily, let us consider an example:
  • Tina and her cousin Monica, go to Uncle James' bakery.
  • They order for \(2\) plates of garlic bread.
  • Each plate has \(5\) slices of garlic bread.
  • Monica eats \(3\) slices from first plate.
  • Tina eats \(4\) slices from second plate.

Now, finding their shares in fraction form.

 Monica's share:

Number of slices Monica ate = \(3\)

Total number of slices = \(5\)

\(\therefore\) Monica's share in fraction form = \(\dfrac{3}{5}\)    

 Tina's share:

Number of slices Tina ate \( = 4\)

Total number of slices = \(5\)

\(\therefore\) Tina's share in fraction form = \(\dfrac{4}{5}\)    

  • Since, \(\dfrac{3}{5}\) and \(\dfrac{4}{5}\) have same denominators. Thus, these are like fractions.

Note:- If two or more fractions are parts of different wholes and each whole has same number of equal parts, then the fractions are like fractions.

Illustration Questions

In each option, two figures are given. Each figure has some shaded part. Which one of the following options represents the like fractions? 

A

B

C

D

×

In option (A),

Number of equal parts in 

   Figure  (I) = \(2\)

   Figure (II) = \(4\)

Shaded parts in 

   Figure (I) = \(1\)

   Figure (II) = \(1\)

Fraction of the shaded parts 

   For Figure (I) = \(\dfrac{1}{2}\)

   For Figure (II) = \(\dfrac{1}{4}\)

\( \dfrac{1}{4}\) and \(\dfrac{1}{2}\) have different denominators. Thus, these are not like fractions.

Hence, option (A) is incorrect.

image

In option (B),

Number of equal parts in 

   Figure (I) = \(5\)

   Figure (II) = \(4\)

Shaded parts in 

   Figure (I) = \(3\)

   Figure (II) = \(3\)

Fraction of the shaded parts

   For Figure (I) = \(\dfrac{3}{5}\)

   For Figure (II) = \(\dfrac{3}{4}\)

\( \dfrac{3}{5}\) and \(\dfrac{3}{4}\) do not have same denominators. Thus, these are not like fractions.

Hence, option (B) is incorrect.

image

In option (C),

Number of equal parts in 

   Figure (I) = \(8\)

   Figure (II) = \(8\)

Shaded parts in 

   Figure (I) = \(3\)

   Figure (II) = \(5\)

Fraction of the shaded parts 

   For Figure (I) = \(\dfrac{3}{8}\)

   For Figure (II) = \(\dfrac{5}{8}\)

\( \dfrac{3}{8}\) and \(\dfrac{5}{8}\) have same denominators. Thus, these are like fractions.

Hence, option (C) is correct.

image

In option (D),

Number of equal parts in 

   Figure (I) = \(2\)

   Figure (II) = \(4\)

Shaded parts  

   Figure (I) = \(1\)

   Figure (II) = \(3\)

Fraction of the shaded parts 

   For Figure (I) = \(\dfrac{1}{2}\)

   For Figure (II) = \(\dfrac{3}{4}\)

\(\dfrac{1}{2}\) and \(\dfrac{3}{4}\) do not have same denominators. Thus, these are not like fractions.

Hence, option (D) is incorrect.

image

In each option, two figures are given. Each figure has some shaded part. Which one of the following options represents the like fractions? 

A image
B image
C image
D image

Option C is Correct

Unlike Fractions

  • Two or more fractions having different denominators are called unlike fractions.

For example:- \(\dfrac{1}{2},\;\dfrac{1}{3},\; \dfrac{5}{6}\) are unlike fractions.

  • Unlike fractions are parts of different wholes having different number of equal parts.
  • To understand it easily, let us consider an example: 
  • Cherri and her classmate Tina, are participating in a painting competition to be held in their city.
  • They buy a lot of colored pens. 

Cherri buys \(21\) colored pens out of which \(10\) are red.

 Fraction of red colored pens (In case of Cherri) = \(\dfrac{10}{21}\)

Tina buys \(23\) colored pens out of which \(11\) are red.

 Fraction of red colored pens (In case of Tina) = \(\dfrac{11}{23}\)

\( \dfrac{10}{21}\) and \(\dfrac{11}{23}\) have different denominators. Thus, these are unlike fractions.

Illustration Questions

Which one of the following options represents a list of unlike fractions?

A \(\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5}\)

B \(\dfrac{2}{13},\dfrac{4}{13},\dfrac{1}{13},\dfrac{6}{13}\)

C \(\dfrac{2}{15},\dfrac{7}{15},\dfrac{6}{15},\dfrac{1}{15}\)

D \(\dfrac{11}{13},\dfrac{7}{13},\dfrac{6}{13},\dfrac{4}{13}\)

×

Unlike fractions have different denominators.

In option A, i.e., \(\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5}\)

Each of the fractions has different denominator ( \(2,3,4,5\) ).

\(\therefore\) Option (A) represents a list of unlike fractions.

Hence, option (A) is correct.

Which one of the following options represents a list of unlike fractions?

A

\(\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5}\)

.

B

\(\dfrac{2}{13},\dfrac{4}{13},\dfrac{1}{13},\dfrac{6}{13}\)

C

\(\dfrac{2}{15},\dfrac{7}{15},\dfrac{6}{15},\dfrac{1}{15}\)

D

\(\dfrac{11}{13},\dfrac{7}{13},\dfrac{6}{13},\dfrac{4}{13}\)

Option A is Correct

Unlike Fractions Using Models

  • Two or more fractions having different denominators are called unlike fractions.

For example:- \(\dfrac{1}{2},\;\dfrac{1}{3},\; \dfrac{5}{6}\) are unlike fractions.

  • Unlike fractions are parts of different wholes having different number of equal parts.

  • To understand it easily, let us consider an example:
  • Robin buys two different cakes.
  • One is of strawberry flavor and another one is of chocolate flavor.
  • Each cake is cut into different number of slices.
  • Total number of slices of 

   Strawberry cake = \(8\)

   Chocolate cake = \(4\)    

  • Robin eats \(3\) slices of the strawberry cake and \(1\) slice of the chocolate cake.
  • Thus, representation of the part of the cakes eaten is 

   Fraction for strawberry cake = \(\dfrac{3}{8}\)

   Fraction for chocolate cake = \(\dfrac{1}{4}\)

\( \dfrac{3}{8}\) and \(\dfrac{1}{4}\) do not have common denominators. Thus, they are unlike fractions.

Illustration Questions

In each option, two figures are given. Each figure has some shaded parts. Which one of the following options represents the unlike fractions?

A

B

C

D

×

In option (A),

Number of equal parts in 

   Figure (I) = \(4\)

   Figure (II) = \(4\)

Shaded parts in

   Figure (I) = \(1\)

   Figure (II) = \(3\)

Fraction of the shaded part

   For Figure (I) = \(\dfrac{1}{4}\)

   For Figure (II) = \(\dfrac{3}{4}\)

\( \dfrac{1}{4}\) and \(\dfrac{3}{4}\) have common denominators. Thus, they do not represent unlike fractions.

Hence, option (A) is incorrect. 

image

In option (B),

Number of equal parts in 

   Figure (I) = \(8\)

   Figure (II) = \(8\)

Shaded parts in

   Figure (I) = \(3\)

   Figure (II) = \(5\)

Fraction of the shaded part

   For Figure  (I) = \(\dfrac{3}{8}\)

   For Figure (II) = \(\dfrac{5}{8}\)

\( \dfrac{3}{8}\) and \(\dfrac{5}{8}\) have common denominators. Thus, they do not represent unlike fractions.

Hence, option (B) is incorrect. 

image

In option (C),

Number of equal parts in 

   Figure (I) = \(8\)

   Figure (II) = \(4\)

Shaded parts in

   Figure (I) = \(3\)

   Figure (II) = \(3\)

Fraction of the shaded part 

   For Figure (I) = \(\dfrac{3}{8}\)

   For Figure (II) = \(\dfrac{3}{4}\)

\(\dfrac{3}{8}\) and \(\dfrac{3}{4}\) have different denominators. Thus, they represent unlike fractions.

Hence, option (C) is correct.

image

In option (D),

Number of equal parts in 

   Figure (I) = \(6\)

   Figure (II) = \(6\)

Shaded parts in

   Figure (I) = \(1\)

   Figure (II) = \(5\)

Fraction of the shaded part

   For Figure (I) = \(\dfrac{1}{6}\)

   For Figure (II) = \(\dfrac{5}{6}\)

\( \dfrac{1}{6}\) and \(\dfrac{5}{6}\) have common denominators. Thus, they do not represent unlike fractions.

Hence, option (D) is incorrect. 

image

In each option, two figures are given. Each figure has some shaded parts. Which one of the following options represents the unlike fractions?

A image
B image
C image
D image

Option C is Correct

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