Comparing Fractions Intro to Algebra.

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Presentation transcript:

Comparing Fractions Intro to Algebra

Comparing Fractions Sometimes we need to compare two fractions to discover which is larger or smaller. There are two easy ways to compare fractions. We are only going to talk about one of them today because it is the same process that is going to help us next week!

Which fraction is bigger? 5 6 and 3 6

If the denominators are the same…. Simply look at the numerator! The number with the bigger numerator is the bigger fraction!

Unfortunately It’s not always that easy. Sometimes we will have to compare fractions that have different denominators.

Which fraction is bigger? 6 5 and 6 3

Which fraction is bigger? 8 12 and 8 16

Another trick What did you notice about the last two examples? Can you figure out a trick for that scenario?

Review Our 2 Tricks! If the denominators are the same: The numerator that is bigger is the bigger fraction If the numerators are the same: The denominator that is smaller is the bigger fraction

Which fraction is bigger? 7 12 and 3 5 Both numerators and denominators are different….no tricks!

To Compare Fractions In order to compare fractions with different numerators and denominators, we will need to make the fractions look more alike. To do this, we must change the fractions so that they have the same numerator. What should that numerator be???

LCM!!! Find the LCM of the two denominators. Rewrite the fractions so that their denominators are the LCM.

REMEMBER! We do not want to change the value of the fraction. Whatever you multiply on the bottom, you must do on the top!

Also…. The following steps are written as if we were comparing two reduced fractions. You might want to make that step 1…..reduce the fractions! Then it will be easier to find the LCM.

7 12 and 3 5 Step 1: Find the LCM of the denominators 60 Step 2: Change the fractions so that their denominators are the LCM 7 12 = ? 60 and 3 5 = ? 60 7 12 = 35 60 and 3 5 = 36 60 Step 3: Compare the changed fractions 35 60 < 36 60 ; therefore, 7 12 < 3 5

Which sign should be used in the space below to compare the numbers? 4 6 10 15

Which sign should be used in the space below to compare the numbers? 3 5 1 5

Which sign should be used in the space below to compare the numbers? 4 6 4 9

Which sign should be used in the space below to compare the numbers? 1 7 5 8

Which sign should be used in the space below to compare the numbers? 6 7 5 8

Which sign should be used in the space below to compare the numbers? 7 9 5 6

Which sign should be used in the space below to compare the numbers? 1 7 1 6

Which sign should be used in the space below to compare the numbers? 1 5 6 22 12

Which sign should be used in the space below to compare the numbers? 3 4 6 10 15

Which sign should be used in the space below to compare the numbers? 2 8 10 142 50