adding and subtracting fractions · •when adding and subtracting fractions, you must have like...
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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.
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