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Lesson 79: Working with Mixed Numbers
In this lesson, we'll talk about how to work with whole numbers combined with fractions, and we'll learn what to do when we have a fraction whose numerator is bigger than its denominator.
First let's talk about what to do if you have what is called an improper fraction. That just means a fraction where the numerator is bigger than the denominator. For example, let's look at 22/7. Remember that fractions are really just division problems.
If we do 22 ÷ 7, we get 3 R 1. We can write the 3 as a whole number, and the 1 that we have left over is really 1/7. The fraction can be written as 3 1/7 (three and one-seventh). In this form, it is called a mixed number. It has a whole number and a fraction.
Sometimes we need to convert from a mixed number back to an
improper fraction. The quickest way to do this is to multiply
the denominator of the fraction times the whole number, and then add
the numerator. The result becomes the numerator, and the
denominator stays the same. In the example above, we do 7x3 + 1 to get 22, and then keep our denominator of 7 to get 22/7.
To add or subtract mixed numbers, first add or subtract the fractions and note your result. Then add or subtract the whole numbers. Your final answer is the combination of your whole number and your fractional result. It can often be easier to just convert each mixed number to an improper fraction, and then add or subtract as you've learned.
To multiply mixed numbers, you can not just multiply the whole numbers, and then multiply the fractions. Your answer will be wrong. You must convert each mixed number to an improper fraction, and then multiply the fractions as you've learned.
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