Adding mixed numbers is the goal of this lesson. We will get you through this with some carefully chosen examples to help you master the topic.

A mixed number is any number that has the following format:

Anything that is a combination of a whole number and a fraction is a mixed number

In our example, the whole number is 4

When adding mixed numbers, it is not necessary to convert a mixed number into an improper fraction before doing the addition

In case you want to do it that way anyway, we will show you how to convert a mixed number into an improper fraction

Follow the guidelines shown below:

**Step 1**. Multiply the whole number by the denominator of the fraction.

**Step 2**. Add the result of step 1 to the numerator of the fraction.

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

**Step 1**. Multiply the whole number by the denominator of the fraction.

**Step 2**. Add the result of step 1 to the numerator of the fraction.

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

Adding mixed numbers with a couple of good examples is what we show next

Convert each mixed number by following the steps outlined above

**Step 1**. Multiply the whole number by the denominator of the fraction. (5 × 2 = 10)

**Step 2**. Add the result of step 1 to the numerator of the fraction (10 + 1 = 11)

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

**Step 1**. Multiply the whole number by the denominator of the fraction. (4 × 2 = 8)

**Step 2**. Add the result of step 1 to the numerator of the fraction (8 + 7 = 15)

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

Now just add the fractions. Since both fractions have the same denominator we can just do this by adding the numerators together

The denominator stays the same. We don’t add denominators when adding fractions

You could have arrived to the answer by not converting the mixed numbers into fractions first.

When adding mixed numbers, you can just add the whole numbers separately and add the fractions separately.

Looking at exercise #1 again, just add 5 and 4. We get 9

Just add the fractions

And 9 + 4 = 13. As you can see, it took less time in this case. When adding mixed numbers, I recommend doing this way.

Add the whole numbers. 6 + 8 = 14

Add the fractions. However, before you do so, make sure both fractions have the same denominator.

Let us put it together. when adding the whole numbers, you got 14

You can keep the answer as a mixed number depends on how your teacher wants the answer

Otherwise, you can write the answer as a fraction

Adding mixed numbers is the goal of this lesson. We will get you through this with some carefully chosen examples to help you master the topic.

A mixed number is any number that has the following format:

Anything that is a combination of a whole number and a fraction is a mixed number

In our example, the whole number is 4

When adding mixed numbers, it is not necessary to convert a mixed number into an improper fraction before doing the addition

In case you want to do it that way anyway, we will show you how to convert a mixed number into an improper fraction. Follow the guidelines shown below:

**Step 1**. Multiply the whole number by the denominator of the fraction.

**Step 2**. Add the result of step 1 to the numerator of the fraction.

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

**Step 1**. Multiply the whole number by the denominator of the fraction.

**Step 2**. Add the result of step 1 to the numerator of the fraction.

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

Adding mixed numbers with a couple of good examples is what we show next

Convert each mixed number by following the steps outlined above

**Step 1**. Multiply the whole number by the denominator of the fraction. (5 × 2 = 10)

**Step 2**. Add the result of step 1 to the numerator of the fraction (10 + 1 = 11)

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

**Step 1**. Multiply the whole number by the denominator of the fraction. (4 × 2 = 8)

**Step 2**. Add the result of step 1 to the numerator of the fraction (8 + 7 = 15)

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

Now just add the fractions. Since both fractions have the same denominator we can just do this by adding the numerators together

The denominator stays the same. We don’t add denominators when adding fractions

## How to Add Mixed Fractions?

In this article, we are going to learn on how to add of mixed fractions or mixed numbers. There are two methods to add the mixed fractions.

### Method 1

In this method, whole numbers separately added. The fractional parts are also added separately. If the fractions have different denominators, then find their L.C.M. and change the fractions into like fractions. The sum of whole numbers and fractions is then calculated.

*Example 1*

2 3 /_{5} + 1 3 /_{10} = (2 + 1) + (3/5 + 3/10)

The L.C.M. of 5 and 10 = 10

= 3 + (3 × 2/5 × 5 + 3 × 1/10 × 1,

*Example 2*

Add the following fraction together: 1 1 /_{6}, 2 1 /_{8} and 3 ¼

= (1 + 2 + 3) + (1/6 + 1/8 + ¼)

L.C.M of 6, 8 and 4 = 24

= 6 + 1 × 4/6 × 4 + 1 × 3/8 × 3 + 1 × 6 /4 × 6

= 6 + 4/24 + 3/24 + 6/24

*Example 3*

Add these fractions together: 5 1 /9, 2 1 / _{12} and ¾

5 1 /9, 2 1 / _{12} and ¾

= (5 + 2 +0) + (1/9 + 1/12 + ¾)

= 7 + 1 × 4/9 × 4 + 1 × 3/12 × 3 + 3 × 9/4 × 9

= 7 + 4/36 + 3/36 + 27/36

*Example 4*

Since the L.C.M =12

= 5 + 5 × 2/6 × 2 + 1 × 6/2 × 6 + 1 × 3/4 × 3

= 5 + 10/12 + 6/12 + 3/12

The fraction 19/12 can be converted into a mixed fraction.

**Method 2**

In the second method, the following steps are followed:

Adding mixed numbers is the goal of this lesson. We will get you through this with some carefully chosen examples to help you master the topic.

A mixed number is any number that has the following format:

Anything that is a combination of a whole number and a fraction is a mixed number

In our example, the whole number is 4

When adding mixed numbers, it is not necessary to convert a mixed number into an improper fraction before doing the addition

In case you want to do it that way anyway, we will show you how to convert a mixed number into an improper fraction

Follow the guidelines shown below:

**Step 1**. Multiply the whole number by the denominator of the fraction.

**Step 2**. Add the result of step 1 to the numerator of the fraction.

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

**Step 1**. Multiply the whole number by the denominator of the fraction.

**Step 2**. Add the result of step 1 to the numerator of the fraction.

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

Adding mixed numbers with a couple of good examples is what we show next

Convert each mixed number by following the steps outlined above

**Step 1**. Multiply the whole number by the denominator of the fraction. (5 × 2 = 10)

**Step 2**. Add the result of step 1 to the numerator of the fraction (10 + 1 = 11)

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

**Step 1**. Multiply the whole number by the denominator of the fraction. (4 × 2 = 8)

**Step 2**. Add the result of step 1 to the numerator of the fraction (8 + 7 = 15)

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

Now just add the fractions. Since both fractions have the same denominator we can just do this by adding the numerators together

The denominator stays the same. We don’t add denominators when adding fractions

You could have arrived to the answer by not converting the mixed numbers into fractions first.

When adding mixed numbers, you can just add the whole numbers separately and add the fractions separately.

Looking at exercise #1 again, just add 5 and 4. We get 9

Just add the fractions

And 9 + 4 = 13. As you can see, it took less time in this case. When adding mixed numbers, I recommend doing this way.

Add the whole numbers. 6 + 8 = 14

Add the fractions. However, before you do so, make sure both fractions have the same denominator.

Let us put it together. when adding the whole numbers, you got 14

You can keep the answer as a mixed number depends on how your teacher wants the answer

Otherwise, you can write the answer as a fraction

A mixed number is any number that has the following format:

Anything that is a combination of a whole number and a fraction is a mixed number

In our example, the whole number is 4

In case you want to do it that way anyway, we will show you how to convert a mixed number into an improper fraction. Follow the guidelines shown below:

**Step 1**. Multiply the whole number by the denominator of the fraction.

**Step 2**. Add the result of step 1 to the numerator of the fraction.

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

**Step 1**. Multiply the whole number by the denominator of the fraction.

**Step 2**. Add the result of step 1 to the numerator of the fraction.

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

Adding mixed numbers with a couple of good examples is what we show next

Convert each mixed number by following the steps outlined above

**Step 1**. Multiply the whole number by the denominator of the fraction. (5 × 2 = 10)

**Step 2**. Add the result of step 1 to the numerator of the fraction (10 + 1 = 11)

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

**Step 1**. Multiply the whole number by the denominator of the fraction. (4 × 2 = 8)

**Step 2**. Add the result of step 1 to the numerator of the fraction (8 + 7 = 15)

**Step 3**. Your numerator is the answer of step 2. Your denominator stays the same

The denominator stays the same. We don’t add denominators when adding fractions

Just like whole numbers, fractions can also be added. The difference is that when counting improper fractions and mixed numbers, we are now counting the number wholes and parts .

Let’s work through an example to demonstrate how we add mixed numbers and improper fractions.

The example is: add the fractions

## Step 1: Convert all mixed numbers into improper fraction.

## Step 2: Do you have a common denominator? If not, find a common denominator.

List the multiples of 4:

List the multiples of 7:

The Lowest Common Multiple (LCM) between 4 and 7 is 28 .

## Step 3: Create equivalent fractions.

We need to find the number when multiplied to the top and bottom of 11/4 we get the LCM of 28 as the new denominator.

4 x 7 = 28, so we need to multiply the numerator and the denominator by 7 .

Now, we need to find the number when multiplied to the top and bottom of 8/7 we get the LCM of 28 as the new denominator.

7 x 4 = 28, so we need to multiply the numerator and the denominator by 4 .

## Step 4: Add the numerators and keep the denominator the same.

## Step 5: Reduce the fraction to a mixed number.

For practice, we offer free fractions worksheets on adding and subtracting mixed numbers and fractions in our grade 4 fractions section, our grade 5 fractions section and our grade 6 fractions section.

## Calculator Use

Do math calculations with mixed numbers (mixed fractions) performing operations on fractions, whole numbers, integers, mixed numbers, mixed fractions and improper fractions. The Mixed Numbers Calculator can add, subtract, multiply and divide mixed numbers and fractions.

### Mixed Numbers Calculator (also referred to as Mixed Fractions):

This online calculator handles simple operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if it exists.

Enter mixed numbers, whole numbers or fractions in the following formats:

- Mixed numbers: Enter as 1 1/2 which is one and one half or 25 3/32 which is twenty five and three thirty seconds. Keep exactly one space between the whole number and fraction and use a forward slash to input fractions. You can enter up to 3 digits in length for each whole number, numerator or denominator (123 456/789).
- Whole numbers: Up to 3 digits in length.
- Fractions: Enter as 3/4 which is three fourths or 3/100 which is three one hundredths. You can enter up to 3 digits in length for each the numerators and denominators (e.g., 456/789).

## Adding Mixed Numbers using the Adding Fractions Formula

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for addition of fractions:

a/b + c/d = (ad + bc) / bd - Reduce fractions and simplify if possible

### Adding Fractions Formula

a b + c d = ( a × d ) + ( b × c ) b × d

### Example

Add 1 2/6 and 2 1/4

1 2 6 + 2 1 4 = 8 6 + 9 4

= ( 8 × 4 ) + ( 9 × 6 ) 6 × 4

= 32 + 54 24 = 86 24 = 43 12

1 2/6 + 2 1/4 = 8/6 + 9/4 = (8*4 + 9*6) / 6*4 = 86 / 24

So we get 86/24 and simplify to 3 7/12

## Subtracting Mixed Numbers using the Subtracting Fractions Formula

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for subtraction of fractions: a/b – c/d = (ad – bc) / bd
- Reduce fractions and simplify if possible

### Subtracting Fractions Formula

a b − c d = ( a × d ) − ( b × c ) b × d

### Example

Subtract 2 1/4 from 1 2/6

1 2/6 – 2 1/4 = 8/6 – 9/4 = (8*4 – 9*6) / 6*4 = -22 / 24

Reduce the fraction to get -11/12

## Multiplying Mixed Numbers using the Multiplying Fractions Formula

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for multiplying of fractions: a/b * c/d = ac / bd
- Reduce fractions and simplify if possible

### Multiplying Fractions Formula

a b × c d = a × c b × d

### Example

multiply 1 2/6 by 2 1/4

1 2/6 * 2 1/4 = 8/6 * 9/4 = 8*9 / 6*4 = 72 / 24

Reduce the fraction to get 3/1 and simplify to 3

## Dividing Mixed Numbers using the Dividing Fractions Formula

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for division of fractions: a/b ÷ c/d = ad / bc
- Reduce fractions and simplify if possible

### Dividing Fractions Formula

a b ÷ c d = a × d b × c

### Example

divide 1 2/6 by 2 1/4

1 2/6 ÷ 2 1/4 = 8/6 ÷ 9/4 = 8*4 / 9*6 = 32 / 54

Reduce the fraction to get 16/27

### Related Calculators

To perform math operations on simple proper or improper fractions use our Fractions Calculator. This calculator simplifies improper fraction answers into mixed numbers.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator.

For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.

This calculator performs the reducing calculation faster than others you might find. The primary reason is that the code utilizes Euclid’s Theorem for reducing fractions which can be found at The Math Forum: LCD, LCM.

**Cite this content, page or calculator as:**

**Example 1:** Martha added four and one-fifth packages of soil to her garden on Monday and three and two-fifths packages of soil on Friday. How many packages of soil did she add in all?

**Analysis:** This problem is asking us to add mixed numbers.

The fractions have like denominators. We will add the whole numbers and add the fractions separately.

In example 1, we arranged the work vertically to make it easier to add the mixed numbers.

To **add mixed numbers** , add the whole numbers and add the fractions separately: **(whole + whole) + (fraction + fraction)**

Let’s look at some more examples.

**Analysis:** The fractions have like denominators. Add the whole numbers and add the fractions separately.

In example 2, it was necessary to simplify the result.

**Analysis:** We are adding a whole number and a mixed number. Think of ten as “ten and zero-sixteenths.”

**Analysis:** The fractions have unlike denominators. We will write equivalent fractions using the LCD, 8.

**Analysis:** The fractions have unlike denominators. We will write equivalent fractions using the LCD, 20.

**Analysis:** The fractions have unlike denominators. We will write equivalent fractions using the LCD, 36.

**Example 7:** An ice cream vendor sold eighteen and five-sixths liters of ice cream on Friday, and nineteen and one-half liters of ice cream on Saturday. How many liters did he sell in all?

**Analysis:** The fractions have unlike denominators. We will write equivalent fractions using the LCD, 6.

**Summary:** To add mixed numbers:

- Examine the fractional part of each mixed number to determine whether the denominators are like or unlike.
- If the denominators are unlike, use the LCD to rewrite them as equivalent fractions.
- Add the whole numbers and add the fractions separately:
**(whole + whole) + (fraction + fraction)** - Simplify the result, if necessary.

**Exercises**

Directions: Add the mixed numbers in each exercise below. **Be sure to simplify your result, if necessary.** Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

**Note: To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.**

1. |

2. |

3. |

4. |

**In one week, the Glosser family drank one and seven-twelfths cartons of regular milk and four and one-twelfth cartons of soy milk. How much milk did they drink in all?**

As you may recall, a mixed number consists of an integer and a proper fraction. Any mixed number can also be written as an improper fraction, in which the numerator is larger than the denominator, as shown in the following example:

*Example 1*

To add mixed numbers, we first add the whole numbers together, and then the fractions.

If the sum of the fractions is an improper fraction, then we change it to a mixed number. Here’s an example. The whole numbers, 3 and 1, sum to 4. The fractions, 2/5 and 3/5, add up to 5/5, or 1. Add the 1 to 4 to get the answer, which is 5.

*Example 2*

If the denominators of the fractions are different, then first find equivalent fractions with a common denominator before adding. For example, let’s add 4 1/3 to 3 2/5. Using the techniques we’ve learned, you can find the least common denominator of 15. The answer is 7 11/15.

Subtracting mixed numbers is very similar to adding them. But what happens when the fractional part of the number you are subtracting is larger than the fractional part of the number you are subtracting from?

Here’s an example: let’s subtract 3 3/5 from 4 1/3. First you find the LCD; here it’s 15.

Write both fractions as equivalent fractions with a denominator of 15.

**How to add mixed numbers?**

We will look at two methods that can be used to add mixed numbers.

**Method 1**

We can convert the mixed numbers to improper fractions and then add them as fractions.

** Example: **

Calculate

** Solution: **

**Method 2**

We can add the whole number part and the fractional part of the mixed numbers separately.

** Example: **

Calculate

** Solution: **

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

5. |