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Math for Kids23 chapters | 325 lessons

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Instructor:
*Laura Pennington*

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions, such as Grand Rapids Community College, Pikes Peak Community College, and Austin Peay State University.

In this lesson, we will take a close look at each of the steps involved in adding mixed fractions with different denominators. After familiarizing ourselves with the process, we will look at an application to put the process to use.

To add mixed fractions with different denominators, we simply need to perform three steps. Of course, this means knowing how to do each step, so let's figure this out together. First of all, a **mixed number** is a number with a fraction part and a whole part.

When we want to add mixed numbers with different denominators, the first step we take is to convert the mixed numbers to improper fractions, where an **improper fraction** is a fraction with a numerator larger than its denominator. When converting a mixed number to an improper fraction, the denominator will remain the same. To find the numerator, we multiply the whole part of the number by the denominator of the fraction part and then add the numerator of the fraction part.

For example, suppose we are converting 3 1/4 to an improper fraction. We know the fraction's denominator remains the same, so it will be 4. To find the numerator, we multiply the whole number 3 by the denominator 4, and then add the numerator 1 to get 3*4 + 1 = 13. Thus, we have that 3 1/4 = 13 / 4.

The second step in adding mixed fractions with different denominators is to add together the two improper fractions that you found in the first step. To do this, you will need to find a common denominator and then add the numerators. This can be accomplished using the illustrated rule.

For example, suppose we are adding 3 1/4 + 1 1/2. We already converted 3 1/4 to 13/4. To convert 1 1/2, we keep the denominator of 2 and find the numerator using our conversion rule. 1 1/2 = (1*2 + 1) / 2 = 3/2. Now, we add the improper fractions 13/4 and 3/2 using our addition rule.

We see that 13/4 + 3/2 = 19/4.

The last step in adding mixed fractions with different denominators is to convert the improper fraction you found in the second step back to a mixed number. To do this, you perform the division indicated (in this case, 19 divided by 4). The **quotient** will be the whole number in the mixed number, the **remainder** will be the numerator in the fraction of the mixed number, and the denominator of the fraction in the mixed number stays the same.

Consider our result 19/4 from our example. To convert this to a mixed number, we perform division to get 19/4 = 4 remainder 3. We now know that the whole number in the mixed number will be 4, the numerator of the fraction in the mixed number will be 3, and the denominator of the fraction in the mixed number will be 4. Therefore, 19/4 = 4 3/4.

Once you get familiar with these steps, adding mixed numbers with different denominators becomes a breeze! Let's look at these steps in a nice, laid out manner.

To add mixed numbers with different denominators, we follow these steps.

- Convert the mixed numbers to improper fractions.
- Add the improper fractions together.
- Convert the result back to a mixed number.

That's not too hard, is it?

Let's get in a bit more practice by looking at an application. Suppose you are baking a cake for a friend's upcoming birthday party. The recipe calls for 1 1/3 cups white flour and 2 3/4 cups brown flour. You want to know how much flour your will need all together. To figure this out, you need to add the amounts of white and brown flour together. Luckily, we just saw how to do exactly this! We are adding the mixed numbers 1 1/3 + 2 3/4 . Let's take it through our steps!

The first step is to convert both of the numbers to improper fractions. To convert 1 1/3, we keep the denominator as 3, and to find the numerator, we multiply 1 by 3 and add 1.

We see that 1 1/3 = 4/3. To convert 2 3/4, we keep the denominator of 4 and then find the numerator by multiplying 2 by 4 and adding 3.

We see that 2 3/4 = 11/4.

The second step is to add the improper fractions we just found. That is, we want to find 4/3 + 11/4. We use our rule that *a* / *b* + *c* / *d* = (*ad* + *bc*) / *bd*.

We see that 4/3 + 11/4 = 49/12.

We just have one more step to go! The last thing we do is convert our improper fraction 49/12 into a mixed number by performing division and finding the quotient and remainder. We know that 49 / 12 = 4 remainder 1. The quotient is the whole number, the remainder is the numerator of the fraction, and the denominator of the fraction stays the same. Therefore, we have that 49/12 = 4 1/12. This tells you that you will have 4 1/12 cups of flour total in your cake.

Mixed numbers show up in many different areas of our lives including baking, measurements, distance, etc. Knowing how to add these types of numbers together is extremely useful information, so it's a good idea to remember this process!

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Math for Kids23 chapters | 325 lessons

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- Comparing Fractions: Lesson for Kids
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- How to Simplify Fractions: Lesson for Kids
- Improper Fractions: Lesson for Kids
- What is a Benchmark Fraction on a Number Line? 3:48
- How to Add Mixed Fractions with Different Denominators
- Simplifying Compound Fractions
- Dividing Compound Fractions
- Adding Compound Fractions
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- How to Subtract Fractions with Variables
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- Definition of Simplest Form: Lesson for Kids
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- How to Add & Subtract Two Fractions with Like Denominators
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- How to Subtract Mixed Fractions with Unlike Denominators
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