For Math Today, You’ll Need...
By the end of this lesson, you will be able to compare fractions and rewrite fractions with common denominators.
Learning Target
Strategies for Comparing Fractions
Lesson 1-4
Comparing Numbers
What do you remember about inequality symbols (>, <)?
Which symbol would you insert between the pairs of numbers below?
456 546 3,200 3,020 99,999 100,000
Compare Fractions
Same Denominator
Insert the correct inequality symbol between these fractions.
4/8 6/8 ⅘ ⅗
How do you know?
⅘ ⅕
Explain how you determined which fraction is greater.
Try to use what you know about unit fractions in your explanation.
Compare Fractions
Same Numerator
Insert the correct inequality symbol between these fractions.
⅖ 2/7
Compare Fractions
Same Numerator
⅖ 2/7
Can anyone explain how to compare these fractions using unit fractions?
Compare Fractions
Same Numerator
⅖ 2/7
These 2 fractions have the same number of unit fractions (2).
However, because fifths are larger than sevenths, 2 fifths would be greater than 2 sevenths.
Student Workbook
Please complete pg. 9 in your workbook independently.
Compare Fractions
Unlike Denominator
3 Ways to Find Common Denominators:
One is a Factor of the Other
Example: ¾ and ⅝
Since 4 goes into 8, 8 is the least common denominator.
Also, we only have to rewrite 1 of the fractions.
Denominators Share a Factor
Example: 4/6 and 2/9
Since 6 and 9 share a common factor, list the multiples of each, and use the lowest one.
Product of the Denominators
Example: 2/7 and ⅘
The only number that goes into both 7 and 5 evenly is 1, so use the product of 7 and 5.
Compare Fractions
Unlike Denominator
Once you have found a common denominator, and have rewritten the fractions as equivalent fractions, compare the numerators.
The greater numerator will be the greater fraction.
4/7 8/11
Special Notes/Reminders
Any common denominator will work for comparing fractions. It does not need to be the least common denominator.
The product of the denominators will always work.
Special Cases
Does anyone know how we can
compare ⅝ and ⅖ without finding a common denominator?
Special Cases
Sometimes you can tell which fraction is bigger by comparing them both to ½.
How does the fraction ⅝ compare to ½? How do you know?
How does the fraction ⅖ compare to ½? How do you know?
Special Cases
Does anyone know how we can
compare ⅚ and 6/7 without finding a common denominator?
Special Cases
Sometimes we can use the benchmark 1 to compare 2 fractions.
Special Cases
Because 1/7 is less than 1/6 , 6/7 is closer to 1. Therefore 6/7 is the greater fraction.
Special Cases
Special cases are usually pretty quick and easy, but they won’t work in all cases.
Finding a common denominator will always work when done correctly.
Student workbook pg. 11-12
Shortcut! Cross Multiply
⅖ 4/7