Question #97f77

To reduce any fraction to its 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.

`"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"`