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# Addition & Subtraction Of Mixed Numbers

## What is a mixed number?

A mixed number is a number expressed as the combination of a whole number and fraction. In general, it denotes a value between two whole numbers.

Consider the mixed number $2\frac{3}{5}$.

In this example,

• 2 is the whole number
• 3 is the numerator of the fraction; and
• 5 is the denominator of the fraction.

## How to convert an improper fraction to a mixed number?

An improper fraction is a fraction that has a numerator greater than the denominator. Improper fractions can be converted into mixed numbers.

Consider the fraction $\frac{21}{8}$.

Since the numerator is greater than the denominator, it is considered as an improper fraction.

To convert improper fractions to mixed numbers:

1. Divide the numerator by the denominator.
2. Write the whole number.
3. Write the remainder as the numerator.
4. Write the same denominator.

Example #1

Convert $\frac{11}{2}$ to a mixed number.

Solution

Example #2

Convert $\frac{27}{7}$ to a mixed number.

Solution

## How to convert a mixed number to an improper fraction?

Converting mixed numbers to an improper fraction is one step that you need to know in adding and subtracting mixed numbers.

To convert mixed numbers to improper fractions:

1. Multiply the denominator with the whole number.
2. Add the numerator to the product of the denominator and whole number.
3. Write the sum on the numerator of the improper fraction.
4. Copy the same denominator.

Example #1

Convert $6\frac{6}{13}$ to an improper fraction.

Solution

Example #2

Convert $2\frac{7}{11}$ to an improper fraction.

Solution

## How to add mixed numbers?

### Adding whole number and mixed number

To add a whole number and a mixed number, follow these steps:

1. Add the given whole number and the whole number of the mixed number.
2. Copy the fraction part of the mixed number on the final answer.

Example #1

What is the sum of 2 and $3\frac{1}{4}$?

Solution

Example #2

Determine the sum of $10\frac{4}{7}$  and 6.

Solution

### Adding mixed numbers with the same denominator

1. Convert the mixed number to an improper fraction.
3. Copy the denominator.
4. Convert the improper fraction to a mixed number.

Example #1

What is the sum of $3\frac{2}{5}$  and $7\frac{4}{5}$?

Solution

Example #2

Determine the sum of $6\frac{5}{7}$ and $3\frac{3}{7}$.

Solution

Example #3

Find the result of $13\frac{2}{3} + 6\frac{1}{3}$.

Solution

Example #4

What is the sum of $5\frac{1}{2}$ and $\frac{7}{2}$?

Solution

### Adding mixed numbers with different denominators

1. Convert the mixed number to an improper fraction.
2. Find the least common denominator (LCD).
3. Divide the LCD by the original denominators of the given mixed numbers.
4. Multiply the quotient to the denominator of the improper fraction.
5. Write the fractions based on the LCD.
7. Copy the LCD.
8. Convert the improper fraction to a mixed number.

Example #1

What is the sum of $4\frac{1}{2}$ and $\frac{3}{4}$?

Solution

Example #2

Determine the result of adding $7\frac{2}{5}$ and $6\frac{1}{3}$.

Solution

## How to subtract mixed numbers?

Subtraction is simply the opposite of addition. When subtracting mixed numbers, we always need to consider the minuends and the subtrahends and the denominators of the two.

### Subtracting whole number and mixed number

We need to consider two cases if we are given a subtraction problem given a whole number and a mixed number.

Case #1: If the minuend is a mixed number

To subtract a whole number from a minuend, follow these steps:

1. Subtract the given whole number from the whole number of the mixed number.
2. Copy the fraction part of the mixed number on the final answer.

Example

What is the difference between $5\frac{6}{7}$ and 3?

Solution

Case #2: If the subtrahend is a mixed number

To subtract a mixed number from a whole number, follow these steps.

1. Convert the whole number to a fraction having the same denominator as the given mixed number.
2. Convert the mixed number to an improper fraction.
3. Subtract the numerators.
4. Copy the denominator.

Example

Find the result of subtracting $1\frac{1}{3}$ from 4.

Solution

### Subtracting mixed numbers with the same denominator

To subtract mixed numbers with the same denominators, follow these steps:

1. Convert the mixed number to an improper fraction.
2. Subtract the numerators.
3. Copy the denominator.
4. Convert the improper fraction to a mixed number.

Example #1

What is the difference between $3\frac{3}{8}$ and $\frac{5}{8}$?

Solution

Example #2

Find the difference of subtracting $3\frac{2}{9}$ from $5\frac{4}{9}$.

Solution

Example #3

What is the result of subtracting $\frac{23}{11}$ from $6\frac{2}{11}$?

Solution

### Subtracting mixed numbers with different denominators

To subtract mixed numbers with different denominators, follow these steps:

1. Convert the mixed number to an improper fraction.
2. Find the least common denominator (LCD).
3. Divide the LCD by the original denominators of the given mixed numbers.
4. Multiply the quotient to the denominator of the improper fraction.
5. Write the fractions based on the LCD.
6. Subtract the numerators.
7. Copy the LCD.
8. Convert the improper fraction to a mixed number.

Example #1

What is the difference between $9\frac{3}{4}$ and $\frac{2}{3}$?

Solution

Example #2

Determine the result of subtracting $3\frac{1}{10}$ from $8\frac{2}{5}$.

Solution