Question

How do you evaluate `3\frac { 7} { 10} \times 3\frac { 1} { 2}`?

Answer 1

See a solution process below:

Explanation:

First, convert each mixed number into an improper fraction:

`3 7/10 xx 3 1/2 =>`

`(3 + 7/10) xx (3 + 1/2) =>`

`([10/10 xx 3] + 7/10) xx ([2/2 xx 3] + 1/2) =>`

`(30/10 + 7/10) xx (6/2 + 1/2) =>`

`(30 + 7)/10 xx (6 + 1)/2 =>`

`37/10 xx 7/2`

Next, multiply the numerators over the denominators multiplied:

`(37 xx 7)/(10 xx 2) =>`

`259/20`

We can now convert this back into a mixed number:

`259/20 => (240 + 19)/20 => 240/20 + 19/20 = 12 + 19/20 = 12 19/20`#

Answer 2

`12 19/20`

Explanation:

`3 7/10=3+7/10" and "3 1/2=3+1/2`
Now `(3+7/10)*(3+1/2)`
`= 3*3 + 7/10*3 + 1/2*3 + 7/10*1/2`

`=9+21/10+3/2+7/20`

`=9+(21*2+3*10+7)/20`

`=9+(42+30+7)/20`

`=9+79/20`

`=9+(20*3+19)/20`
`=9+3+19/20`
`=12 19/20`

The process is being lengthy one can use the below method.
At first convert it to improper fraction.

That is `3 7/10=(3*10+7)/10 = 37/10" and "3 1/2=(3*2+1)/2 =7/2`
Now `37/10 * 7/2`
`= (37*7)/(10*2)`

`=259/20`

`=(20*12+19)/20`

`=12+19/20`

`=12 19/20`