Jamit Fractions - Lesson Contents 
 
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Lesson 6: Putting it All Together


  1. Practice Game.
  2. What Is in the Practice Game.
  3. Example 1
  4. Example 2
  5. Example 3
  6. Example 4
  7. Example 5

WHAT IS IN THE PRACTICE GAME

In the practice game you are presented with 2 fractions and all you have to do is to decide if they are equivalent or find which one is greater and which one is smaller. All you need to know for this task you have already learned. The examples below may refresh your skills and prepare you for the game.

Do you remember signs ">" and "<"?

Sign  >  means  greater ( 2 > 1 means "2 is greater than 1") 

Sign  <  means  smaller ( 2 < 99 means "2 is smaller than 99")

If you have problems with the questions in this practice game, go back and learn about the equivalent fractions, mixed fractions and how to compare fractions.


  EXAMPLE 1

Replace the sign ? with <, > or =.

  5 ? 3
  8 6

The two fractions have different denominators, so we have to find the Lowest Common Denominator.
But first we can reduce the second fraction:

  3 = 1 (Both the numerator and the denominator are divided by 3)
  6 2

The Lowest Common Denominator of 8 and 2 is 8. We have:

  1 = 4 (Both the numerator and the denominator are multiplied by 4)
  2 8

Finally,  we can compare fractions:

  5 > 4
  8 8

Answer: The sign to replace ?  is > (greater).


EXAMPLE 2

Replace the sign ? with <, > or =.

  3 15 ? 5 33
  87 65

Does it look difficult? Well, it is the simplest example. We have 2 mixed fractions with different whole parts.
All we have to do is to compare the whole numbers.
 

3 < 5, so 3 15 < 5 33
87 65

Answer: The sign to replace ?  is < (smaller).  


EXAMPLE 3

Replace the sign ? with <, > or =.

  3 5 ? 3
  8 5
 

What is the whole part of each fraction? 

  3 5 has a whole part of 3
  8

      3 does not have a whole part, or it has a whole part of 0
  5

 

3 > 0, so 3 5 > 3
8 5

Answer: The sign to replace ?  is > (greater).


EXAMPLE 4

Replace the sign ? with <, > or =.

  1 15 ? 7
  20 4

  7 is an improper fraction (because 7 > 4).
 
  4
We have to convert it to a mixed fraction:
  7 = 1 3
  4 4

Now we see that both mixed fractions have the same whole parts of 1.

We have to compare the fraction parts 15 and 3
20 4

We can reduce 15 = 3 (both the numerator and the denominator are divided by 5).
20 4

So 1 15 = 7
20 4

Answer: The sign to replace ?  is = (equal).


EXAMPLE 5

Replace the sign ? with <, > or =.

    30 ? 17
  12 6

Both fractions are improper, so we have to convert them to mixed fractions.

  30 = 2 6
  12 12

  17 = 2 5
  6 6

Both mixed fractions have the same whole parts of 2.

We have to compare the fraction parts 6 and 5
12 6

The Lowest Common Denominator of 12 and 6 is 12.

 

  5 = 10

(Both the numerator and the denominator are multiplied by 2)

  6 12

 

  6 < 10 so 30 < 17
  12 12 12 6

Answer: The sign to replace ?  is < (smaller).

NOTE: In the example above we could reduce 6 to 1
12 2

But because the Lowest Common Denominator of 2 and 6 is 12, it was better to leave it.


 

 

 


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