Add and Subtract Mixed Numbers

In this lesson, we will add and subtract mixed numbers.


Example 1).

The first step is to add the whole numbers which are shown in red. Then you can add the numerators. The denominator remains the same.


We have to rename the fraction by finding the LCD as we did in example 2. First, you will subtract the numerators and the denominator will remain the same and then subtract the whole numbers. Lastly, you need to reduce the fraction to simplest form.











Example 2).

Step 1.In order to add mixed numbers with different denominators we must find their LCD(least common denominator). The least common denominator is also the smallest whole number both denominators have in common. To find the LCD we have to find the multiples of each number.You can do this by mumultiplying the numbers by 2,3,4,5 etc...

2: 4, 6,8,10

3: 6, 9, 12

Notice the smallest whole number they have in common is 6. Step 2 we have to rename to fractions to have a denominator of 6. We will multiply 1/2 by 3 and 1/3 by 2.






Example 3).








To subtract a whole number from a mixed number we have to change the whole number to a mixed number:

Step 2:

After changing 7 to a mixed number, we need to find the LCD:

6: 6, 12

2: 4, 6

Step 3:

Once we have renamed the fraction to have a denominator of 6, we need to subtract the fractions first. Remember the denominator remains the same, just subtract the numerators.

Step 4:

We need to reduce the fraction to lowest terms by its Greatest Common Factor (GCF). The GCF is 3. Divide the numerator and denominator by 3.

Activity: Mixed Number Showdown

You can hold up a large piece of paper with a problem and the student who answers the problem first wins a prize or a homework pass. Repeat this several times with different problems of course.


Found on the Web:


Adding & Subtracting Mixed Numbers

Adding & Subtracting Mixed Numbers

Web Games:

Clara Fraction's Ice Cream Shop

Mixed Numbers- identify and define mixed number parts


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Figure This Challenge #56

  • Complete Solution will be given on May 17, 2015

Complete Solution:



Created by Wanda Collins May 10, 2015 at 1:56pm. Last updated by Wanda Collins May 10, 2015.

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Fun Math Facts:

Math Limerick

Question: Why is this a mathematical limerick?

( (12 + 144 + 20 + 3 Sqrt[4]) / 7 ) + 5*11 = 92 + 0 .


A dozen, a gross, and a score,
plus three times the square root of four, divided by seven, plus five times eleven, is nine squared and not a bit more.

---Jon Saxton (math textbook author)

Presentation Suggestions:
Challenge students to invent their own math limerick!

The Math Behind the Fact:
It is fun to mix mathematics with poetry.


Su, Francis E., et al. "Math Limerick." Math Fun Facts.


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