What is a mixed number in math?

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Mixed Number: Mixed number commonly known as a mixed fraction is a mathematical expression that comprises a whole number as well as a fraction.

For example:

3\frac{1}{2},4\frac{4}{7},5\frac{8}{9}

Parts of a Mixed Fraction

There are basically three parts of a mixed fraction: whole number, numerator and denominator.

For example: Consider the mixed fraction $7\frac{{23}}{{37}}$

Here, 7 is the whole number and $\frac{{23}}{{37}}$ is a fraction. 23 is the numerator and 37 is the denominator.

It is the other representation form of improper fraction.

Types of fractions

There are mainly two types of fractions:

Proper fraction: A fraction is called proper fraction when numerator is less than denominator. These types of fractions are always less than 1.

For example: $\frac{7}{{10}}$

Here 7 (numerator) is less than 10 (denominator). So, this is termed as proper fraction.

Improper fraction: In a fraction, when numerator is greater than denominator it is known as improper fraction. These types of fractions are always greater than 1.

For example: $\frac{7}{3}$

Here 7 (numerator) is greater than 3 (denominator). So, it is an improper fraction.

Only an improper fraction can be converted into a mixed number and vice versa.

Steps to convert improper fraction to mixed fraction or number?

Follow these steps to convert improper fraction into a mixed number.

Step 1: Divide numerator by denominator. Here numerator becomes dividend and denominator become divisor (d).

Step 2: Make a note of quotient (q) and reminder (r).

Step 3: Now, your mixed number is $q\frac{r}{d}$

Let’s practice it with the help of an example:

Problem: Convert $\frac{{18}}{7}$ into mixed number

Step1: Taking 18 as dividend and 7 as divisor, perform the division.

Step 2: On dividing 18 / 7, quotient is 2 and remainder is 4.

Step 3: So your mixed fraction is $2\frac{4}{7}$

This can also be written as $2+\frac{4}{7}$ where 2 is the whole number and $\frac{4}{7}$ is the fraction part.

How to convert mixed number into a fraction?

A mixed number can only be converted into an improper fraction. Here are the steps.

Step1: Multiply the whole number part of the mixed number with the denominator.

Step2: Now add the numerator to the product received in step 1.

Step3: Now the number received in step 2 will become your new numerator of the fraction. The denominator will remain the same.

Problem: Convert $5\frac{8}{7}$ into mixed number

Here 5 is the whole number, 8 is the numerator and 7 is the denominator.

Step1: Multiply the whole number with numerator.

5 x 7 = 35

Step2: Add 8 (numerator) and 35 (answer of step 1)

8 + 35 = 43

Step3: Your fraction becomes $\frac{{43}}{7}$

Why mixed fractions?

Mixed fractions hold a very significant role in our daily lives. It’s easier for us to say that we have eaten $1\frac{3}{4}$ apples rather than saying $\frac{7}{4}$ apples.

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