51. subtract and simplify:\na. $3\\frac{1}{2}-1\\frac{1}{3}$\nb. $5\\frac{1}{16}-2\\frac{3}{4}$\nc…

• 1}{2}=\frac{7}{2}$ and $1\frac{1}{3}=\frac{1\times3+1}{3}=\frac{4}{3}$. b. $5\frac{1}{16}=\frac{5\times16 + 1}{16}=\frac{81}{16}$ and $2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}$. c. $9\frac{1}{4}=\frac{9\times4+1}{4}=\frac{37}{4}$ and $3\frac{5}{8}=\frac{3\times8 + 5}{8}=\frac{29}{8}$.

Step2: Find a common denominator

a. The common denominator of 2 and 3 is 6. $\frac{7}{2}=\frac{7\times3}{2\times3}=\frac{21}{6}$ and $\frac{4}{3}=\frac{4\times2}{3\times2}=\frac{8}{6}$. b. The common denominator of 16 and 4 is 16. $\frac{11}{4}=\frac{11\times4}{4\times4}=\frac{44}{16}$. c. The common denominator of 4 and 8 is 8. $\frac{37}{4}=\frac{37\times2}{4\times2}=\frac{74}{8}$.

Step3: Subtract the fractions

a. $\frac{21}{6}-\frac{8}{6}=\frac{21 - 8}{6}=\frac{13}{6}=2\frac{1}{6}$. b. $\frac{81}{16}-\frac{44}{16}=\frac{81 - 44}{16}=\frac{37}{16}=2\frac{5}{16}$. c. $\frac{74}{8}-\frac{29}{8}=\frac{74 - 29}{8}=\frac{45}{8}=5\frac{5}{8}$.

Answer:

a. $2\frac{1}{6}$ b. $2\frac{5}{16}$ c. $5\frac{5}{8}$