Question

Please answer the math problems 1:
`6 (1)/(2) - 3 (9)/(11)`

2:
`7 (2)/(9) - 2 (5)/(12)` 3:
`9(8)/(10)-6 (1)/(2) -1 4:(1)/(5)` 4:
`5(1)/(7) - 1(1)/(3)`

Answer 1

for the 1st one, is noteworthy that the denominators of 2 and 11 are both prime numbers, meaning the LCD from that is just their product, or namely 22.

`\stackrel{mixed}{6(1)/(2)}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}} ~\hfill \stackrel{mixed}{3(9)/(11)} \implies \cfrac{3\cdot 11+9}{11} \implies \stackrel{improper}{\cfrac{42}{11}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{13}{2}~~ - ~~\cfrac{42}{11}\implies \cfrac{(11)13~~ - ~~(2)42}{\underset{\textit{using this LCD}}{22}}\implies \cfrac{143-84}{22}\implies \cfrac{59}{22}\implies 2(15)/(22) \\\\[-0.35em] \rule{34em}{0.25pt}`

`\stackrel{mixed}{7(2)/(9)}\implies \cfrac{7\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{65}{9}} ~\hfill \stackrel{mixed}{2(5)/(12)} \implies \cfrac{2\cdot 12+5}{12} \implies \stackrel{improper}{\cfrac{29}{12}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{65}{9}~~ - ~~\cfrac{29}{12}\implies \cfrac{(4)65~~ - ~~(3)29}{\underset{\textit{using this LCD}}{36}}\implies \cfrac{260-87}{36}\implies \cfrac{173}{36}\implies 4(29)/(36)`