5) 4(5)/(6)-3(5)/(8) 6) 1(2)/(19)cdot 1(2)/(7) 7) 1(8)/(21)+3(2)/(7) 8) 2-1(12)/(19)

5) $4\frac {5}{6}-3\frac {5}{8}$<br />To solve this problem, we need to convert the mixed numbers to improper fractions and then subtract them.<br /><br />First, let's convert $4\frac {5}{6}$ to an improper fraction:<br />$4\frac {5}{6} = \frac{4 \times 6 + 5}{6} = \frac{29}{6}$<br /><br />Next, let's convert $3\frac {5}{8}$ to an improper fraction:<br />$3\frac {5}{8} = \frac{3 \times 8 + 5}{8} = \frac{29}{8}$<br /><br />Now, we can subtract the two improper fractions:<br />$\frac{29}{6} - \frac{29}{8} = \frac{29 \times 8 - 29 \times 6}{6 \times 8} = \frac{232 - 174}{48} = \frac{58}{48} = \frac{29}{24}$<br /><br />Therefore, the answer is $\frac{29}{24}$.<br /><br />6) $1\frac {2}{19}\cdot 1\frac {2}{7}$<br />To solve this problem, we need to convert the mixed numbers to improper fractions and then multiply them.<br /><br />First, let's convert $1\frac {2}{19}$ to an improper fraction:<br />$1\frac {2}{19} = \frac{1 \times 19 + 2}{19} = \frac{21}{19}$<br /><br />Next, let's convert $1\frac {2}{7}$ to an improper fraction:<br />$1\frac {2}{7} = \frac{1 \times 7 + 2}{7} = \frac{9}{7}$<br /><br />Now, we can multiply the two improper fractions:<br />$\frac{21}{19} \cdot \frac{9}{7} = \frac{21 \times 9}{19 \times 7} = \frac{189}{133}$<br /><br />Therefore, the answer is $\frac{189}{133}$.<br /><br />7) $1\frac {8}{21}+3\frac {2}{7}$<br />To solve this problem, we need to convert the mixed numbers to improper fractions and then add them.<br /><br />First, let's convert $1\frac {8}{21}$ to an improper fraction:<br />$1\frac {8}{21} = \frac{1 \times 21 + 8}{21} = \frac{29}{21}$<br /><br />Next, let's convert $3\frac {2}{7}$ to an improper fraction:<br />$3\frac {2}{7} = \frac{3 \times 7 + 2}{7} = \frac{23}{7}$<br /><br />Now, we can add the two improper fractions:<br />$\frac{29}{21} + \frac{23}{7} = \frac{29 \times 7 + 23 \times 21}{21 \times 7} = \frac{203 + 483}{147} = \frac{686}{147} = \frac{58}{7}$<br /><br />Therefore, the answer is $\frac{58}{7}$.<br /><br />8) $2-1\frac {12}{19}$<br />To solve this problem, we need to convert the mixed number to an improper fraction and then subtract it from 2.<br /><br />First, let's convert $1\frac {12}{19}$ to an improper fraction:<br />$1\frac {12}{19} = \frac{1 \times 19 + 12}{19} = \frac{31}{19}$<br /><br />Now, we can subtract the improper fraction from 2:<br />$2 - \frac{31}{19} = \frac{38}{19} - \frac{31}{19} = \frac{7}{19}$<br /><br />Therefore, the answer is $\frac{7}{19}$.