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### Course: 3rd grade (Eureka Math/EngageNY)>Unit 5

Lesson 6: Topic F: Comparison, order, and size of fractions

# Comparing fractions with > and < symbols

When comparing fractions, remember that the numerator is the top number and the denominator is the bottom number. With the same denominator, the larger numerator means a larger fraction. With the same numerator, the smaller denominator means a larger fraction. Two fractions can be equivalent even with different numerators and denominators. Created by Sal Khan.

## Want to join the conversation?

• How can 3/4 be larger than 3/7? 3/4 has a smaller denominator. Can someone help me?
• If you have a bigger denominator it is smaller because then you have more parts, and that makes it smaller. fractions can also be turned into decimals, so 3/7= 3 divided by seven, which is about 0.4285. but 3 divided by 4 is 0.75.
• How do you know if a fraction is equivelent to another fraction?
• There are a few ways to check:

1) You can fully reduce both fractions. In reduced form, they should be identical to each other. For example: is 5/10 equal to 21/42. Yes because they both reduce to 1/2

2) You can convert them to a common denominator. Once they have a common denominator, it the numerators are the same, then the fractions are equal.

3) You can test to see if they create a proportion. Proportions have a unique characteristic that if you multiply along the diagonals, the results will be equal if the fractions are equal.
Example: Is 2/7 = 14/49 ? Multiply 2*49 and see if it equals 7*14. These are equal as both create 98.
(1 vote)
• So if you had 12/12, would that equal 1 whole?
• yes because its like 1/1 which is one whole
• Are fractions like division
• Fractions and division have some things in common. For instance, if you want to convert a fraction into a decimal, you would divide the two numbers.

Example: 1/4 (spoken one quarter) To convert 1/4 into a decimal, you would take 1 divided by 4 and you would get 0.25

If you look at that as money, it would be \$0.25 and that is also what we call "one quarter." Looking at it another way, one quarter is 1/4 of a dollar.
• wait but what if the 3/7 pieces where much bigger than how sal cut them and the 3/4 where the same so you cant always know. Is there an other operation that tells you what to do with that.
• As mentioned in prior discussions, you have to assume the whole units are the same size. If they aren't, the problem will tell you they aren't and you will need to convert them to units that are equal size. For example: We don't compare liters and gallons without converting to a common unit of measure. You need either both numbers in liters or both numbers in gallons to work with them.
• I understand what <,>, & = equals, but what does the < and > mean with a line under it?
• Do you mean ≤ and ≥?

≥ is equal to or greater than. For example, you could use 2 ≥ 1 or 4 ≥ 4.

≤ is equal to or less than. For example, you could use 5 ≤ 8 or 8 ≤ 8.
Hope this helped! <3
• Can you simplify 5/30?
• Yes. If you divide both the numerator and denominator by 5, it will simplify to 1/6.
5/30 ÷ 5/5 = 1/6
• can fractions have decimals?
• Yes, and this is common in basketball. For example, a player who attempts 10.6 shots per game and makes 5.3 of them can be represented by the fraction 5.3/10.6 (which, of course, means the player makes half of their shot attempts)
• How do you remember that the top is the numerator and the bottom is the denominator?
• I can think of it as the top is "New" and the bottom as "Den"
The numerator has sprung out of the floor, "New" as ever.
The denominator is under the line, so it is in it's "Den"