**Fractions**

Types of Fractions

** Fraction:**

A **fraction** is a quantity that expresses **a part of the whole**.

** Example :**

Suppose we divide a rectangle into **4 equal parts and colour 1 part**.

** Terms of a fraction**

**Simplest form of the fraction**

** Definition: **If numerator and denominator have only one common factor that
is
1, then that form is the simplest form of the fraction.

** Example :**

**Answer:**

**Note: To get the simplest form divide numerator and denominator by the greatest common factor.**

Divide numerator and denominator by 7.

Now, 4 and 5 donâ€™t have any common factor other than 1.

So,There are different types of fractions. Letâ€™s learn the following types of fractions:

Unit Fractions

A fraction with numerator 1 is known as a unit fraction.

** Example :**

All the fractions have numerator 1. So all of these are unit fractions.

Proper Fractions

A fraction with its numerator smaller than its denominator is known as a proper fraction.

** Example :**

Here, 5 < 8, 3 < 8, 2 < 6

Each numerator is smaller than its denominator. Hence, all of these are proper fractions.

Improper Fractions

A fraction with numerator greater than or equal to its denominator is known as an Improper fraction.

** Example :**

Each circle is divided into 8 parts, in which 11 parts are coloured.

Here, 11 > 8 → Numerator is greater than the denominator.

Each hexagon is divided into 6 parts, in which 12 parts are coloured.

Here, 12 > 6 → Numerator is greater than the denominator.

Mixed Fractions

Sum of a whole number and a proper fraction is known as a mixed fraction.

** Example :**

In the above example, each circle is divided into 8 parts and there 17 parts are coloured. So, we can write above example in the form of Improper fraction as:

**Conversion of improper fractions into mixed fractions**

**Step 1:** Divide numerator by denominator.

**Step 2:** Write the quotient as a whole number.

**Step 3:** Write remainder as numerator.

**Step 4:** Keep the denominator as it is.

** Example :**

**Answer:**

**Step 1:** Divide numerator by denominator.

**Step 2:** Write the quotient as a whole number.

**Step 3:** Write remainder as numerator.

**Step 4:** Keep the denominator as it is.

**Conversion of mixed fractions into improper fractions**

We know that,

Dividend = Divisor Ă— Quotient + Remainder.

Follow the steps to convert mixed fraction into improper fraction.

**Step 1:** Find the numerator of the improper fraction by using:

Denominator Ă— whole number + numerator.

This will be our numerator of the improper fraction.

**Step 2:** Keep the denominator as it is.

** Example :**

**Answer:**

**Step 1:** Denominator Ă— whole number + numerator.

4 Ă— 7 + 3 = 28 + 3 = 31

So, 31 is our numerator of the improper fraction.

**Step 2:** Keep the denominator as it is.

We got the correct answer.

Equivalent Fractions

Fractions that have different numerators and denominators but their simplest form is the same are called equivalent fractions.

** Example :**

All above fractions are equivalent fractions as they represent the half part of the circle.

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Simplest form of

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Like Fractions

Fractions that have the same denominator are called like fractions.

** Example :**

All fractions have the same denominator as 6. So, all of these are like fractions.

Unlike fractions

Fractions that have different denominators are called unlike fractions

** Example :**

All fractions have different denominators. So, these are unlike fractions.