These are the formulas used for calculating with fraction numbers:[br][br][math]\Large \textcolor{blue}{1. \quad\frac{a}{c}+\frac b c=\frac{a+b}{c}}[/math][br][math]\Large \textcolor{blue}{2. \quad\frac a b +\frac c d=\frac {^{d)}a}{b}+\frac {^{b)}c}{d}=\frac{a\cdot d}{b\cdot d}+\frac{b\cdot c}{b\cdot d}=\frac{a\cdot d+b\cdot c}{b\cdot d}}[/math][br][math]\Large \textcolor{blue}{3. \quad\frac a b \cdot \frac c d = \frac{a\cdot c}{b\cdot d}}[/math][br][math]\Large \textcolor{blue}{4. \quad\frac a b \div \frac c d= \frac a b \cdot \frac d c = \frac{a \cdot d}{b\cdot c}}[/math][br][br]A mixed number can be rewrite as a fraction number as followed:[br][br][math]\Large a\frac b c = \frac{a\cdot c+b}{c}[/math]

Addition and subtraction with fractions requires denominators to be the same. When this is accomplished, numerators are summed and the result is divided with a common denominator.[br][br][color=#0000ff]Example 1[/color]. [math] \frac{^{5)}3}{4}-\frac{^{4)}1}{5}+\frac{^{2)}4}{10}=\frac{5\cdot 3}{5\cdot 4}-\frac{4\cdot 1}{4\cdot 5}+\frac{2\cdot 4}{2\cdot 10}=\frac{15-4+8}{20}=\frac{19}{20}[/math][br] [br][color=#0000ff][color=#000000][br]If numbers are given as mixed numbers, they must be transformed to fraction numbers before performing calculations[br][/color][br]Example 2[/color]. [math] 2\frac{2}{3}+4\frac{5}{6}=\frac{2\cdot 3 +2}{3}+\frac{4\cdot 6+5}{6}=\frac{^{2)} 8}{3}+\frac{29}{6}=\frac{45^{(3}}{6}=\frac{15}{2}=7\frac{1}{2}.[/math][br][br]If fractions numbers are multiplied with each other, numerators can be multiplied with each other and denominators with each others. Before actual multiplication, numbers could be cancelled as much as possible. In the next example, the number 3 in the numerator can be cancelled with the number 9 in the denominator. [br] [br][color=#0000ff]Example 3[/color]. [math] \frac{3}{5}\cdot \frac{2}{9}=\frac{ \cancel 3 \cdot 2}{5\cdot \cancel 9_3 }=\frac{2}{15}[/math][br][br][br]When fraction numbers are divided with each other, it can be transformed into multiplication by inversing the divisor. In the next example, the divisor is [math] \frac{2}{3}[/math] and its inverse number is [math] \frac{3}{2}:[/math] [br] [br][color=#0000ff]Example 4[/color]. [math] \frac{4}{5}\div \frac{2}{3}=\frac{4}{5}\cdot\frac{3}{2}=\frac{\cancel 4^2\cdot 3}{5\cdot \cancel 2}=\frac{6}{5}[/math]