+1006 $${\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$
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.)
+1006 $${\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$
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.)
