Addition and subtraction of dissimilar rational algebraic expression.express your answer in simpliest form.
1. ½+4/3=
2. 5/8+3/8=
3. -4/8+3/10=
4. ½-4/3=
5. ¼-3/2=

Answer:[tex]1. \: \frac{1}{2} + \frac{4}{3}[/tex] - Find the least common denominator (LCD), which is 6. - Convert each fraction: [tex]\frac{1}{2} = \frac{3}{6}[/tex]and [tex]\frac{4}{3} = \frac{8}{6}.[/tex] - Add the fractions: [tex]\frac{3}{6} + \frac{8}{6} = \frac{11}{6}.[/tex][tex]2. \: \frac{5}{8} + \frac{3}{8}[/tex] - The denominators are already the same. - Add the numerators: [tex]\frac{5 + 3}{8} = \frac{8}{8} = 1.[/tex][tex]3. \: -\frac{4}{8} + \frac{3}{10}[/tex] - Simplify the first fraction: [tex]-\frac{4}{8} = -\frac{1}{2}.[/tex] - Find the LCD, which is 20. - Convert each fraction: [tex]-\frac{1}{2} = -\frac{10}{20} [/tex]and [tex]\frac{3}{10} = \frac{6}{20}.[/tex] - Add the fractions: [tex]-\frac{10}{20} + \frac{6}{20} = -\frac{4}{20} = -\frac{1}{5}.[/tex][tex]4. \: \frac{1}{2} - \frac{4}{3}[/tex] - Find the LCD, which is 6. - Convert each fraction: [tex]\frac{1}{2} = \frac{3}{6} [/tex]and [tex]\frac{4}{3} = \frac{8}{6}.[/tex] - Subtract the fractions: [tex]\frac{3}{6} - \frac{8}{6} = -\frac{5}{6}.[/tex][tex]5. \: \frac{1}{4} - \frac{3}{2}[/tex] - Find the LCD, which is 4. - Convert each fraction: [tex]\frac{1}{4} = \frac{1}{4} [/tex]and [tex]\frac{3}{2} = \frac{6}{4}.[/tex] - Subtract the fractions: [tex]\frac{1}{4} - \frac{6}{4} = -\frac{5}{4}.[/tex]

Answered by MisterOrangeGuy | 2024-09-03