**Fractions**

A fraction represents a part of the whole. In a
fraction, the top number is called the numerator and the
bottom number is called the denominator. In ¾, 3 is
the numerator and 4 is the denominator.

Remember that the numerator tells us the number of parts taken
while the denominator tells us the total number of parts that the whole number
is divided into.

##
**Types
of Fractions**

There are mainly three types of fractions:

1.
Proper fractions

2.
Improper fractions

3.
Mixed fractions

We have two other types of fractions as follows:

1.
Like fractions

2.
Unlike fractions

**Proper Fractions**

Fractions in which the numerator is smaller
than the denominator are called the proper fractions. A proper fraction is a
part of a whole. For example,

^{1}⁄_{2 },^{3}⁄_{4 },^{5}⁄_{9 },^{11}⁄_{13}**Improper Fractions**

Fractions in which the numerator is greater
than the denominator are called the improper fractions. They are greater than a
whole. For example,

^{7}⁄_{5},^{9}⁄_{5}**Mixed Fractions **

###
When we combine a whole number and a proper fraction together, we get a mixed fraction. For example, 2^{1}⁄_{2 }, 5^{3}⁄_{4 }

^{1}⁄

_{2 }, 5

^{3}⁄

_{4 }

**Converting Improper Fractions into Mixed Fractions**

###
To convert ^{7}⁄_{5 }into mixed
fraction, divide the numerator by the denominator. Write the quotient as the
whole number, remainder as the numerator and divider as the denominator. Thus, ^{7}⁄_{5 } = 1^{2}⁄_{5}

^{7}⁄

_{5 }into mixed fraction, divide the numerator by the denominator. Write the quotient as the whole number, remainder as the numerator and divider as the denominator. Thus,

^{7}⁄

_{5 }= 1

^{2}⁄

_{5}

**Converting Mixed Fractions into Improper Fractions**

###
To convert ^{7}⁄_{5 }into improper
fraction, multiply the denominator with the whole number and add the product
with numerator and write the denominator as it is.
Thus, 2^{1}⁄_{2 }= (2 × 2 + 1)/2 = 5/2

^{7}⁄

_{5 }into improper fraction, multiply the denominator with the whole number and add the product with numerator and write the denominator as it is.

^{1}⁄

_{2 }= (2 × 2 + 1)/2 = 5/2

**Like Fractions**

**All those fractions whose denominators are the same are called like fractions. For example, 1/7, 3/7, 4/7, 6/7, etc. are all like fractions.**

**Unlike Fractions**

**All those fractions whose denominators are not the same are called unlike fractions. For example, 1/2, 5/8, 3/4, 9/16, etc. are all unlike fractions.**

**Converting Unlike Fractions into Like
Fractions**

**To convert 1/2, 5/8, 3/4, 9/16, in like fractions, we first find the LCM of the denominators of all the unlike fractions, i.e., 2, 8, 4 and 16.**

**LCM of 2, 8, 4 and 16 = 16**

**Now, find the equivalent fractions for all the fractions with denominator 16.**

**1/2 = 1 × 8 / 2 × 8 = 8/16**

**5/8 = 5 × 2 / 8 × 2 = 10/16**

**3/4 = 3 × 4 / 4 × 4 = 12/16**

**9/16 = 9 × 1 / 16 × 1 = 9/16**

**Thus, 8/16, 10/16, 12/16 and 9/16 are like fractions.**

##
Equivalent Fractions

Two or more than two fractions are said to be equivalent if both have
the same value after simplification. Let us say, a/b and c/d are two fractions,
if after simplification they both result in equal fraction, say e/f, then they are
equivalent to each other.

For example, 1/3 and 5/15 are the equivalent fractions, because if
we simplify 5/15, its value is the same as 1/3. Similarly, 1/2 and 2/4 are also
the equivalent fractions.

**The biggest question here can be, why do they have equal values in spite of having different number?**

The answer to this question is that, as the numerator and
denominator are not co-prime numbers, therefore they have a common multiple
which on division gives an exactly the same value.

**Take for an example:**

1/2 = 2/4 = 4/8

But, it is clearly seen that the above fractions have different numbers
as numerators and denominators.

Dividing both numerator and denominator by their common factor, we
have:

4/8 = 4÷4 / 8÷4 = 1/2

In the same way, if we simplify 2/4, we again get 1/2.

2/4 = 2÷2 / 4÷2 = 1/2

Here’s an example of equivalent fractions.

**How to find equivalent
fractions?**

By multiplying
the numerator and the denominator of a fraction by the same non-zero whole
number, we can get an equivalent fraction. But it will not change its value.
Equivalent fractions may look different, but they have the same value. Let's
look at some more examples of equivalent fractions.

**For example:**to find equivalent fraction of 2/3, we multiply both the numerator and the denominator by 2, then we get equivalent fraction 4/6.

Again to find one more equivalent fraction of
2/3, we multiply both the numerator and the denominator by 3, then we get
equivalent fraction 6/9.

Similarly, we can multiply both the numerator
and the denominator by 2, 3, 4, 5, 6, etc. to get equivalent fractions of
a given fraction.

**How to check two or more
fractions are equivalent fractions?**

Simplify all fractions. If they reduce to be
the same fraction, then the fractions are equivalent.

**For example:**Check the fractions 6/15 and 10/50 are equivalent or not.

We will simplify both the fractions-

6÷3 / 15÷3 =
2/5

10÷10 / 50÷10 =
1/5

The fractions 2/5 and 1/5 are not the same, hence fractions are not equivalent.

**Use cross-multiplication to check two fractions are equivalent or not**

The products are equal. Therefore, the fractions are
equivalent.

**Lowest Form of a Fraction **

A fraction is said to be in its lowest form if
the only common factor of the numerator and the denominator is 1.

For example, /3, 2/5, 3/7, 4/9, etc. are in their lowest forms.

**Reducing a Fraction to its Lowest Form **

A
fraction can be reduced to its lowest form by dividing both the numerator and
the denominator by a common factor.

**Example:**Reduce 45/75 to its lowest form.

**Solution:**

(45 ÷ 3)/(75 ÷ 3) = 15/25

But 15/25 is not in its lowest form, so repeat the process till
the numerator and the denominator have no common factor except 1.

15/25 = (15 ÷ 5)/(25 ÷ 5) = 3/5

Therefore, the lowest form of 45/75 is 3/5 .