Slide 1:
COMPARING AND ORDERING FRACTIONS Slide 2:
TO COMPARE AND ORDER FRACTIONS Method 1: List the multiples of each denominator. Find the least common multiple. Using the LCM, find equivalent fractions. Slide 3:
I dare ya…betcha can’t do it!!! Slide 4:
Try TRY IT!! List the MULTIPLES of 8…
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112 List the MULTIPLES OF 7…
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98 Slide 5:
Try List the MULTIPLES of 8…
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112 List the MULTIPLES OF 7…
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98 What are the common multiples? 56 …and…56 is the LCM too! TRY IT!! Slide 6:
If you
added 7/8 and 6/7… or… you wanted to know which fraction is greater … and… you knew that the Least Common Multiple for 8 and 7 is 56… Slide 7:
THEN…. Your work is… Soooo EASY! Oh, yeah…how’s that? Slide 8:
= X 7 X 7 = X 8 X 8 Now you can see, 7/8 is greater than 6/7. Also, you can now add or subtract these fractions because there is a common denominator. Slide 9:
THE END
of Method 1 Next…Method 2 Slide 10:
Method 2: Use Prime Factorization. After you have the GCF, multiply the GCF with all the left over prime numbers. Use that number to find the equivalent fractions. TO COMPARE AND ORDER FRACTIONS Slide 11:
2 9 3 3 TRY IT!! 2 x 3 x 3 24 2 12 2 6 2 3 18 2 x 2 x 2 x 3 Slide 12:
GCF = 2 x 3 = 6 Slide 13:
OKAY…SO MULTIPLY THE GCF (6) WITH ALL THE LEFT OVER PRIME NUMBERS (2, 2, 3) 6 X 2 X 2 X 3 = 72 LCM = 72 Slide 14:
= X 4 X 4 = X 3 X 3 Now you can see, 8/18 is less than 11/24. Also, you can now add or subtract these fractions because there is a common denominator. Slide 15:
THE END
of Method 2 Next…Methods 3 and 4 Slide 16:
TO COMPARE AND ORDER FRACTIONS Method 3: Comparing fractions with the same denominator.
Method 4: Comparing fractions with the same numerator. Slide 17:
If two fractions have the SAME DENOMINATOR but different numerators, how can you tell which of the fractions is greater?
The fraction with the GREATER NUMERATOR is greater. The same denominator says you are working with same-sized pieces. The fraction with the greater numerator has more pieces, so it is greater. Slide 18:
For example: and 5/8 is greater because 5 is greater than 3. Really?
Cool ! Slide 19:
If two fractions have the SAME NUMERATOR but different denominators, how can you tell which of the fractions is greater?
The fraction with the SMALLER DENOMINATOR is greater. The same numerator tells you that the two fractions represent the same number of pieces of the whole, but a smaller denominator means larger pieces, so the fraction with the smaller denominator is greater. Slide 20:
For example: and 7/8 is greater than 7/9 because eights are larger pieces than ninths. mmm…That’s kind of confusing. Slide 21:
THINK ABOUT IT… What’s larger? Halves or Fourths? Why…halves of course! Slide 22:
THE END of Methods 3 and 4 Next…Methods 5 and 6 Slide 23:
TO COMPARE AND ORDER FRACTIONS Method 5: Writing fractions with the same denominator so that you can determine which fraction is greater. Method 6: Writing fractions with the same numerator so that you can determine which fraction is greater. Slide 24:
When you are given two fractions to compare, how can you quickly find
equivalent fractions with a common denominator?
To write the fractions with a common denominator, multiply both parts of each fraction by the other fraction’s denominator. Slide 25:
Oh yeah??? That makes absolutely no sense! Slide 26:
To write the fractions with a common denominator, multiply both parts of each fraction by the other fraction’s denominator. Sure it does but you really need to focus on the directions. Can you do it? Slide 27:
So now you can either
add 4/5 and 3/6… or… determine which fraction is greater … Easy! Easy! Easy! Easy! Easy! Slide 28:
For example: and
4 x 6 = and 5 x 6 =
3 x 5 = and 6 x 5 =
So: = and = 24 30 15 30 Slide 29:
So…as you can see, 4/5 (24/30) is greater than 3/6 (15/30). COOL! Slide 30:
You have learned 5 different methods for comparing and ordering fractions (as well as adding and/or subtracting fractions). Are you ready for the last method? Sure, I think so. Slide 31:
When you are given two fractions to compare, how can you quickly find
equivalent fractions with a common numerator?
To write the fractions with a common numerator, multiplY both parts of each fraction by the other fraction’s numerator. Slide 32:
Oh yeah??? Again,that makes absolutely no sense! Slide 33:
Again, you need to focus on the directions. Can you do it? To write the fractions with a common numerator, multiply both parts of each fraction by the other fraction’s numerator. Slide 34:
For example: and 6 x 4 = and 6 x 7 = 24 42 4 x 6 = 24 and 4 x 9 = and 24 36 So… = and = Slide 35:
So…as you can see, 4/7 (24/36) is greater than 6/9 (24/42). COOL! Slide 36:
THE END