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How do you simplify #abs(1/5-1/3)#?

Answer 1

Avery Alexander

#2/15#

#"evaluating the fractions as a first step"#

#"Before subtracting we require a "color(blue)"common denominator"#

#"the lowest common multiple of 5 and 3 is 15"#

#rArr1/5-1/3=(1xx3)/(5xx3)-(1xx5)/(3xx5)=3/15-5/15#

#"subtract the numerators leaving the denominator"#

#rArr3/15-5/15=(3-5)/15=-2/15#

#"the "color(blue)"absolute value is always positive"#

#rArr|-2/15|=2/15#

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Answer 2

Kennedy Adams

To simplify ( | \frac{1}{5} - \frac{1}{3} | ), first, find a common denominator for ( \frac{1}{5} ) and ( \frac{1}{3} ), which is ( 15 ). Then, calculate the expression:

[ | \frac{1}{5} - \frac{1}{3} | = | \frac{3}{15} - \frac{5}{15} | ]

[ = | \frac{3-5}{15} | ]

[ = | -\frac{2}{15} | ]

[ = \frac{2}{15} ]

So, ( | \frac{1}{5} - \frac{1}{3} | ) simplifies to ( \frac{2}{15} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.