GoldenLeaf

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GoldenLeaf  Apr 29, 2015
 #1
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$${\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$

 

Think of the fractions as added onto the whole numbers. Take the equation and add the whole numbers together. Separate the fractions.

 

$$\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right){\mathtt{\,\small\textbf+\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)$$

 

3+2 is 5, but what about 1/2 + 1/3? To add fractions, find the LCM, or Least Common Multiple.

 

2: 2, 4, 6, 8, 10...

3: 3, 6, 9, 12, 15...

 

The first number where these two have the same factor is 6, so, in order to add these numbers together, make the denominators of both 6. For 1/2, we pultiply the top and the bottom by 3, and for 1/3 we multiply both by 2.

 

(1*3)/(2*3) = 3/6

(1*2)/(3*2) = 2/6

 

Now, since they have a common denominator, add the numerators together:

 

$${\frac{{\mathtt{3}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{6}}}} = {\frac{{\mathtt{5}}}{{\mathtt{6}}}} = {\mathtt{0.833\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

 

Final answer: 5 5/6

 

(Another method of finding the LCM is to multiply the two numerators: In this case, multiplying 2 and 3:

 

$${\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}} = {\mathtt{6}}$$

 

In the end, the answer is still 6.

 

From there, you can then multiply one factor's denominator by the other's and vice versa. After that, proceed as normal.)

Feb 6, 2015
 #8
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+5
Dec 19, 2014