Fractions

(i) We know that,

A fraction is a number which represents part of a whole.

Here, the whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

2 parts are shaded out of 4 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be 2/4.

(ii) We know that,

A fraction is a number which represents part of a whole.

Here, the whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

8 parts are shaded out of 9 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be 8/9

(iii) We know that,

A fraction is a number which represents part of a whole.

Here,

The whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

4 parts are shaded out of 8 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be

(iv) We know that,

A fraction is a number which represents part of a whole.

Here,

The whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

1 parts are shaded out of 4 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be

(v) We know that,

A fraction is a number which represents part of a whole.

Here,

The whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

3 parts are shaded out of 7 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be

(vi) We know that,

A fraction is a number which represents part of a whole.

Here,

The whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

3 parts are shaded out of 12 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be

(vii) We know that,

A fraction is a number which represents part of a whole.

Here,

The whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

10 parts are shaded out of 10 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be or

(viii) We know that,

A fraction is a number which represents part of a whole.

Here,

The whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

4 parts are shaded out of 9 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be

(ix) We know that,

A fraction is a number which represents part of a whole.

Here,

The whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

4 parts are shaded out of 8 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be

(x) We know that,

A fraction is a number which represents part of a whole.

Here,

The whole may be a single object or a group of objects.

Now,

We can observe in the given figure that,

1 parts are shaded out of 2 equal parts

Hence,

We can conclude that,

The fraction representing the shaded portion would be

(i) We have,

Fraction representing the shade portion as

Now,

We can see that,

The figure is divided into 6 equal parts.

Hence,

According to the question,

Any of the one part needs to be shaded out of 6 equal parts.

Thus, the figure can be redrawn as:

(ii) We have,

Fraction representing the shade portion as

Now,

We can see that,

The figure is divided into 4 equal parts.

Hence,

According to the question,

Any of the one part needs to be shaded out of 4 equal parts.

Thus, the figure can be redrawn as:

(iii) We have,

Fraction representing the shade portion as

Now,

We can see that,

The figure is divided into 3 equal parts.

Hence,

According to the question,

Any of the one part needs to be shaded out of 3 equal parts.

Thus, the figure can be redrawn as:

(iv) We have,

Fraction representing the shade portion as

Now,

We can see that,

The figure is divided into 4 equal parts.

Hence,

According to the question,

Any of the three parts needs to be shaded out of 4 equal parts.

Thus, the figure can be redrawn as:

(v) We have,

Fraction representing the shade portion as

Now,

We can see that,

The figure is divided into 9 equal parts.

Hence,

According to the question,

Any of the four parts needs to be shaded out of 9 equal parts.

Thus the figure can be redrawn as:

We know that,

A fraction is a number which represents part of a whole and the parts needs to be equally divided.

Here,

The whole may be a single object or a group of objects.

But we can see that,

Among the given shape, not a single shape is divided into equal parts.

Hence,

The given figures do not represent the fractions.

We know that,

There are in all 24 hours in a day.

Now,

We are required to represent 8 hours out of those 24 hours.

Hence,

The fraction of 8 hours in a day can be represented as:

We know that,

There are in all sixty minutes in an hour.

Now,

We need to represent 40 minutes out of those 60 minutes.

Hence,

The fraction of 40 minutes in a day can be represented as

(a) We know that,

Arya has brought two sandwiches, one made of vegetable and the other of jam.

Therefore,

To divide both the sandwiches equally among them,

He will divide each sandwich into three equal parts.

Then,

He will give one part of each sandwich to each one of them.

(b) Since,

We know that each sandwich is divided into three equal parts.

Hence,

Each boy will get part of each sandwich.

According to the question:

Number of Dresses dyed so far = 20

Total number of dresses = 30

Hence,

The fraction of dresses that she has finished =

At first,

Natural numbers from 2 to 12 are as follows:

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Now,

Prime numbers among them are:

2, 3, 5, 7, 11

Hence,

There are total 5 prime numbers out of 11 natural numbers.

Therefore,

The required fraction is

At first,

Natural numbers from 102 to 113 are as follows:

102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113

Now,

Prime numbers among them are:

103, 107, 109, 113

Hence,

There are total 4 prime numbers out of 12 natural numbers.

Therefore,

The required fraction is

We can see that,

There are in all 8 circles given in the question.

And,

4 circles among them has X in them.

Hence,

According to the question,

The fraction representing the X circles is 4/8.

According to the question,

Total number of CDs that Kristin had on her birthday = 3 + 5

= 8

Now,

Among those 8 CD,

3 CDs were bought by her

And,

5 CDs were gifted to her on her birthday.

Hence,

She bought and received CDs as gifts in fraction as respectively.

(a) The given points can be located on the number line as follows:

(b)The given points can be located on the number line as follows:

(c) The given points can be located on the number line as follows:

(a) We know that,

A mixed fraction is a whole number and a fraction which is combined into one ‘mixed’ number.

Now,

We can write the given fraction as mixed fraction as follows:

(b) We know that,

A mixed fraction is a whole number and a fraction which is combined into one ‘mixed’ number.

Now,

We can write the given fraction as mixed fraction as follows:

(c) We know that,

A mixed fraction is a whole number and a fraction which is combined into one ‘mixed’ number.

Now,

We can write the given fraction as mixed fraction as follows:

(d) We know that,

A mixed fraction is a whole number and a fraction which is combined into one ‘mixed’ number.

Now,

We can write the given fraction as mixed fraction as follows:

(e) We know that,

A mixed fraction is a whole number and a fraction which is combined into one ‘mixed’ number.

Now,

We can write the given fraction as mixed fraction as follows:

(f) We know that,

A mixed fraction is a whole number and a fraction which is combined into one ‘mixed’ number.

Now,

We can write the given fraction as mixed fraction as follows:

(a) We know that,

A fraction in which the numerator is greater than the denominator is known as an improper fraction.

Now,

The given mixed fraction can be converted into improper fraction as follows:

7

(b) We know that,

A fraction in which the numerator is greater than the denominator is known as an improper fraction.

Now,

The given mixed fraction can be converted into improper fraction as follows:

5

(c) We know that,

A fraction in which the numerator is greater than the denominator is known as an improper fraction.

Now,

The given mixed fraction can be converted into improper fraction as follows:

2

(d) We know that,

A fraction in which the numerator is greater than the denominator is known as an improper fraction.

Now,

The given mixed fraction can be converted into improper fraction as follows:

10

(e) We know that,

A fraction in which the numerator is greater than the denominator is known as an improper fraction.

Now,

The given mixed fraction can be converted into improper fraction as follows:

9

(f) We know that,

A fraction in which the numerator is greater than the denominator is known as an improper fraction.

Now,

The given mixed fraction can be converted into improper fraction as follows:

8

(a) We can see that,

In the given circles,

One out of two,

Two out of four,

Three out of six,

And,

Four out of eight

Equal parts are shaded respectively.

Hence,

These circles represent.

Also, these fractions are equivalent

(b) We can see that,

In the given circles,

One out of two,

Two out of four,

Three out of six,

And,

Four out of eight

Equal parts are shaded respectively

Hence,

These circles represent

We see, not all these fractions are equivalent.

(a) Here,

The figure is divided into two equal parts

And,

One part is shaded out of these two parts

Hence,

We can conclude that,

The figure represents a fraction of 1/2.

(b) Here,

The figure is divided into six equal parts

And,

Four parts are shaded out of these six parts

Hence,

We can conclude that,

The figure represents a fraction of 4/6 or 2/3

(c) Here,

The figure is divided into nine equal parts

And,

Three parts are shaded out of these nine parts

Hence,

We can conclude that,

The figure represents a fraction of

(d) Here,

The figure is divided into eight equal parts

And,

Two parts are shaded out of these eight parts

Hence,

We can conclude that,

The figure represents a fraction of .

(e) Here,

The figure is divided into four equal parts

And,

Three parts are shaded out of these four parts

Hence,

We can conclude that,

The figure represents a fraction of 3/4

i. Here,

The figure is divided into eighteen equal parts

And,

Six parts are shaded out of these eighteen parts

Hence,

We can conclude that,

The figure represents a fraction of

ii. Here,

The figure is divided into eight equal parts

And,

Four parts are shaded out of these eight parts

Hence,

We can conclude that,

The figure represents a fraction of

iii. Here,

The figure is divided into sixteen equal parts

And,

Twelve parts are shaded out of these sixteen parts

Hence,

We can conclude that,

The figure represents a fraction of

iv. Here,

The figure is divided into twelve equal parts

And,

Eight parts are shaded out of these twelve parts

Hence,

We can conclude that,

The figure represents a fraction of

v. Here,

The figure is divided into sixteen equal parts

And,

Four parts are shaded out of these sixteen parts

Hence,

We can conclude that,

The figure represents a fraction of

(a) We can calculate the following as follows:

Hence,

28 is the required blank

(b) We can calculate the following as follows:

Hence,

16 is the required blank

(c) We can calculate the following as follows:

Hence,

12 is the required blank

(d) We can calculate the following as follows:

Hence,

20 is the required blank

(e) We can calculate the following as follows:

Hence,

3 is the required blank

(a)

3× 20 = 5× ?

3 × 2 × 2 × 5 = 5 × ?

12 = ?

Hence,

The required fraction is

(b)

3× ? = 5× 9

5 × 3 × 3 = 3 × ?

15 = ?

Hence,

The required fraction is

(c)

3× 30 = 5× ?

3 × 2 × 3 × 5 = 5 × ?

18 = ?

Hence,

The required fraction is

(d)

3× ?= 5× 27

5 × 3 × 3 × 3= 3 × ?

45 = ?

Hence,

The required fraction is

(a)

36 × = 48 × 9

2 × 2 × 3 × 3 × …= 3 × 2 × 2 × 3 × 3 × 2 × 2

12 =

Hence,

The required fraction is

(b)

36 × 4 = 48 ×

2 × 2 × 3 × 3 × 2 × 2 = 2 × 2 × 3 × 2 × 2

3 =

Hence,

The required fraction is

(a) At first, check if the two given pairs are equivalent,

We will do following steps:

Hence,

We can clearly observe that,

Both the given pairs are equivalent

(b) At first, check if the two given pairs are equivalent,

We will do following steps:

Hence,

We can clearly observe that,

The given pair of fractions is not equivalent

(c) At first, check if the two given pairs are equivalent,

We will do following steps:

Hence,

We can clearly observe that,

The given pair of fractions is not equivalent

(a) To reduce the fraction to its simplest form,

We will follow the following steps:

Hence,

We can clearly observe that

is the simplest fraction

(b) In order to reduce the fraction to its simplest form,

We will follow the following steps:

Hence,

We can clearly observe that

is the simplest fraction

(c) In order to reduce the fraction to its simplest form,

We will follow the following steps:

Hence,

We can clearly observe that

is the simplest fraction

(d) In order to reduce the fraction to its simplest form,

We will follow the following steps:

Hence,

We can clearly observe that

is the simplest fraction

(e) In order to reduce the fraction to its simplest form,

We will follow the following steps:

Hence,

We can clearly observe that

is the simplest fraction.

We have,

Pencils with Ramesh = 20

Pencils used by Ramesh = 10

Fractions of pencils used by Ramesh =

Pencils with Sheelu = 50

Pencils used by Sheelu = 25

Fractions of pencils used by Sheelu =

Pencils with Jamaal = 80

Pencils used by Jamaal = 40

Fractions of pencils used by Jamaal =

Therefore,

Yes, all of them used equal fraction of pencils i.e. =

i. We have,

Hence,

(i) and (d) are pairs

Two more fractions are:

ii. We have,

Hence,

(ii) and (e) are pairs

Two more fractions are:

iii. We have,

Hence,

(iii) and (a) are pairs.

Two more fractions are:

iv. We have,

Hence,

(iv) and (c) are pairs.

Two more fractions are:

v. We have,

Hence,

(v) and (b) are pairs.

Two more fractions are:

(a) In the first diagram,

First circle represents 3 shaded portions out of 8 equal parts

Therefore,

It is in the fraction

In the second circle, there are 6 shaded parts out of 8 equal parts

Therefore,

It is in the fraction

In the third circle, there are 4 shaded parts out of 8 equal parts

Therefore,

It is in the fraction

In the fourth circle, there are 1 shaded part out of 8 equal parts

Therefore,

It is in the fraction

We can arrange these fractions as follows:

(b) In the above given diagram, we have:

In the first square, there are 8 shaded portions out of 9 equal parts

Therefore,

It is in the fraction

In the second square, there are 4 shaded portions out of 9 equal parts

Therefore,

It is in the fraction

In the third square, there are 3 shaded portions out of 9 equal parts

Therefore,

It is in the fraction

In the fourth square, there are 6 shaded portions out of 9 equal parts

Therefore,

It is in the fraction

We can arrange these fractions as follows:

< < <

(c) We need to represent in a number line. These can be represented as follows:

Therefore,

>

> 0

<

>

(a) In the above given numbers, both having same denominator

Therefore, the fraction having greater numerator will be greater

Hence,

<

(b) In this question, we will make same denominator of both the fraction

Therefore,

=

Also,

=

Therefore, the fraction having greater numerator will be greater

Hence,

<

(c) In the above given numbers, both having same denominator

Therefore, the fraction having greater numerator will be greater

Hence,

<

(d) In the above given numbers, both having same numerator

Therefore, the fraction having lesser denominator will be greater

Hence,

(i)

In this question we have,

The denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

Therefore,

<

(ii)

In this question we have,

The numerator of both the fractions are equal

Hence, fraction having lesser denominator will be greater

Therefore,

<

(iii)

In this question, we have

The denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

Therefore,

>

(iv)

In this question, we have

The denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

Therefore,

<

(v)

In this question, we have

The denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

Therefore,

>

(a) In this question, we have

The numerator of both the fractions are equal

Hence, fraction having lesser denominator will be greater

Therefore,

<

(b) In this question first of all we have to make same denominator of both the fractions:

=

Also,

=

Now, the denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

As, 9 > 4

Therefore,

>

(c) In this question we have

The numerator of both the fractions are equal

Hence, fraction having lesser denominator will be greater

Therefore,

>

(d) In this question, we have

= 1

Also,

= 1

Therefore,

1 = 1

Hence,

=

(e) In this question we have

The numerator of both the fractions are equal

Hence, fraction having lesser denominator will be greater

Therefore,

<

(a) In this question, we have

The numerator of both the fractions are equal

Hence, fraction having lesser denominator will be greater

Therefore,

>

(b) In this question, we have

=

Also,

=

As, =

Therefore,

=

(c) In this question first of all we have to make same denominator of both the fractions:

=

Also,

=

Now, the denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

As, 9 < 10

Therefore,

<

(d) In this question we have,

=

Now, the denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

Therefore,

>

(e) In this question we have,

Denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

Therefore,

<

(f) In this question we have,

Denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

Therefore,

>

(g) In this question, we have

=

Therefore,

(h) In this question we have,

=

Now, the denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

As, 3 < 4

Therefore,

<

(i) In this question, firstly wehave to make same denominators

=

Now, the denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

As, 6 < 7

Therefore,

<

(j) In this question we have,

=

Now, the denominators of both the fractions are equal

Hence, fraction having greater numerator will be greater

Therefore,

<

(k) In this question, we have

=

As, =

Therefore,

=

(a) In this question, we have

= =

(b) In this question, we have

= =

(c) In this question, we have

= =

(d) In this question, we have

= =

(e) In this question, we have

= =

(f) In this question, we have

= =

(g) In this question, we have

= =

(h) In this question, we have

= =

(i) In this question, we have

= =

(j) In this question, we have

= =

(k) In this question, we have

= =

(l) In this question, we have

In the above solved questions, there are three groups of equivalent fractions:

= (a), (e), (h), (j) and (k)

= (b), (f) and (g)

= (c), (d), (i) and (l)

(a) First of all, we have to convert above given fractions into like fractions:

× =

And,

× =

As,

Therefore,

is not equal to

(b) First of all, we have to convert above given fractions into like fractions:

× =

And,

× =

As,

Therefore,

is not equal to

(c) In this question, we have

= =

Therefore,

=

Hence,

is equal to

(d) In this question, we have

= =

As,

Therefore,

is not equal to

Given in the question that,

Number of pages read by Lalita =

= 2×20
= 40

Also,

Number of pages read by Ila = 25

Hence, Ila has read less number of pages.

It is given in the question that,

Rafiq exercised book for of an hour

Also,

Rohit exercised book for of an hour

Now, to convert these fractions into like fractions:

× =

Also,

× =

Therefore,

>

Hence,

Rohit exercised for a longer time.

It is given in the question that,

From Class A students who passed in first class = =

Also,

From Class B students who passed in first class = =

Therefore, from above results it is clear that in the both the classes equal fraction of students passed in the first class

(a) In the above diagram, it can clearly be observed that:

In the 1^st and 2^nd rectangle there are 1 and 2 shaded portions out of 5 equal parts respectively

Also, the third rectangle represents 3 shaded portions out of 5 equal parts

Therefore,

The fraction represented by the third rectangle is the sum of fraction represented by 1^st and 2^nd rectangle

Hence,

=

(b) In the above diagram, it can clearly be observed that:

In the 1^st and 2^nd circle there are 5 and 3 shaded portions out of 5 equal parts respectively

Also, the third circle represents 2 shaded portions out of 5 equal parts

Therefore,

The fraction represented by the third circle is the difference of fraction represented by 1^st and 2^nd circle

Hence,

=

(c) In the above diagram, it can clearly be observed that:

In the 1^st and 2^nd rectangle there are 2 and 3 shaded portions out of 6 equal parts respectively

Also, the third rectangle represents 5 shaded portions out of 6 equal parts

Therefore,

The fraction represented by the third rectangle is the sum of fraction represented by 1^st and 2^nd rectangle

Hence,

=

(a)

We have,

=

=

=

(b)

We have,

=

=

(c)

We have,

=

=

(d)

We have,

=

=

= 1

(e)

We have,

=

=

=

(f)

We have,

=

=

= 1

(g)

We have,

=

=

=

(h)

We have,

=

=

(i) 3-

We have,

= –

=

=

It is given in the question that,

Space of room painted by Shubham = of the room

Also,

Space of room painted by Madhavi = of the room

Hence,

Total space painted by them together = +

=

=

= 1 complete wall

(a) We have to find the missing space:

Let the missing space be x

Therefore,

- x =

x = –

=

=

=

(b) We have to find the missing space:

Let the missing space be x

Therefore,

x – =

x = +

=

=

(c) We have to find the missing space:

Let the missing space be x

Therefore,

x – =

x = +

=

= 1

(d) We have to find the missing space:

Let the missing space be x

Therefore,

x + =

x = –

=

=

Given in the question that,

Ractions given to Javed =

Therefore,

Total fraction left in the basket =

= –

=

=

(a)

We have,

=

LCM of 3 and 7 is 21.

=

=

(b)

We have,

LCM of 10 and 15 is 30,

=

=

=

(c)

We have,

LCM of 9 and 7 is 63,

=

=

=

(d)

We have,

LCM of 7 and 3 is 21,

=

=

=

(e)

We have,

LCM of 5 and 6 is 30,

=

=

=

(f)

We have,

LCM of 5 and 3 is 15,

=

=

=

(g)

We have,

LCM of 4 and 3 is 12,

=

=

=

(h)

We have,

LCM of 6 and 3 is 12,

=

=

=

=

(i)

We have,

LCM of 3,4,2 is 12,

=

=

=

(j)

We have,

=


LCM of 2,3,6 is 12,

=

=

= 1

(k)

We have,

1 + 3

=

=

=

= 5

(l)

We have,

4 + 3

= +

=

=

=

(m)

We have,

=

=

(n)

We have,

LCM of 3 and 2 is 6,

=

=

=

It is given in the question that,

Length of ribbon bought by Sarita = m

Also,

Length of ribbon bought by Lalita = m

Therefore,

Total length of ribbon bought by them = +

=

=

= m

It is given in the question that,

Fraction got by Naina = 1 =

Also,

Fraction got by Najma = 1 =

Therefore,

Total amount of cake given to them = +

=

=

=

= 2

(a) We have to find the missing space:

Let the missing space be x

Therefore,

x – =

x =

=

=

=

(b) We have to find the missing space:

Let the missing space be x

Therefore,

x – =

x = +

=

=

=

(c) We have to find the missing space:

Let the missing space be x

Therefore,

- x =

x = –

=

=

=

=

(a) We have,

+ = = = 2

= 1

=

=

= 1

Therefore,

The above given number box can be completed as:

(b) We have,

= = =

= = =

= = =

= = =

Also,

= = = =

Therefore, the above given table can be completed as follows:

It is given in the question that,

Length of one piece = m

It is also given that, a piece of wire of length m is being broken into two pieces

Therefore,

Length of the other piece of wire =

=

=

= m

It is given in the question that,

Total distance = km

Distance for which Nandini took bus = km

Therefore,

Distance for which she walked = Total distance – Distance for which Nandini took bus

= –

=

=

=

= km

It is given in the question that,

Fraction of Asha’s shelf =

Fraction of Samuel’s shelf =

Converting these into like fractions, we get

= × =

= × =

Clearly,

>

Therefore, Asha’s shelf is more full

Difference = –

= –

=

It is given in the question that,

Time taken by Jaidev = 2 minutes = minutes

Time taken by Rahul = minutes

Now, by converting these into like fractions we get:

= × =

Also,

= × =

Therefore,

>

>

Hence, Rahul takes lesser time

Difference = –

= –

= min