How do you evaluate #12\frac { 1} { 4} \div 3\frac { 1} { 2} #?

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Answer 1 · 2017-08-13T12:34:04

See the Explanation

#12 1/4 -: 3 1/2#

#a b/c=>(a*c+b)/c.# Apply this formula,

#=>12 1/4=>(12*4+1)/4=>(48+1)/2=>49/4#

#=>3 1/2=>(3*2+1)/2=>(6+1)/2=>7/2#

Now Divide these,

#=>49/4-:7/2#

#a/b-:c/d=>a/b*d/c=>(a*d)/(b*c).# Apply this formula,

#=>49/4-:7/2=>49/4*2/7=>(49*2)/(4*7)=>(49*2)/(2*2*7)=>(49*cancelcolor(red)2)/(cancelcolor(red)2*2*7)#

#=>49/(2*7)=>49/14#

The answer is #49/14.#

Answer 2 · 2017-08-13T12:36:18

#12 1/4 div 3 1/2 =color(red)(3 1/2)#

#12 1/4 =12 +1/4#

#color(white)("XXX")=48/4+1/4#

#color(white)("XXX")=49/4#

#3 1/2 = 3 + 1/2#

#color(white)("XXX")=6/2 + 1/2#

#color(white)("XXX")=7/2#

Therefore
#12 1/4 div 3 1/2#

#color(white)("XXX")=49/4 div 7/2#

and since division is the reciprocal of multiplication
#color(white)("XXX")=49/4 xx2/7#

#color(white)("XXX")=(color(green)(cancel(49)^7))/(color(blue)(cancel(4)_2))xxcolor(blue)(cancel(2))/(color(green)(cancel(7)))#

#color(white)("XXX")=7/2#

#color(white)("XXX")=3 1/2#