Question

in 7–22, find the sum or difference.

1. $\frac{4}{50}$

$+\frac{3}{5}$

1. $\frac{2}{3}$

$-\frac{7}{12}$

1. $\frac{9}{10}$

$+\frac{2}{100}$

1. $\frac{4}{9}$

$+\frac{1}{4}$

1. $\frac{17}{15} - \frac{1}{3}$
2. $\frac{7}{16} + \frac{3}{8}$
3. $\frac{2}{5} + \frac{1}{4}$
4. $\frac{1}{7} + \frac{1}{2}$
5. $\frac{1}{2} - \frac{3}{16}$
6. $\frac{7}{8} - \frac{2}{3}$
7. $\frac{11}{12} - \frac{4}{6}$
8. $\frac{7}{18} + \frac{5}{9}$
9. $(\frac{7}{8} + \frac{1}{12}) - \frac{1}{2}$
10. $(\frac{11}{18} - \frac{4}{9}) + \frac{1}{6}$
11. $\frac{13}{14} - (\frac{1}{2} + \frac{2}{7})$
12. $\frac{1}{6} + (\frac{15}{15} - \frac{7}{10})$

Explanation:

Problem 7:

Step1: Convert to common denominator

$\frac{3}{5} = \frac{30}{50}$

Step2: Add fractions

$\frac{4}{50} + \frac{30}{50} = \frac{34}{50} = \frac{17}{25}$

Problem 8:

Step1: Convert to common denominator

$\frac{2}{3} = \frac{8}{12}$

Step2: Subtract fractions

$\frac{8}{12} - \frac{7}{12} = \frac{1}{12}$

Problem 9:

Step1: Convert to common denominator

$\frac{9}{10} = \frac{90}{100}$

Step2: Add fractions

$\frac{90}{100} + \frac{2}{100} = \frac{92}{100} = \frac{23}{25}$

Problem 10:

Step1: Convert to common denominator

$\frac{4}{9} = \frac{16}{36}$, $\frac{1}{4} = \frac{9}{36}$

Step2: Add fractions

$\frac{16}{36} + \frac{9}{36} = \frac{25}{36}$

Problem 11:

Step1: Convert to common denominator

$\frac{1}{3} = \frac{5}{15}$

Step2: Subtract fractions

$\frac{17}{15} - \frac{5}{15} = \frac{12}{15} = \frac{4}{5}$

Problem 12:

Step1: Convert to common denominator

$\frac{3}{8} = \frac{6}{16}$

Step2: Add fractions

$\frac{7}{16} + \frac{6}{16} = \frac{13}{16}$

Problem 13:

Step1: Convert to common denominator

$\frac{2}{5} = \frac{8}{20}$, $\frac{1}{4} = \frac{5}{20}$

Step2: Add fractions

$\frac{8}{20} + \frac{5}{20} = \frac{13}{20}$

Problem 14:

Step1: Convert to common denominator

$\frac{1}{7} = \frac{2}{14}$, $\frac{1}{2} = \frac{7}{14}$

Step2: Add fractions

$\frac{2}{14} + \frac{7}{14} = \frac{9}{14}$

Problem 15:

Step1: Convert to common denominator

$\frac{1}{2} = \frac{8}{16}$

Step2: Subtract fractions

$\frac{8}{16} - \frac{3}{16} = \frac{5}{16}$

Problem 16:

Step1: Convert to common denominator

$\frac{7}{8} = \frac{21}{24}$, $\frac{2}{3} = \frac{16}{24}$

Step2: Subtract fractions

$\frac{21}{24} - \frac{16}{24} = \frac{5}{24}$

Problem 17:

Step1: Convert to common denominator

$\frac{4}{6} = \frac{8}{12}$

Step2: Subtract fractions

$\frac{11}{12} - \frac{8}{12} = \frac{3}{12} = \frac{1}{4}$

Problem 18:

Step1: Convert to common denominator

$\frac{5}{9} = \frac{10}{18}$

Step2: Add fractions

$\frac{7}{18} + \frac{10}{18} = \frac{17}{18}$

Problem 19:

Step1: Add inside parentheses

$\frac{7}{8} + \frac{1}{12} = \frac{21}{24} + \frac{2}{24} = \frac{23}{24}$

Step2: Subtract $\frac{1}{2}$

$\frac{23}{24} - \frac{12}{24} = \frac{11}{24}$

Problem 20:

Step1: Subtract inside parentheses

$\frac{11}{18} - \frac{4}{9} = \frac{11}{18} - \frac{8}{18} = \frac{3}{18} = \frac{1}{6}$

Step2: Add $\frac{1}{6}$

$\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$

Problem 21:

Step1: Add inside parentheses

$\frac{1}{2} + \frac{2}{7} = \frac{7}{14} + \frac{4}{14} = \frac{11}{14}$

Step2: Subtract from $\frac{13}{14}$

$\frac{13}{14} - \frac{11}{14} = \frac{2}{14} = \frac{1}{7}$

Problem 22:

Step1: Subtract inside parentheses

$\frac{15}{15} - \frac{7}{10} = \frac{30}{30} - \frac{21}{30} = \frac{9}{30} = \frac{3}{10}$ (Note: Assume typo, $\frac{15}{15}$→$\frac{15}{30}$ correction: $\frac{15}{15}$ is 1, correct common denominator for $\frac{15}{15}$ (1) and $\frac{7}{10}$ is 10: $1 - \frac{7}{10} = \frac{3}{10}$)

Step2: Add $\frac{1}{6}$

$\frac{3}{10} + \frac{1}{6} = \frac{9}{30} + \frac{5}{30} = \frac{14}{30} = \frac{7}{15}$

Answer:

1. $\frac{17}{25}$
2. $\frac{1}{12}$
3. $\frac{23}{25}$
4. $\frac{25}{36}$
5. $\frac{4}{5}$
6. $\frac{13}{16}$
7. $\frac{13}{20}$
8. $\frac{9}{14}$
9. $\frac{5}{16}$
10. $\frac{5}{24}$
11. $\frac{1}{4}$
12. $\frac{17}{18}$
13. $\frac{11}{24}$
14. $\frac{1}{3}$
15. $\frac{1}{7}$
16. $\frac{7}{15}$