Question

1. $3\frac{3}{8}-\frac{8}{12}=$ __________ 8. $40\frac{1}{5}-10\frac{5}{10}=$ ________ 9. $\frac{5}{12}+1\frac{5}{8}+4\frac{3}{6}=$ ________ 10. $20 - (\frac{3}{9}+2\frac{1}{6})=$ __________

Explanation:

Step1: Convert mixed - numbers to improper fractions for 7

$3\frac{3}{8}=\frac{3\times8 + 3}{8}=\frac{27}{8}$

Step2: Find a common denominator for 7

The common denominator of 8 and 12 is 24. $\frac{27}{8}=\frac{27\times3}{8\times3}=\frac{81}{24}$, $\frac{8}{12}=\frac{8\times2}{12\times2}=\frac{16}{24}$

Step3: Subtract the fractions for 7

$\frac{81}{24}-\frac{16}{24}=\frac{81 - 16}{24}=\frac{65}{24}=2\frac{17}{24}$

Step4: Convert mixed - numbers to improper fractions for 8

$40\frac{1}{5}=\frac{40\times5+1}{5}=\frac{201}{5}$, $10\frac{5}{10}=\frac{10\times10 + 5}{10}=\frac{105}{10}=\frac{21}{2}$

Step5: Find a common denominator for 8

The common denominator of 5 and 2 is 10. $\frac{201}{5}=\frac{201\times2}{5\times2}=\frac{402}{10}$, $\frac{21}{2}=\frac{21\times5}{2\times5}=\frac{105}{10}$

Step6: Subtract the fractions for 8

$\frac{402}{10}-\frac{105}{10}=\frac{402 - 105}{10}=\frac{297}{10}=29\frac{7}{10}$

Step7: Convert mixed - numbers to improper fractions for 9

$1\frac{5}{8}=\frac{1\times8 + 5}{8}=\frac{13}{8}$, $4\frac{3}{6}=\frac{4\times6+3}{6}=\frac{27}{6}=\frac{9}{2}$
The common denominator of 12, 8 and 2 is 24. $\frac{5}{12}=\frac{5\times2}{12\times2}=\frac{10}{24}$, $\frac{13}{8}=\frac{13\times3}{8\times3}=\frac{39}{24}$, $\frac{9}{2}=\frac{9\times12}{2\times12}=\frac{108}{24}$
$\frac{10}{24}+\frac{39}{24}+\frac{108}{24}=\frac{10 + 39+108}{24}=\frac{157}{24}=6\frac{13}{24}$

Step8: Convert mixed - numbers to improper fractions for 10

$2\frac{1}{6}=\frac{2\times6 + 1}{6}=\frac{13}{6}$, $\frac{3}{9}=\frac{1}{3}$
The common denominator of 3 and 6 is 6. $\frac{1}{3}=\frac{1\times2}{3\times2}=\frac{2}{6}$
$\frac{3}{9}+2\frac{1}{6}=\frac{2}{6}+\frac{13}{6}=\frac{2 + 13}{6}=\frac{15}{6}=\frac{5}{2}$
$20-\frac{5}{2}=\frac{20\times2}{1\times2}-\frac{5}{2}=\frac{40 - 5}{2}=\frac{35}{2}=17\frac{1}{2}$

Answer:

1. $2\frac{17}{24}$
2. $29\frac{7}{10}$
3. $6\frac{13}{24}$
4. $17\frac{1}{2}$