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How do you evaluate #\frac { \frac { 1} { 2} + \frac { 2} { 3} } { 1\frac { 1} { 5} }#?

Answer 1

Mila Anderson

#35/36#

#(1/2+2/3)/(1 1/5#

#:.=((3+4)/6)/(6/5)#

#:.=(7/6)/(6/5)#

#:.=7/6 xx 5/6#

#:.=35/36#

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Answer 2

Benjamin Altschul

To evaluate ( \frac { \frac { 1} { 2} + \frac { 2} { 3} } { 1\frac { 1} { 5} } ), follow these steps:

Convert the mixed number ( 1\frac { 1} { 5} ) to an improper fraction: ( \frac {6} {5} ).
Rewrite the expression as ( \frac { \frac { 1} { 2} + \frac { 2} { 3} } { \frac {6} {5} } ).
Find a common denominator for the fractions in the numerator: ( \frac { \frac {3} {6} + \frac {4} {6} } { \frac {6} {5} } ).
Combine the fractions in the numerator: ( \frac { \frac {7} {6} } { \frac {6} {5} } ).
Invert the divisor and multiply: ( \frac { \frac {7} {6} } { \frac {6} {5} } \times \frac {5} {6} ).
Multiply the numerators and denominators: ( \frac {7 \times 5} {6 \times 6} ).
Calculate the result: ( \frac {35} {36} ).

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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.