Adding Subtracting
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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.
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.
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