Understanding Subtraction of Fractions:

Under the Addition of Fractions, we saw how placing the fractions on number lines necessitated determining an equal number of subdivisions for both lines. That same approach applies when working with subtraction.

On the "thirds" line, if we cut each "third" into two equal sections we will get 6 in total.
On the "halves" line, if we cut each "half" into three equal sections we will get 6 in total.
(This number 6 will be called our common denominator.)

Subtract:
sub1
addline

Now that both lines contain subdivisions of the same size (both have 6 sections), we can express our fractions using this new subdivision size of 1/6. Then we can subtract the fractions.
sub2

Let's combine our number lines onto one line to demonstrate this difference.
addlinesum

 

Same Denominators:
When the fractions have the same denominators, adding and subtracting are easy.
Think of it as already dealing with equal sections on the number line.

When adding (or subtracting) fractions with the same denominators,
just add (or subtract) the numerators.

asb4
Since the denominators are the same, the answer can be found by subtracting the numerators (tops).
asb1
This answer can be simplified (reduced).
asb2
49

had2
asb33
Using the "separate parts" method: asb5

     beware

Notice the parentheses in the first line. You must subtract the ENTIRE amount of the second mixed number. When the parentheses are removed, notice that 5/11 is also being subtracted. (The subtraction has been distributed across the parentheses.)
Sometimes, during subtraction, you need to borrow, so you will have a sufficient amount from which to subtract. Consider the following:
7to6
We just borrowed a "1" from 7, changed it to "5/5" and created a fraction with a larger numerator. A fraction with a larger numerator may be useful when subtrating.

ass1
Using the "line up" method:
You can immediately see a problem: you cannot subtract 4/5 from 2/5. We need to borrow a "1" or "5/5" from the 7, and add that amount to the 2/5.
  ass1 arrowup

ass1 Visualize:
hat2pic


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Different Denominators:
When fractions have different denominators, you must work with common denominators. Think of it as finding the needed number of subdivisions for the number line.

When adding (or subtracting) fractions with different denominators,
you must
find a common denominator before adding (or subtracting).

addd10
Least common denominator of 6 and 9 is 18.

     addd11  


addd7
Least common denominator of 4 and 6 is 12. Borrowing will be needed.
     addd8 

s1
beware This type of problem can be confusing. Think carefully before writing your final answer.

First, let's LOOK at what the answer should be.

bw1

The answer
should be
bw2.

arrowup

 

guyslook

"Separate parts horizontally method":
For this question, this method can be a bit confusing. Be careful!
bw3

"Line up vertically":
This method gives you a bit of a hint that something is missing in this problem. Be careful not to simply "drop" the 2/3 down into the answer.
bw4

You could think of the empty
oval as
bw6g
.

We need to "borrow" 1 from the 4:
bw5

 

ti84c
For help with fractions
on your calculator,
click here.

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