how do you add #2\frac { 1} { 2} + 2\frac { 2} { 3}#?

Answer 1

See below.

First, the numbers must be changed to an improper fraction, meaning that there are no whole numbers. I am going to demonstrate how to do this with the #2 1/2#.

Step 1: To start off, you must multiply the denominater

#2 1/color(red)2#

by the whole number

#color(blue)2 1/color(red)2#
to get the equation #color(blue)2*color(red)2#, which equals #4#.

Step 2: Now, you must add the number we just got

#color(green)4#

to the numerator

#2 color(teal)1/2#
getting the equation #color(green)4+color(teal)1#, which equals #5#. Now that 5, becomes our numerator, but the denominater stays the same, which leaves us with the improper fraction of #5/2#.
You can now do the same thing with the other fraction, resulting in the equation #5/2+8/3#.
The next step to solve this problem is to change the denominators so that they are common, or the same number. The first common number they have, is #6#, since #2*3=6# and #3*2=6#.

Since 2 (the denominater) has to be multiplied by 3 to get to 6, 5 (the numerator) must also be multiplied by 3.

#(5*3)/ (2*3)#
This results in the fraction of #15/6#.

Now, in the other fraction, since 3 (denominater) must be multiplied by 2 to get 6, 8 (the numerator) must also be multiplied by 2.

#(8*2)/(3*2)#
This results in the fraction of #16/6#.

Now that the denominaters are the same, the numerators must be added to complete the problem.

#15+16=31#
That is your new numerator, which is put over the common denominater of 6, to get #31/6#.
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Answer 2

To add (2\frac{1}{2}) and (2\frac{2}{3}), first convert the mixed numbers to improper fractions, then add the fractions together, and finally simplify if needed.

(2\frac{1}{2}) as an improper fraction is (2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}).

(2\frac{2}{3}) as an improper fraction is (2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}).

Now, add the fractions: [ \frac{5}{2} + \frac{8}{3} = \frac{15}{6} + \frac{16}{6} = \frac{15 + 16}{6} = \frac{31}{6} ]

So, (2\frac{1}{2} + 2\frac{2}{3} = 2\frac{31}{6}).

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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.

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.

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.

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.

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