How do you reduce 84/98 to its lowest terms?

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Jim G. Share
Dec 27, 2017

Answer:

#6/7#

Explanation:

#"reduce the fraction by dividing the numerator/denominator"#
#"by the "color(blue)"highest common factor"#

#"in this case the highest common factor is 14"#

#rArr84/98=(84-:color(red)(14))/(98-:color(red)(14))=6/7#

#"this is often expressed using "color(blue)"cancelling"#

#rArrcancel(84)^6/cancel(98)^7=6/7#

#"if you do not see that 14 is the highest common factor"#

#"then begin by using smaller common factors"#

#"2 is a common factor of both numbers"#

#rArrcancel(84)^(42)/cancel(98)^(49)=42/49#

#"now repeat using the common factor of 7"#

#rArrcancel(42)^6/cancel(49)^7=6/7larrcolor(red)"in simplest form"#

#"A fraction is in "color(red)"simplest form"" when no other"#
#"factor but 1 divides into the numerator/denominator"#

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Dec 29, 2017

Answer:

#6/7#

Explanation:

To reduce any fraction to it's lowest terms means to reduce it to a fraction which cannot be reduced further.

So, to find the lowest term for the fraction #84/98#, the following steps should be done:

Step1. Divide the numerator and denominator by a common factor which is #2# (though it can be divided by #14# as well if we take LCD of both numbers. But in case one forgets the concept of LCD, then also the question can be done stepwise)

which is, #(cancel(84)^42)/(cancel(98)_49)# or, #42/49#

Step 2: Divide #42/49# by a common factor again, which is #7#

So, #cancel42^6/cancel49_7# = #6/7#

Remember, when no common factor other than #1# is there for dividing the numerator and denominator, then that step will be the last step to find the lowest term.

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