Download Adding and Subtracting Fractions

Adding and Subtracting
Fractions
Like and Unlike Fractions
In the Beginning…like
fractions
• When we add or
subtract like
fractions we have
two steps
– 1st write the
denominator. It
does not change
– 2nd add or subtract
the numerators
4 + 1
6
6
11
3
-
4
3
=
=
5
6
7
3
Always remember!
• When adding and subtracting fractions,
you must have like denominators. If
they are not the same, you cannot
solve the problem.
• This is different for multiplication and
division. That is a different
presentation. BEWARE…
What if you have to add or
subtract fractions with
unlike denominators?
• Don’t panic. To solve unlike fractions,
there are a couple extra steps (like 7 if
you want to know…).
Unlike Fractions
• These fractions
cannot be added.
We must change
the fractions to like
fractions.
• Meaning the bottom
!
numbers must be
the same.
!
4
6
+
7
3
Step One
• First, we focus on the
denominators: 3 & 6.
• We need to find the Least
Common Denominator.
• List on multiples of 3 and
6 until one overlaps.
• In this case, it is 6.!12
overlaps but we want the
smallest overlapping
number.
!
4
6
+
7
3
6: 6, 12, 18,
24, 30
3: 3, 6, 9, 12,
15
Step 2
• Set-up a
multiplication
problem and solve
for the missing
+
number in the
denominator.!
• Note: parenthesis is
a multiplication sign.
!
4
6
( )=
6
7
3
( )
6
!
!
=
Step 3
• Complete the
multiplication
problem.
+
4
6
( )=
6
7
3
( )
6
=
!
!
!
6x_ =6
3x_=6
6x1=6! 3x2=6
Rule
• What you multiple
the bottom by, you
must multiply the
top by.
• We call this a
‘fraction of one’
when the top and
bottom numbers are
the same.
6
6
Step 4
• Write the fraction of
one in the
parenthesis.
• Each fraction will be
different, based on
the missing
!
multiplication
!
problem.
(see slide 8)
!
+
4
6
( )=
6
7
3
( )
6
1
1
2
2
!
!
!
=
Step 5
4x1=4
• Multiple the top
numbers for both
fractions.
4
6
!
+
( )=
1
1
7 x 2 = 14
7
3
( )
2
2
!
!
!
!
!
=
4
6
14
6
Step 6
• Add the new fraction
problem.
• Remember the
bottom number
stays the same.
!
• Add only the top.
+
4
6
( )
14
6
( )=
7
3
2
2
!
!
!
!
1
1
4
6
!
=
18
6
Step 7
• To simplify: Solve
as a division
problem and solve
3
6!)18
!
!
18
= 6)18
6
18
=3
6
How about subtracting
unlike fractions?
Subtracting Unlike
fractions
• It is the same process!
• EXCEPT for step 6: Subtract the new
fractions set; do not add.