Fractions
FRACTIONS-SUBTRACTING & COMPARING

Subtracting fractions
Subtraction problems that involve borrowing
Subtraction word problem
Comparing fractions
Comparison word problem
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SUBTRACTION

One truck can hold a maximum of 52 1/2 lbs.
A second truck can only hold 23 4/5 lbs.
How much more weight can the first truck carry compared to the second truck?

This problem involves subtracting fractions, so let's spend a few minutes discussing subtraction.

Subtraction is the same as addition. You still need that pesky common denominator, even if you have to force the issue by using the LCD. The only change is now instead of adding the numerators, you'll be subtracting one from the other.

So 8/10 - 3/10 = (8-3)/10 = 5/10 = 1/2
and 5/12 - 3/12 = (5-3)/12 = 2/12 = 1/6
In the case of mixed fractions, again we'll attempt to treat them just like we did in the addition problems. Subtract whole numbers from whole numbers and fractions from fractions. Note: there is an exception to this rule coming up soon.
So 4 13/21 - 1 4/21 = 3 9/21 = 3 3/7
and 2 2/3 - 1/3 = 2 1/3
Lastly, if two fractions have different denominators, you must convert them into fractions with the LCD
So 4/5 - 1/15 = 12/15 - 1/15 = (12-1)/15 = 11/15. [15 is found to be the LCD and 4/5 = (4*3)/(5*3) = 12/15]
and 13 3/8 - 2 1/6 = 13 9/24 - 2 4/24 = 11 5/24. [24 is the LCD. By multiplying both the numerator and denominator by 3 we can conclude 13 3/8 = 13 9/24. By multiplying both the numerator and denominator by 4 we can conclude 2 1/6 = 2 4/24]
The following problems will help you practice subtraction. But, be prepared, because as soon as you finish I'm going to throw you a curve ball.
Exercise 1
11 7/8 - 3 5/8
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
11 7/8 = 3 5/8 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

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Exercise 2
2 4/5 - 1 1/6
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
2 4/5 = 1 1/6 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

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Exercise 3
9/10 - 1/2
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
9/10 = 1/2 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

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Exercise 4
4 10/16 - 1 1/4
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
4 10/16 = 1 1/4 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

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Exercise 5
2 3/4 - 1 1/12
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
2 3/4 = 1 1/12 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next section.

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Okay ready for one a little more tricky.

4 1/5 - 1 3/5
We could try to proceed the same way as before, until we note that 3/5 is actually greater than 1/5.
So what do we do now you may ask?
The answer comes from borrowing.
First rewrite 4 1/5 as 4 + 1/5
Now 4 = 3 + 1
So 4 1/5 = 3 + 1 + 1/5
Now we know 5/5=1 (that is five divided by itself is equal to one)
So 4 1/5 = 3 + 5/5 + 1/5 = 3 6/5
Now 4 1/5 - 1 3/5 = 3 6/5 - 1 3/5 = 2 3/5.
Got that. By borrowing one from the whole number, we can increase the numerator of it's corresponding fraction part. Here it is again
4 5/12 - 1 3/4
The LCD of 12 and 4 is 12
1 3/4 = 1 9/12.
4 5/12 - 1 3/4 = 4 5/12 - 1 9/12
9/12 is actually greater than 5/12 so we need to borrow
4 5/12 = 3 + 1 +5/12 = 3 + 12/12 + 5/12 = 3 17/12
4 5/12 - 1 3/4 = 4 17/12 - 1 9/12 = 3 6/12 = 3 1/2
Now you try it with the following exercises
Exercise 1
8 1/8 - 2/3
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
8 1/8 = 2/3 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

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Exercise 2
2 3/14 - 1 5/21
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
2 3/14 = 1 5/21 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

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Exercise 3
3 4/7 - 6/7
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
3 4/7 = 6/7 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

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Exercise 4
1 1/14 - 3/14
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
1 1/14 = 3/14 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next exercise.

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Exercise 5
3 3/62 - 1 5/62
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
3 3/62 = 1 5/62 =
Step 3: Subtract the fractions
Step 4:Reduce your answer to lowest terms. If your answer is already in lowest terms, go on to the next section.

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Now back to our trucks

Question:
One truck can hold a maximum of 52 1/2 lbs.
A second truck can only hold 23 4/5 lbs.
How much more weight can the first truck carry compared to the second truck?
Answer1: Who cares?
Answer2: The difference in weight is 52 1/2 - 23 4/5
The LCD of 2 and 5 is 10
52 1/2 = 52 5/10
23 4/5 = 23 8/10
52 1/2 - 23 4/5 = 52 5/10 - 23 8/10
52 1/2 = 52 5/10 = 51 15/10
52 1/2 - 23 4/5 = 52 5/10 - 23 8/10 = 51 15/10 - 23 8/10 = 28 7/10. The difference in weightload is 28 7/10 lbs.

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COMPARING FRACTIONS

Your high school baseball team played 25 games this year and won 21 of them.
Your high school football team played 15 games this year and won 11 of them.
Which team had a better season?

The baseball team had a winning ratio of 21/25. the football team had a winning ratio of 11/15.
So this problem comes down to asking which fraction is greater 21/25 or 11/15?
We'll come back gto this problem after examining how to compare fractions.

In an example on borrowing I mentioned that 3/5 was greater than 1/5. I knew this since the two fractions both had a common denominator, and then just by looking at the numerators I could tell that 3 was greater than 1.

Similarly if I wanted to compare 4/5 and 2/3 I could change them both to fractions with the LCD and then compare the numerators.
4/5=12/15 ; 2/3=10/15 since 12 is greater than 10, we can conclude that 4/5 is greater than 2/3
Another way of writing this is to say 2/3 is less than 4/5.

Now rather than continually writing less than (or greater than) there are some shortcut symbols

So in the above examples we could write
3/5 > 1/5 (3/5 is greater than 1/5) or 1/5 < 3/5 (1/5 is less than 3/5)
4/5 > 2/3 (4/5 is greater than 2/3) or 2/3 < 4/5 (2/3 is less than 4/5)
4/5=12/15 (4/5 is equal to 12/15)
10/15=2/3 (10/15 is equal to 2/3)

Remember that to compare two fractions, just make sure they have a common denominator and then compare the numerators.
Okay, that doesn't sound too hard, does it?

Exercise 1
Compare 1/3 and 1/2
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
1/3 = 1/2 =
Step 3: Place <, >, or = in the text box between the fractions 1/3 1/2

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Exercise 2
Compare 3/7 and 5/14
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
3/7 = 5/14 =
Step 3: Place <, >, or = in the text box between the fractions 3/7 5/14

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Exercise 3
Compare 21/28 and 3/4
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
21/28 = 3/4 =
Step 3: Place <, >, or = in the text box between the fractions 21/28 3/4

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Exercise 4
Compare 5/12 and 1/6
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
5/12 = 1/6 =
Step 3: Place <, >, or = in the text box between the fractions 5/12 1/6

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Exercise 5
Compare 1/8 and 3/10
Step 1: If necessary find the LCD
Step 2: If necessary, change both fractions to ones with the LCD
1/8 = 3/10 =
Step 3: Place <, >, or = in the text box between the fractions 1/8 3/10

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Now we'll end by going back to our two teams

Your high school baseball team played 25 games this year and won 21 of them.
Your high school football team played 15 games this year and won 11 of them.
Which team had a better season?

The baseball team had a winning ratio of 21/25. the football team had a winning ratio of 11/15.
So this problem comes down to asking which fraction is greater 21/25 or 11/15?

First we need the LCD
15 does not divide 25, so 25 is not the LCD.
25*2=50
25 divides 50, but 15 doe not, so let's go on.
25*3=75
25 diveds 75, and 15 divides 75. 75 is the lCD
75/25=3 so 21/25=63/75 (the baseball team)
75/15=5 so 11/15=55/75 (the football team) since 63/75 > 55/75 we could conclude that
the baseball team had a better year than the football team.

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