How to Raise and Reduce Fractions

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  • 0:02 Raising & Reducing
  • 2:14 Raise a Fraction
  • 4:01 Reduce a Fraction
  • 4:59 An Example
  • 5:40 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

When working with fractions, you sometimes need to change your fraction to make it easier to work with. Watch this video lesson to learn how you can raise and reduce fractions to make your problem solving easier.

Raising and Reducing Fractions

When you are working with fractions, sometimes you need to change your fractions so you can easily solve your problem. The times that you need to change your fractions are when you are adding or subtracting your fractions. When you add or subtract fractions, your denominator (the bottom number) needs to be the same before you can complete your operation. Why is this? Well, think of adding 1/4 to 1/2. When you first look at your problem, you might think, how in the world am I supposed to add those? But, if you stop and think about it in terms of slices of your favorite pie, things might make a little more sense.

You know that 1/4 means that your pie is sliced into 4 slices where you have 1 piece; 1/2 means that your pie is sliced into 2 slices where you have 1 piece. You can't say that you have 2 slices because that answer doesn't explain that you have 2 different-sized slices. So, is there a way to cut your pies so that your pie slices are the same for both fractions? Yes, there is!

If you change your 1/2 fraction so that we have 4 slices instead of 2, we can take 2 of our 4 slices so that we still end up with 1/2 of our pie. So, our new fraction here would be 2/4. Since the pie is sliced the same as our 1/4 fraction, we can easily see that adding 1/4 to 1/2 would give us 3/4, or 3 slices out of a pie that is sliced into 4.

What we have just done is raise our fraction. Mathematically, raising a fraction involves multiplying the numerator and denominator by the same number. Reducing a fraction involves dividing the numerator and denominator by the same number. We reduce fractions when we have a fraction where we can divide both the numerator and denominator by the same number, such as 6/8, which can be divided by 2 on both top and bottom. Now, let's see how to raise and reduce fractions mathematically.

How to Raise a Fraction

We begin with raising fractions. If we have a problem such as 2/5 + 1/3, we see that we need to raise our fractions so that they have the same denominator, and we can answer our problem. We look at each of our fractions and compare it with the other. If I think about my pie slices, I ask myself if there is a way to the cut the pies so that the slices are the same size in both pies. I look at the denominator in both. I have a 5 and a 3. Well, I can't change my 3 to a 5 that easily. But I can change both to 15 easily. All I would have to do is multiply my 3 by 5 and my 5 by 3.

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