Operations with Unlike Fractions Worksheets - 15 Worksheets Library - Free Printable

Here are the step-by-step solutions for each problem. To add fractions with different denominators, we first find a common denominator, convert the fractions, add the numerators, and then simplify if possible.

1) $\frac{9}{5} + \frac{15}{10}$
* Common denominator is 10.
* Convert $\frac{9}{5}$: Multiply top and bottom by 2 to get $\frac{18}{10}$.
* Add: $\frac{18}{10} + \frac{15}{10} = \frac{33}{10}$.
* This cannot be simplified further (as a proper fraction), but can be written as $3 \frac{3}{10}$. We will keep it as an improper fraction $\frac{33}{10}$ or mixed number depending on standard practice. Usually, improper fractions are acceptable unless specified otherwise. Let's provide the simplified improper fraction or mixed number. $\frac{33}{10}$ is already in simplest terms relative to integers.

2) $\frac{18}{4} + \frac{7}{5}$
* Common denominator is 20.
* Convert $\frac{18}{4}$: Multiply by 5/5 $\rightarrow \frac{90}{20}$.
* Convert $\frac{7}{5}$: Multiply by 4/4 $\rightarrow \frac{28}{20}$.
* Add: $\frac{90 + 28}{20} = \frac{118}{20}$.
* Simplify: Divide by 2 $\rightarrow \frac{59}{10}$.

3) $\frac{15}{6} + \frac{19}{12}$
* Common denominator is 12.
* Convert $\frac{15}{6}$: Multiply by 2/2 $\rightarrow \frac{30}{12}$.
* Add: $\frac{30}{12} + \frac{19}{12} = \frac{49}{12}$.

4) $\frac{21}{15} + \frac{12}{5}$
* Common denominator is 15.
* Convert $\frac{12}{5}$: Multiply by 3/3 $\rightarrow \frac{36}{15}$.
* Add: $\frac{21}{15} + \frac{36}{15} = \frac{57}{15}$.
* Simplify: Divide by 3 $\rightarrow \frac{19}{5}$.

5) $\frac{18}{12} + \frac{21}{9}$
* Simplify first: $\frac{18}{12} = \frac{3}{2}$ and $\frac{21}{9} = \frac{7}{3}$.
* Common denominator for 2 and 3 is 6.
* Convert $\frac{3}{2} \rightarrow \frac{9}{6}$.
* Convert $\frac{7}{3} \rightarrow \frac{14}{6}$.
* Add: $\frac{9}{6} + \frac{14}{6} = \frac{23}{6}$.

6) $\frac{25}{15} + \frac{20}{3}$
* Simplify $\frac{25}{15}$ by dividing by 5 $\rightarrow \frac{5}{3}$.
* Add: $\frac{5}{3} + \frac{20}{3} = \frac{25}{3}$.

7) $\frac{9}{5} + \frac{10}{3}$
* Common denominator is 15.
* Convert $\frac{9}{5} \rightarrow \frac{27}{15}$.
* Convert $\frac{10}{3} \rightarrow \frac{50}{15}$.
* Add: $\frac{27}{15} + \frac{50}{15} = \frac{77}{15}$.

8) $\frac{14}{9} + \frac{5}{3}$
* Common denominator is 9.
* Convert $\frac{5}{3} \rightarrow \frac{15}{9}$.
* Add: $\frac{14}{9} + \frac{15}{9} = \frac{29}{9}$.

9) $\frac{21}{15} + \frac{12}{5}$
* Simplify $\frac{21}{15}$ by dividing by 3 $\rightarrow \frac{7}{5}$.
* Add: $\frac{7}{5} + \frac{12}{5} = \frac{19}{5}$.

10) $\frac{15}{9} + \frac{9}{5}$
* Simplify $\frac{15}{9}$ by dividing by 3 $\rightarrow \frac{5}{3}$.
* Common denominator for 3 and 5 is 15.
* Convert $\frac{5}{3} \rightarrow \frac{25}{15}$.
* Convert $\frac{9}{5} \rightarrow \frac{27}{15}$.
* Add: $\frac{25}{15} + \frac{27}{15} = \frac{52}{15}$.

11) $\frac{18}{10} + \frac{14}{5}$
* Simplify $\frac{18}{10}$ by dividing by 2 $\rightarrow \frac{9}{5}$.
* Add: $\frac{9}{5} + \frac{14}{5} = \frac{23}{5}$.

12) $\frac{12}{9} + \frac{4}{3}$
* Simplify $\frac{12}{9}$ by dividing by 3 $\rightarrow \frac{4}{3}$.
* Add: $\frac{4}{3} + \frac{4}{3} = \frac{8}{3}$.

13) $\frac{21}{15} + \frac{17}{10}$
* Simplify $\frac{21}{15}$ by dividing by 3 $\rightarrow \frac{7}{5}$.
* Common denominator for 5 and 10 is 10.
* Convert $\frac{7}{5} \rightarrow \frac{14}{10}$.
* Add: $\frac{14}{10} + \frac{17}{10} = \frac{31}{10}$.

14) $\frac{30}{12} + \frac{15}{4}$
* Simplify $\frac{30}{12}$ by dividing by 6 $\rightarrow \frac{5}{2}$.
* Common denominator for 2 and 4 is 4.
* Convert $\frac{5}{2} \rightarrow \frac{10}{4}$.
* Add: $\frac{10}{4} + \frac{15}{4} = \frac{25}{4}$.

15) $\frac{19}{14} + \frac{7}{2}$
* Common denominator is 14.
* Convert $\frac{7}{2} \rightarrow \frac{49}{14}$.
* Add: $\frac{19}{14} + \frac{49}{14} = \frac{68}{14}$.
* Simplify: Divide by 2 $\rightarrow \frac{34}{7}$.

16) $\frac{15}{4} + \frac{25}{8}$
* Common denominator is 8.
* Convert $\frac{15}{4} \rightarrow \frac{30}{8}$.
* Add: $\frac{30}{8} + \frac{25}{8} = \frac{55}{8}$.

17) $\frac{10}{7} + \frac{5}{2}$
* Common denominator is 14.
* Convert $\frac{10}{7} \rightarrow \frac{20}{14}$.
* Convert $\frac{5}{2} \rightarrow \frac{35}{14}$.
* Add: $\frac{20}{14} + \frac{35}{14} = \frac{55}{14}$.

18) $\frac{7}{3} + \frac{21}{15}$
* Simplify $\frac{21}{15}$ by dividing by 3 $\rightarrow \frac{7}{5}$.
* Common denominator for 3 and 5 is 15.
* Convert $\frac{7}{3} \rightarrow \frac{35}{15}$.
* Convert $\frac{7}{5} \rightarrow \frac{21}{15}$.
* Add: $\frac{35}{15} + \frac{21}{15} = \frac{56}{15}$.

Final Answer:
1) $\frac{33}{10}$
2) $\frac{59}{10}$
3) $\frac{49}{12}$
4) $\frac{19}{5}$
5) $\frac{23}{6}$
6) $\frac{25}{3}$
7) $\frac{77}{15}$
8) $\frac{29}{9}$
9) $\frac{19}{5}$
10) $\frac{52}{15}$
11) $\frac{23}{5}$
12) $\frac{8}{3}$
13) $\frac{31}{10}$
14) $\frac{25}{4}$
15) $\frac{34}{7}$
16) $\frac{55}{8}$
17) $\frac{55}{14}$
18) $\frac{56}{15}$