Informative line

# 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.  #### 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): 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): 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): 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): 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? A B C D 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.

#### 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.

#### 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. 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. 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. 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. ### 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 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.

#### 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.  #### 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. 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. 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. 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. ### 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 Option C is Correct