To solve, simply find a common denominator and add.

Multiply the first fraction by  \(\displaystyle \frac{3}{3}\) to get 15 as the common denomintor and then add the numerators.

Thus,

\(\displaystyle \frac{3}{5}*\frac{3}{3}+\frac{2}{15}=\frac{9}{15}+\frac{2}{15}=\frac{11}{15}\)

The easiest way is to convert each fraction to a decimal first, then add. \(\displaystyle \frac{1}{8}\) can be converted to a decimal by dividing 1 by 8; \(\displaystyle \frac{1}{5}\) can be converted similarly:

\

Add:

\(\displaystyle \begin{matrix} 0.125\\ \underline{0.200}\\ 0.325 \end{matrix}\)

\(\displaystyle -1\frac{1}{3} < 1 \frac{1}{3}\)

\(\displaystyle -4 \frac{1}{2} - 1\frac{1}{3 } < -4 \frac{1}{2}+ 1\frac{1}{3 }\)

\(\displaystyle A-B < A+B\)

so \(\displaystyle A + B\) can be eliminated as the least of the four.

\(\displaystyle 1 \frac{1}{3}\), which is equal to \(\displaystyle \frac{4}{3}\), has as its reciprocal \(\displaystyle \frac{3}{4}\), and:

\(\displaystyle 1 \frac{1}{3} > 1 > \frac{3}{4}\)

\(\displaystyle -4 \frac{1}{2} \cdot 1 \frac{1}{3} < -4 \frac{1}{2} \cdot \frac{3}{4}\)

\(\displaystyle -4 \frac{1}{2} \cdot 1 \frac{1}{3} < -4 \frac{1}{2} \div 1 \frac{1}{3}\)

\(\displaystyle A \cdot B< A \div B\)

so \(\displaystyle A \div B\) can be eliminated as the least of the four.

To find the least of the four, we only need to compare \(\displaystyle A \cdot B\) and \(\displaystyle A-B\):

\(\displaystyle A \cdot B =-4 \frac{1}{2} \cdot 1 \frac{1}{3}\)

\(\displaystyle =- \frac{4 \cdot 2+ 1}{2} \cdot \frac{1 \cdot 3 + 1}{3}\)

\(\displaystyle =- \frac{9}{2} \cdot \frac{4}{3} = - \frac{36}{6} = -6\)

\(\displaystyle A - B =-4 \frac{1}{2}- 1 \frac{1}{3}\)

\(\displaystyle =-4 \frac{1}{2} + \left (- 1 \frac{1}{3} \right )\)

\(\displaystyle =-4 \frac{3}{6} + \left (- 1 \frac{2}{6} \right )\)

\(\displaystyle =-5\frac{5}{6}\)

\(\displaystyle A \cdot B < A - B\);

\(\displaystyle A \cdot B\) is the least of the four and is the correct choice.

To add fractions, they must have a common denominator.  

Both \(\displaystyle 2\) and \(\displaystyle 3\) have \(\displaystyle 6\) as a multiple.

You must multiple the first fraction by \(\displaystyle 3\) to get \(\displaystyle \frac{9}{6}\) and the second by \(\displaystyle 2\) to get \(\displaystyle \frac{2}{6}\).  

Then you just add the two numerators \(\displaystyle 9+2=11\) to get \(\displaystyle \frac{11}{6}\).

Since \(\displaystyle 2\) is an actual factor of \(\displaystyle 4\), you can just use \(\displaystyle 4\) as your common denominator which is less than \(\displaystyle 8\).

\(\displaystyle \frac{5}{9} + \frac{7}{9} =\)

These two fractions are like fractions, because they have the same denominator.

Just add the numerators and write the sum over the denominator. Then simplify.

\(\displaystyle \frac{5}{9} + \frac{7}{9} = \frac{12}{9}\)

\(\displaystyle \frac{12}{9} = 1\frac{3}{9} = 1\frac{1}{3}\)

\(\displaystyle \frac{4}{5} - (-\frac{3}{5})\)

When subtracting a negative, the subtraction and negative sign become an addition sign.

\(\displaystyle \frac{4}{5} - (-\frac{3}{5}) = \frac{4}{5} + \frac{3}{5}\) 

\(\displaystyle \frac{4}{5} + \frac{3}{5} = \frac{7}{5}\)

\(\displaystyle \frac{7}{5}\) is an improper fraction because the numerator is greater than the denominator. Therefore, it needs to be simplified.  This is done by dividing the numerator by the denominator.

\(\displaystyle 7\div 5 = 1 \frac{2}{5}\) 

Find \(\displaystyle a-b\) if 

\(\displaystyle a = 6\frac{1}{3}\) and

\(\displaystyle b=-1\frac{1}{3}\)

\(\displaystyle 6\frac{1}{3} - (-1\frac{1}{3}) = 6\frac{1}{3} + 1\frac{1}{3}\)

When subtracting a negative, the sign becomes a plus sign which indicates addition.

\(\displaystyle 6\frac{1}{3} + 1\frac{1}{3} = (6+1) + \frac{1+1}{3}\)

\(\displaystyle 7\frac{2}{3}\)

\(\displaystyle 8\frac{1}{10 } - 3\frac{7}{10}\)

Because the numerator of the second mixed number (7) is greater than the numerator of the first mixed number (1) and the operation is subtraction, convert both mixed numbers into improper fractions.

\(\displaystyle 8\frac{1}{10} = \frac{(10\times 8)+1}{10} = \frac{81}{10}\)

\(\displaystyle 3\frac{7}{10 } = \frac{(10\times 3)+7}{10} = \frac{37}{10}\)

\(\displaystyle \frac{81}{10} -\frac{37}{10} =\frac{81-37}{10}\)

\(\displaystyle \frac{44}{10} = 4\frac{4}{10} = 4\frac{2}{5}\)

Find \(\displaystyle a + b\) if

 \(\displaystyle a = 5/12\)  and

\(\displaystyle b = -1\frac{1}{12}\)

\(\displaystyle \frac{5}{12} + (-1\frac{1}{12})\)

Convert the mixed number to an improper fraction.

\(\displaystyle \frac{5}{12} + (-\frac{13}{12}) =\)

\(\displaystyle \frac{5+ (-13)}{12} = \frac{-8}{12}\)

Reduce to simplest form by dividing the numerator and the denominator by the GCF or the Greatest Common Factor which is 4.

\(\displaystyle \frac{-8\div 4}{12\div 4} = -\frac{2}{3}\)