Adding and Subtracting Mixed Numbers

Contributor: Erika Wargo. Lesson ID: 12800

Can you write your own mixed-numbers problems? If mixed numbers are a problem for you, learn how to deal with those crazy whole numbers and fractions, even improper ones, then write your own problems!

categories

Elementary

subject
Math
learning style
Visual
personality style
Otter
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Why would you stir a bowl of numbers?

Your math homework said to create mixed numbers. Ouch.

A mixed number, or a mixed fraction, is a whole number with a fraction.

It is a fraction that is greater than 1. Adding and subtracting mixed numbers is similar to adding and subtracting fractions, with a bit of a twist. When adding mixed numbers, add or subtract the fractions first, then add or subtract the whole numbers. Remember that fractions need to have a common denominator in order to add or subtract them. The denominator is the bottom number of a fraction, and the top number of a fraction is the numerator.

Learn how to add and subtract mixed numbers by completing the following steps:

  1. Go to Add & Subtract Mixed Numbers (Scholastic Study Jams!) and click on theSTEP-BY-STEP button to watch how to add mixed numbers.
  2. Click on the NEXT and SHOW ME buttons to progress through the steps.
  3. Write the steps in your math journal.
  4. Click on WATCH OUT! to watch how to subtract a mixed number with different denominators.
  5. Click on the NEXT and SHOW ME buttons to progress through the steps.
  6. Write the steps in your math journal.

As you saw in the activity above, one way to add and subtract mixed numbers is to find common denominators.

  • Step 1: Write the problem vertically.
  • Step 2: Convert the fractions to have common denominators, then add or subtract the numerators.
  • Step 3: Add or subtract the whole numbers.
  • Step 4: Rewrite the fraction in simplest form by reducing.

Example 1

  1  1   
  6  
       
+ 2  5   
12  
__________________

 

6 and 12 have a least common multiple of 12, since 6 x 2 = 12. Multiply the top fraction by 2 to convert 16 to 212.

  1  1  = 1  2   
  6 12  
             
+ 2  5  = 2  5   
12 12  
_________________________________

 

Add the numerators, then add the whole numbers:

  1  1  = 1  2   
  6 12  
             
+ 2  5  = 2  5   
12 12  
_________________________________
        3  7   
        12  

 

Another method to use when adding or subtracting mixed numbers is to change the mixed numbers to improper fractions. In your math journal, write down the steps shown as you watch a video by Shmoop, Shmoop Sidebar: Adding and Subtracting Mixed Numbers by Shmoop:

 

Look over the same example from above that is solved by using improper fractions:

  • Step 1: Convert the mixed numbers to improper fractions. Multiply the denominator of the fraction by the whole number and then add the numerator. Write the total as the numerator of the improper fraction and keep the denominator the same.
  • Step 2: Find a common denominator and multiply each fraction by the number to create the common denominator.
  • Step 3: Add or subtract the numerator of the improper fractions, but keep the denominator the same.
  • Step 4: Convert the improper fractions back to a mixed number by using long division.
  1  1  =  7     7  x  2  =  14         
  6 6   6 2 12        
                             
+ 2  5  =  29             29         
12 12           12        
_________________________________________________________________________
                     43  = 3  7   
                    12 12  

 

Sometimes in math, there are tricks that you can use to solve certain problems. One math trick is called the “butterfly method.” This method does not involve finding a common denominator. As you watch a video describing this method, write down the steps used to add and subtract mixed numbers in your math journal.

Discuss the steps for the butterfly method with a parent or teacher after watching the video, Adding & Subtracting Mixed Numbers (Mr. Peters’ Classroom):

 

The butterfly method is not a common method to use when adding or subtracting fractions, but if used correctly, it can be a helpful math trick.

Butterfly Method

  • Step 1: Add or subtract the whole numbers first.
  • Step 2: Multiply the numerators and denominators diagonally. Add each product together to form the new numerator.
  • Step 3: Multiply the denominators straight across and this becomes your new denominator.
  • Step 4: Rewrite the fraction in simplest form by reducing.

 

  1  1           
  6          
+ 2  5            
12          
______________________        
  3            
               
 1  +  5  = 30 + 12 = 42
6 12 72 72
               
Reduce by 6.  
               
42 ÷  6  =  7       
72 6 12      
               
3  7             
12            

 

The butterfly method may seem more difficult because you have to reduce a larger fraction, but it can be helpful if you struggle with finding common denominators.

In your math journal, write a response to the following questions:

  • How do you find the least common multiple (LCM) of two numbers to form a common denominator?
  • Which method for adding and subtracting mixed numbers do you prefer? Why?

Now, you will move on to the Got It? section to complete interactive practice with adding and subtracting mixed numbers.

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