Adding and Subtracting Fractionsdenominator. It does not change –2nd add or subtract the...
Transcript of Adding and Subtracting Fractionsdenominator. It does not change –2nd add or subtract the...
Adding and SubtractingAdding and SubtractingFractionsFractions
Like and Unlike FractionsLike and Unlike Fractions
In the Beginning…likefractions
• When we add orsubtract likefractions we havetwo steps– 1st write the
denominator. Itdoes not change
– 2nd add or subtractthe numerators
4
6 61+
-113
4
3
6
5
7
3
=
=
Always remember!• When adding and subtracting fractions,
you must have like denominators. Ifthey are not the same, you cannotsolve the problem.
• This is different for multiplication anddivision. That is a differentpresentation. BEWARE…
What if you have to add orsubtract fractions withunlike denominators?
• Don’t panic. To solve unlike fractions,there are a couple extra steps (like 7 ifyou want to know…).
Unlike Fractions• These fractions
cannot be added.We must changethe fractions to likefractions.
• Meaning the bottomnumbers must bethe 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 thesmallest overlappingnumber.
!
4
6
!
7
3
+
6: 6, 12, 18,24, 30
3: 3, 6, 9, 12,15
Step 2• Set-up a
multiplicationproblem and solvefor the missingnumber in thedenominator.
• Note: parenthesis isa multiplication sign.
!
4
6
!
7
3
+
( )
( )!
6
!
6
=
=
Step 3• Complete the
multiplicationproblem.
!
4
6
!
7
3
+
( )
( )!
6
!
6
=
=
6 x _ = 66 x 1 = 6
3 x _ = 63 x 2 = 6
Rule• What you multiple
the bottom by, youmust multiply thetop by.
• We call this a‘fraction of one’when the top andbottom numbers arethe same.
!
6
6
Step 4• Write the fraction of
one in theparenthesis.
• Each fraction will bedifferent, based onthe missingmultiplicationproblem.(see slide 8)
!
4
6
!
7
3
+
( )
( )!
6
!
6
=
=!
1
1
!
2
2
Step 5• Multiple the top
numbers for bothfractions.
!
4
6
!
7
3
+
( )
( )!
4
6
!
14
6
=
=!
1
1
!
2
2
4 x 1 = 4
7 x 2 = 14
Step 6• Add the new fraction
problem.• Remember the
bottom numberstays the same.
• Add only the top.!
4
6
!
7
3
+
( )
( )!
4
6
!
14
6
=
=!
1
1
!
2
2
!
18
6
Step 7• To simplify: Solve
as a divisionproblem and solve
!
18
6= 6 18)
!
6 18
3
)
!
18
6= 3
How about subtractingHow about subtractingunlike fractions?unlike fractions?
Subtracting Unlikefractions
• It is the same process!• EXCEPT for step 6: Subtract the new
fractions set; do not add.