Question

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

Answer 1

See the Explanation

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

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

Explanation:

`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`