Denominatorand Numerator CommonDenominator

Simplifying, or Reducing theFraction
Numerator / Denominator
Wecallthe top numberthe Numerator, it is thenumberof parts we have.
Wecallthebottomnumberthe Denominator, it is thenumberof parts thewhole is dividedinto.
Numerator/Denominator
Youjusthave to rememberthosenames! (Ifyouforgetjustthink "Down"-ominator)

Thedefinitionof a denominatormeanssomethingthat is shared, or is thestandard, or thenumberbelowtheline in a fraction.

Anexampleof a denominator is theredhaircolorsharedbyallmembersof a family.

Anexampleof a denominator is a commonlevelofwritingexpected in a compositionclass.

Anexampleof a denominator is the "2" in thefraction "½."

AddingFractions

It is easy to addfractionswiththe samedenominator (samebottomnumber):

^1/4	+	^1/4	=	^2/4	=	^1/2
(One-Quarter)		(One-Quarter)		(Two-Quarters)		(One-Half)
	+		=		=

One-quarter plus one-quarterequalstwo-quarters, equalsone-half
Anotherexample:

^5/8	+	^1/8	=	^6/8	=	^3/4
	+		=		=

Five-eighths plus one-eighthequals six-eighths, equalsthree-quarters
AddingFractionswithDifferentDenominators
But whataboutwhenthe denominators (thebottomnumbers) arenotthesame?

^3/8	+	^1/4	=	?
	+		=

Three-eighths plus one-quarterequals ... what?
Wemust somehow makethedenominatorsthesame.
In thiscase it is easy, becauseweknowthat ¹/₄ is thesameas ²/₈ :

^3/8	+	^2/8	=	^5/8
	+		=

Three-eighths plus two-eighthsequalsfive-eighths
Therearetwopopularmethods to makethedenominatorsthesame:

• 
  LeastCommonDenominator or
  
• 
  CommonDenominator
  

(Theybothworknicely, usetheoneyouprefer.)

DefinitionofDenominator

Whenaninteger is expressedas a fraction, thenthereappeartwonumbersseparatedby a horizontalline. Thedenominator is thenumberthatappearsatthebottomofthehorizontalline, whereasthenumberabovetheline is thenumerator. It is notnecessarythatonlynumericalvaluesareexpressed in thenumeratoranddenominatorform, instead, thevariablesarealsoexpressed in thesameformsuchas x/y, p/q, m/n, etc., where y, q, and n arethedenominatorsrespectively.
A fractionconsistsoftwonumbers. Symbolically it is representedbytwonumbersseparatedby a horizontalline (–) or slashline (/). Thenumberabovetheline is thenumerator, andthenumberbelowtheline is thedenominator. Thetermdenominator is widelyused in ratioandproportion concept.

In theabovefigure, 4, 2, and 4 arethedenominatorsof 1/4, 1/2, and 3/4 respectively.

Thedenominatorvalueshouldnotbe zero. Because, ifthevalueofthedenominator is zero, thefractionvalueshouldbeundefined. Forexample, 5/0 is a fraction, which is undefinedasthedenominatorvalue is zero.