Answer :
To solve the problems given, we need to add fractions. This involves ensuring that the fractions have a common denominator before adding them. Let's solve each problem step-by-step.
[tex]\frac{12}{15} + \frac{20}{25}[/tex]
- First, simplify the fractions: [tex]\frac{12}{15} = \frac{4}{5}[/tex] and [tex]\frac{20}{25} = \frac{4}{5}[/tex].
- Both fractions already have the same denominator, so add them: [tex]\frac{4}{5} + \frac{4}{5} = \frac{8}{5}[/tex], which is an improper fraction. As a mixed number, it is [tex]1\frac{3}{5}[/tex].
[tex]\frac{18}{24} + \frac{14}{21}[/tex]
- Simplify: [tex]\frac{18}{24} = \frac{3}{4}[/tex] and [tex]\frac{14}{21} = \frac{2}{3}[/tex].
- Find a common denominator, which is 12.
- Convert [tex]\frac{3}{4}[/tex] to [tex]\frac{9}{12}[/tex] and [tex]\frac{2}{3}[/tex] to [tex]\frac{8}{12}[/tex].
- Add: [tex]\frac{9}{12} + \frac{8}{12} = \frac{17}{12}[/tex], or [tex]1\frac{5}{12}[/tex] as a mixed number.
[tex]\frac{22}{33} + \frac{15}{20}[/tex]
- Simplify: [tex]\frac{22}{33} = \frac{2}{3}[/tex] and [tex]\frac{15}{20} = \frac{3}{4}[/tex].
- Common denominator is 12.
- [tex]\frac{2}{3}[/tex] becomes [tex]\frac{8}{12}[/tex] and [tex]\frac{3}{4}[/tex] becomes [tex]\frac{9}{12}[/tex].
- Add: [tex]\frac{8}{12} + \frac{9}{12} = \frac{17}{12}[/tex], which is [tex]1\frac{5}{12}[/tex].
[tex]\frac{25}{35} + \frac{16}{24}[/tex]
- Simplify: [tex]\frac{25}{35} = \frac{5}{7}[/tex] and [tex]\frac{16}{24} = \frac{2}{3}[/tex].
- Common denominator is 21.
- [tex]\frac{5}{7}[/tex] becomes [tex]\frac{15}{21}[/tex] and [tex]\frac{2}{3}[/tex] becomes [tex]\frac{14}{21}[/tex].
- Add: [tex]\frac{15}{21} + \frac{14}{21} = \frac{29}{21}[/tex], or [tex]1\frac{8}{21}[/tex].
[tex]\frac{30}{45} + \frac{28}{42}[/tex]
- Simplify: [tex]\frac{30}{45} = \frac{2}{3}[/tex] and [tex]\frac{28}{42} = \frac{2}{3}[/tex].
- They have the same denominator: [tex]\frac{2}{3} + \frac{2}{3} = \frac{4}{3}[/tex], which is [tex]1\frac{1}{3}[/tex].
[tex]\frac{21}{28} + \frac{27}{36}[/tex]
- Simplify: [tex]\frac{21}{28} = \frac{3}{4}[/tex] and [tex]\frac{27}{36} = \frac{3}{4}[/tex].
- They have the same denominator: [tex]\frac{3}{4} + \frac{3}{4} = \frac{6}{4}[/tex], or [tex]1\frac{1}{2}[/tex] when simplified.
[tex]\frac{24}{32} + \frac{18}{27}[/tex]
- Simplify: [tex]\frac{24}{32} = \frac{3}{4}[/tex] and [tex]\frac{18}{27} = \frac{2}{3}[/tex].
- Common denominator is 12.
- [tex]\frac{3}{4}[/tex] becomes [tex]\frac{9}{12}[/tex] and [tex]\frac{2}{3}[/tex] becomes [tex]\frac{8}{12}[/tex].
- Add: [tex]\frac{9}{12} + \frac{8}{12} = \frac{17}{12}[/tex], or [tex]1\frac{5}{12}[/tex].
[tex]\frac{26}{39} + \frac{20}{30}[/tex]
- Simplify: [tex]\frac{26}{39} = \frac{2}{3}[/tex] and [tex]\frac{20}{30} = \frac{2}{3}[/tex].
- They have the same denominator: [tex]\frac{2}{3} + \frac{2}{3} = \frac{4}{3}[/tex], or [tex]1\frac{1}{3}[/tex].
[tex]\frac{32}{40} + \frac{15}{25}[/tex]
- Simplify: [tex]\frac{32}{40} = \frac{4}{5}[/tex] and [tex]\frac{15}{25} = \frac{3}{5}[/tex].
- Add: [tex]\frac{4}{5} + \frac{3}{5} = \frac{7}{5}[/tex], or [tex]1\frac{2}{5}[/tex].
[tex]\frac{36}{48} + \frac{14}{21}[/tex]
- Simplify: [tex]\frac{36}{48} = \frac{3}{4}[/tex] and [tex]\frac{14}{21} = \frac{2}{3}[/tex].
- Common denominator is 12.
- [tex]\frac{3}{4}[/tex] becomes [tex]\frac{9}{12}[/tex] and [tex]\frac{2}{3}[/tex] becomes [tex]\frac{8}{12}[/tex].
- Add: [tex]\frac{9}{12} + \frac{8}{12} = \frac{17}{12}[/tex], or [tex]1\frac{5}{12}[/tex].
By simplifying and finding common denominators, we can add these fractions to find the solutions.
