Math210
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Chapter4section1
Equivalentfractions
Vocabulary:
fraction:form:
ch4se1Redwood2nd
a
b
numerator:a
denominator:b
EquivalentFractions-representthesamenumericalvalue
Visualization
1 3 2
6
1 2
Visualizationofequivalentfractions: = 3 6
1
Noticethatifstartwithfraction, andmultiplybothnumeratoranddenominatorby2
3
1 1i2
2
=
theresultsis 3 3i2
6
Createequivalentfractions:
Startwithafraction,thenmultiplybothitsnumeratoranddenominatorbysamenumber,the
resultingfractionisequivalenttotheoriginalfraction
a ai x
=
b bi x
Thereversisalsotrue.Insteadofmultiplying,onecandivide.
2 2÷ 2
1
=
,theresultsis 6 6 ÷ 2
3
Divisor,factor
36isdividedby4,remainderof0,therefore4isadivisorof36,4isafactorof36
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Math210
ch4se1Redwood2nd
25isdividedby4,remainderisnotzero,therefore4isnotadivisorof25,4isnotafactorof25.
Divisors
18:1,2,3,6,918
24:1,2,3,4,6,8,12,24
Commondivisors:1,2,3,6
Greatestcommonfactor(GCF):6
Reducefractionstolowestterms:
AfractionisreducedtolowerstermsiftheGCF=1
18
Reduce: TheGCFbetween18and24is6,sodivideby6
24
18 ÷ 6
24 ÷ 6
3
4
Orfactor
6isadivisor
6isafactor
18 3i6
=
24 4 i6
Useafactortreetofindtheprimefactorsof18and24
18
2i3i3
=
reduce
24 2i2i2i3
3
4
Reducefractionswithvariables
56x 2 y
2
60xy
Equivalentfractionsinhigherterms.
Page 3 of 3
Math210
3
withadenominatorof20
5
Negativefractions
placementofnegativesign
3 −3
3
=
= − 5
−5 5
Practice
18
54x 3 y 3
1)
2)
2
60xy
20
ch4se1Redwood2nd
3)
50x 3
5
−75x
−12xy 2
4)
2
−18x
y