Add Subtract Positive Negative Fractions Worksheet | PDF ... - Free Printable

Here are the step-by-step solutions for each problem. Remember the rule: subtracting a negative number is the same as adding. So, we will rewrite every subtraction problem as an addition problem first.

1) $(-\frac{4}{5}) - \frac{7}{8}$
* Rewrite as addition: $(-\frac{4}{5}) + (-\frac{7}{8})$
* Find a common denominator for 5 and 8, which is 40.
* Convert fractions: $-\frac{4 \times 8}{40} + (-\frac{7 \times 5}{40}) = -\frac{32}{40} + (-\frac{35}{40})$
* Add the numerators: $-32 + (-35) = -67$
* Result: $-\frac{67}{40}$ or $-1 \frac{27}{40}$

2) $\frac{1}{3} - (-\frac{5}{3})$
* Rewrite as addition: $\frac{1}{3} + \frac{5}{3}$
* The denominators are already the same (3).
* Add the numerators: $1 + 5 = 6$
* Result: $\frac{6}{3}$, which simplifies to 2.

3) $(-\frac{1}{3}) + \frac{3}{8}$
* Find a common denominator for 3 and 8, which is 24.
* Convert fractions: $-\frac{1 \times 8}{24} + \frac{3 \times 3}{24} = -\frac{8}{24} + \frac{9}{24}$
* Add the numerators: $-8 + 9 = 1$
* Result: $\frac{1}{24}$

4) $(-\frac{10}{7}) + \frac{1}{6}$
* Find a common denominator for 7 and 6, which is 42.
* Convert fractions: $-\frac{10 \times 6}{42} + \frac{1 \times 7}{42} = -\frac{60}{42} + \frac{7}{42}$
* Add the numerators: $-60 + 7 = -53$
* Result: $-\frac{53}{42}$ or $-1 \frac{11}{42}$

5) $\frac{9}{5} + (-\frac{4}{3})$
* Find a common denominator for 5 and 3, which is 15.
* Convert fractions: $\frac{9 \times 3}{15} + (-\frac{4 \times 5}{15}) = \frac{27}{15} + (-\frac{20}{15})$
* Add the numerators: $27 + (-20) = 7$
* Result: $\frac{7}{15}$

6) $2 - \frac{13}{8}$
* Rewrite 2 as a fraction with denominator 8: $\frac{16}{8}$
* Rewrite subtraction as addition: $\frac{16}{8} + (-\frac{13}{8})$
* Add the numerators: $16 + (-13) = 3$
* Result: $\frac{3}{8}$

7) $\frac{9}{5} - \frac{5}{8}$
* Rewrite as addition: $\frac{9}{5} + (-\frac{5}{8})$
* Find a common denominator for 5 and 8, which is 40.
* Convert fractions: $\frac{9 \times 8}{40} + (-\frac{5 \times 5}{40}) = \frac{72}{40} + (-\frac{25}{40})$
* Add the numerators: $72 + (-25) = 47$
* Result: $\frac{47}{40}$ or $1 \frac{7}{40}$

8) $(-\frac{4}{3}) - (-\frac{3}{2})$
* Rewrite as addition: $(-\frac{4}{3}) + \frac{3}{2}$
* Find a common denominator for 3 and 2, which is 6.
* Convert fractions: $-\frac{4 \times 2}{6} + \frac{3 \times 3}{6} = -\frac{8}{6} + \frac{9}{6}$
* Add the numerators: $-8 + 9 = 1$
* Result: $\frac{1}{6}$

9) $-\frac{6}{9} + (-\frac{2}{3})$
* First, simplify $-\frac{6}{9}$ by dividing top and bottom by 3: $-\frac{2}{3}$
* Now the problem is: $(-\frac{2}{3}) + (-\frac{2}{3})$
* Add the numerators: $-2 + (-2) = -4$
* Result: $-\frac{4}{3}$ or $-1 \frac{1}{3}$

10) $-\frac{4}{5} - (\frac{3}{7})$
* Rewrite as addition: $-\frac{4}{5} + (-\frac{3}{7})$
* Find a common denominator for 5 and 7, which is 35.
* Convert fractions: $-\frac{4 \times 7}{35} + (-\frac{3 \times 5}{35}) = -\frac{28}{35} + (-\frac{15}{35})$
* Add the numerators: $-28 + (-15) = -43$
* Result: $-\frac{43}{35}$ or $-1 \frac{8}{35}$

Final Answer:
1) $-\frac{67}{40}$
2) $2$
3) $\frac{1}{24}$
4) $-\frac{53}{42}$
5) $\frac{7}{15}$
6) $\frac{3}{8}$
7) $\frac{47}{40}$
8) $\frac{1}{6}$
9) $-\frac{4}{3}$
10) $-\frac{43}{35}$