Math worksheet for practicing adding and subtracting fractions, featuring 12 problems to solve.

Here are the step-by-step solutions for each problem on the worksheet. To solve these, we need to find a common denominator for the fractions so we can add or subtract them. Then, we simplify the result if possible.

1. $\frac{19}{2} - \frac{13}{2}$
* The denominators are already the same (2).
* Subtract the numerators: $19 - 13 = 6$.
* Result: $\frac{6}{2}$.
* Simplify: $6 \div 2 = 3$.

2. $\frac{17}{4} - \frac{7}{4}$
* The denominators are the same (4).
* Subtract the numerators: $17 - 7 = 10$.
* Result: $\frac{10}{4}$.
* Simplify: Both numbers are even, so divide by 2. $\frac{10 \div 2}{4 \div 2} = \frac{5}{2}$.

3. $\frac{19}{3} - \frac{17}{3}$
* The denominators are the same (3).
* Subtract the numerators: $19 - 17 = 2$.
* Result: $\frac{2}{3}$.
* This cannot be simplified further.

4. $\frac{5}{6} + \frac{21}{4}$
* Find the Least Common Denominator (LCD) for 6 and 4. The LCD is 12.
* Convert $\frac{5}{6}$: Multiply top and bottom by 2 $\rightarrow \frac{10}{12}$.
* Convert $\frac{21}{4}$: Multiply top and bottom by 3 $\rightarrow \frac{63}{12}$.
* Add numerators: $10 + 63 = 73$.
* Result: $\frac{73}{12}$.
* This is an improper fraction. As a mixed number: $73 \div 12 = 6$ with a remainder of 1. So, $6 \frac{1}{12}$.

5. $\frac{17}{2} - \frac{19}{3}$
* Find the LCD for 2 and 3. The LCD is 6.
* Convert $\frac{17}{2}$: Multiply top and bottom by 3 $\rightarrow \frac{51}{6}$.
* Convert $\frac{19}{3}$: Multiply top and bottom by 2 $\rightarrow \frac{38}{6}$.
* Subtract numerators: $51 - 38 = 13$.
* Result: $\frac{13}{6}$.
* As a mixed number: $13 \div 6 = 2$ with a remainder of 1. So, $2 \frac{1}{6}$.

6. $\frac{19}{4} - \frac{15}{12}$
* Find the LCD for 4 and 12. The LCD is 12.
* Convert $\frac{19}{4}$: Multiply top and bottom by 3 $\rightarrow \frac{57}{12}$.
* The second fraction is already over 12.
* Subtract numerators: $57 - 15 = 42$.
* Result: $\frac{42}{12}$.
* Simplify: Divide both by 6. $42 \div 6 = 7$ and $12 \div 6 = 2$.
* Final simplified fraction: $\frac{7}{2}$ (or $3 \frac{1}{2}$).

7. $1 \frac{1}{2} - \frac{7}{11}$
* First, change the mixed number to an improper fraction: $1 \frac{1}{2} = \frac{3}{2}$.
* Find the LCD for 2 and 11. The LCD is 22.
* Convert $\frac{3}{2}$: Multiply top and bottom by 11 $\rightarrow \frac{33}{22}$.
* Convert $\frac{7}{11}$: Multiply top and bottom by 2 $\rightarrow \frac{14}{22}$.
* Subtract numerators: $33 - 14 = 19$.
* Result: $\frac{19}{22}$.

8. $\frac{7}{3} + \frac{2}{5}$
* Find the LCD for 3 and 5. The LCD is 15.
* Convert $\frac{7}{3}$: Multiply top and bottom by 5 $\rightarrow \frac{35}{15}$.
* Convert $\frac{2}{5}$: Multiply top and bottom by 3 $\rightarrow \frac{6}{15}$.
* Add numerators: $35 + 6 = 41$.
* Result: $\frac{41}{15}$.
* As a mixed number: $41 \div 15 = 2$ with a remainder of 11. So, $2 \frac{11}{15}$.

9. $\frac{2}{3} - \frac{5}{7}$
* Find the LCD for 3 and 7. The LCD is 21.
* Convert $\frac{2}{3}$: Multiply top and bottom by 7 $\rightarrow \frac{14}{21}$.
* Convert $\frac{5}{7}$: Multiply top and bottom by 3 $\rightarrow \frac{15}{21}$.
* Subtract numerators: $14 - 15 = -1$.
* Result: $-\frac{1}{21}$.

10. $\frac{19}{4} - \frac{1}{12}$
* Find the LCD for 4 and 12. The LCD is 12.
* Convert $\frac{19}{4}$: Multiply top and bottom by 3 $\rightarrow \frac{57}{12}$.
* Subtract numerators: $57 - 1 = 56$.
* Result: $\frac{56}{12}$.
* Simplify: Divide both by 4. $56 \div 4 = 14$ and $12 \div 4 = 3$.
* Final simplified fraction: $\frac{14}{3}$ (or $4 \frac{2}{3}$).

11. $\frac{11}{4} - \frac{1}{4}$
* The denominators are the same (4).
* Subtract numerators: $11 - 1 = 10$.
* Result: $\frac{10}{4}$.
* Simplify: Divide by 2. $\frac{5}{2}$ (or $2 \frac{1}{2}$).

12. $\frac{21}{4} - \frac{9}{2}$
* Find the LCD for 4 and 2. The LCD is 4.
* Convert $\frac{9}{2}$: Multiply top and bottom by 2 $\rightarrow \frac{18}{4}$.
* Subtract numerators: $21 - 18 = 3$.
* Result: $\frac{3}{4}$.

Final Answer:
1. 3
2. $\frac{5}{2}$ (or $2 \frac{1}{2}$)
3. $\frac{2}{3}$
4. $\frac{73}{12}$ (or $6 \frac{1}{12}$)
5. $\frac{13}{6}$ (or $2 \frac{1}{6}$)
6. $\frac{7}{2}$ (or $3 \frac{1}{2}$)
7. $\frac{19}{22}$
8. $\frac{41}{15}$ (or $2 \frac{11}{15}$)
9. $-\frac{1}{21}$
10. $\frac{14}{3}$ (or $4 \frac{2}{3}$)
11. $\frac{5}{2}$ (or $2 \frac{1}{2}$)
12. $\frac{3}{4}$