Question

extra practice add, subtract, multiply, or divide as indicated. some problems will require finding a common denominator. express answers in lowest terms. 1. $\frac{1}{5}+\frac{4}{5}=$ 2. $\frac{12}{15}+\frac{20}{15}=$ 3. $\frac{6}{8}-\frac{2}{3}=$ 4. $\frac{8}{12}-\frac{9}{36}=$ 5. $\frac{6}{15}cdot\frac{2}{6}=$ 6. $\frac{1}{4}div\frac{1}{2}=$ 7. $\frac{7}{9}-\frac{1}{9}=$ 8. $3 - \frac{11}{9}=$ 9. $\frac{5}{7}+\frac{2}{4}=$ 10. $\frac{1}{4}cdot\frac{2}{4}=$ 11. $4cdot\frac{4}{6}=$ 12. $\frac{80}{20}-\frac{30}{20}=$ 13. $2\frac{1}{6}cdot\frac{4}{9}=$ 14. $2\frac{5}{6}cdot1\frac{3}{4}=$ 15. $\frac{3}{4}div1\frac{1}{2}=$ 16. $4\frac{1}{4}div\frac{1}{8}=$ 17. $\frac{18}{4}-1\frac{2}{3}=$ 18. $\frac{24}{8}-2-\frac{1}{2}=$ 19. $\frac{1}{7}+\frac{5}{4}+\frac{8}{16}=$ 20. $1\frac{2}{3}cdot(\frac{1}{4}div\frac{3}{8})=$

Explanation:

Step1: Add fractions with same denominator

For $\frac{1}{5}+\frac{4}{5}$, since the denominators are the same, we add the numerators. $\frac{1 + 4}{5}=\frac{5}{5}=1$.

Step2: Add fractions with same denominator

For $\frac{12}{15}+\frac{20}{15}$, add the numerators: $\frac{12 + 20}{15}=\frac{32}{15}$.

Step3: Find common - denominator and subtract

For $\frac{6}{8}-\frac{2}{3}$, the common denominator of 8 and 3 is 24. $\frac{6\times3}{8\times3}-\frac{2\times8}{3\times8}=\frac{18}{24}-\frac{16}{24}=\frac{18 - 16}{24}=\frac{2}{24}=\frac{1}{12}$.

Step4: Find common - denominator and subtract

For $\frac{8}{12}-\frac{9}{36}$, the common denominator of 12 and 36 is 36. $\frac{8\times3}{12\times3}-\frac{9}{36}=\frac{24}{36}-\frac{9}{36}=\frac{24 - 9}{36}=\frac{15}{36}=\frac{5}{12}$.

Step5: Multiply fractions

For $\frac{6}{15}\times\frac{2}{6}$, multiply the numerators and denominators: $\frac{6\times2}{15\times6}=\frac{12}{90}=\frac{2}{15}$.

Step6: Divide fractions

For $\frac{1}{4}\div\frac{1}{2}$, remember that dividing by a fraction is multiplying by its reciprocal. So $\frac{1}{4}\times\frac{2}{1}=\frac{1\times2}{4\times1}=\frac{2}{4}=\frac{1}{2}$.

Step7: Subtract fractions with same denominator

For $\frac{7}{9}-\frac{1}{9}$, subtract the numerators: $\frac{7 - 1}{9}=\frac{6}{9}=\frac{2}{3}$.

Step8: Rewrite whole - number as fraction and subtract

For $3-\frac{11}{9}$, rewrite 3 as $\frac{27}{9}$. Then $\frac{27}{9}-\frac{11}{9}=\frac{27 - 11}{9}=\frac{16}{9}$.

Step9: Find common - denominator and add

For $\frac{5}{7}+\frac{2}{4}$, the common denominator of 7 and 4 is 28. $\frac{5\times4}{7\times4}+\frac{2\times7}{4\times7}=\frac{20}{28}+\frac{14}{28}=\frac{20 + 14}{28}=\frac{34}{28}=\frac{17}{14}$.

Step10: Multiply fractions

For $\frac{1}{4}\times\frac{2}{4}$, multiply the numerators and denominators: $\frac{1\times2}{4\times4}=\frac{2}{16}=\frac{1}{8}$.

Step11: Multiply whole - number and fraction

For $4\times\frac{4}{6}$, rewrite 4 as $\frac{4}{1}$. Then $\frac{4}{1}\times\frac{4}{6}=\frac{16}{6}=\frac{8}{3}$.

Step12: Subtract fractions with same denominator

For $\frac{80}{20}-\frac{30}{20}$, subtract the numerators: $\frac{80 - 30}{20}=\frac{50}{20}=\frac{5}{2}$.

Step13: Convert mixed - number to improper fraction and multiply

For $2\frac{1}{6}\times\frac{4}{9}$, convert $2\frac{1}{6}$ to $\frac{13}{6}$. Then $\frac{13}{6}\times\frac{4}{9}=\frac{13\times4}{6\times9}=\frac{52}{54}=\frac{26}{27}$.

Step14: Convert mixed - numbers to improper fractions and multiply

For $2\frac{5}{6}\times1\frac{3}{4}$, convert $2\frac{5}{6}$ to $\frac{17}{6}$ and $1\frac{3}{4}$ to $\frac{7}{4}$. Then $\frac{17}{6}\times\frac{7}{4}=\frac{119}{24}$.

Step15: Convert mixed - number to improper fraction and divide

For $\frac{3}{4}\div1\frac{1}{2}$, convert $1\frac{1}{2}$ to $\frac{3}{2}$. Then $\frac{3}{4}\div\frac{3}{2}=\frac{3}{4}\times\frac{2}{3}=\frac{3\times2}{4\times3}=\frac{6}{12}=\frac{1}{2}$.

Step16: Convert mixed - number to improper fraction and divide

For $4\frac{1}{4}\div\frac{1}{8}$, convert $4\frac{1}{4}$ to $\frac{17}{4}$. Then $\frac{17}{4}\div\frac{1}{8}=\frac{17}{4}\times\frac{8}{1}=\frac{17\times8}{4\times1}=34$.

Step17: Convert mixed - number to improper fraction and subtract

For $\frac{18}{4}-1\frac{2}{3}$, convert $1\frac{2}{3}$ to $\frac{5}{3}$. The common denominator of 4 and 3 is 12. $\frac{18\times3}{4\times3}-\frac{5\times4}{3\times4}=\frac{54}{12}-\frac{20}{12}=\frac{54 - 20}{12}=\frac{34}{12}=\frac{17}{6}$.

Step18: Simplify fraction and subtract

For $\frac{24}{8}-2-\frac{1}{2}$, simplify $\frac{24}{8}$ to 3. Then $3 - 2-\frac{1}{2}=1-\frac{1}{2}=\frac{1}{2}$.

Step19: Find common - denominator and add

For $\frac{1}{7}+\frac{5}{4}+\frac{8}{16}$, simplify $\frac{8}{16}=\frac{1}{2}$. The common denominator of 7, 4 and 2 is 28. $\frac{1\times4}{7\times4}+\frac{5\times7}{4\times7}+\frac{1\times14}{2\times14}=\frac{4}{28}+\frac{35}{28}+\frac{14}{28}=\frac{4 + 35+14}{28}=\frac{53}{28}$.

Step20: Divide and multiply mixed - number and fraction

For $1\frac{2}{3}\times(\frac{1}{4}\div\frac{3}{8})$, first $\frac{1}{4}\div\frac{3}{8}=\frac{1}{4}\times\frac{8}{3}=\frac{2}{3}$. Convert $1\frac{2}{3}$ to $\frac{5}{3}$. Then $\frac{5}{3}\times\frac{2}{3}=\frac{10}{9}$.

Answer:

1. 1
2. $\frac{32}{15}$
3. $\frac{1}{12}$
4. $\frac{5}{12}$
5. $\frac{2}{15}$
6. $\frac{1}{2}$
7. $\frac{2}{3}$
8. $\frac{16}{9}$
9. $\frac{17}{14}$
10. $\frac{1}{8}$
11. $\frac{8}{3}$
12. $\frac{5}{2}$
13. $\frac{26}{27}$
14. $\frac{119}{24}$
15. $\frac{1}{2}$
16. 34
17. $\frac{17}{6}$
18. $\frac{1}{2}$
19. $\frac{53}{28}$
20. $\frac{10}{9}$