Question

How do you evaluate `\frac { 15} { 6} \div \frac { 35} { 24} \times 8\frac { 1} { 2}`?

Answer 1

`102/7` OR `14 4/7`

Explanation:

First, let's turn `8 1/2` into an improper fraction.

`8*2+1=17`

`8 1/2=17/2`

Next, you go from left to right using PEMDAS. So, you will divide then multiply. Let's focus in on `15/6 div 35/24`. Remember that whatever you divide by gets flipped, so that you are multiplying fraction. We can simplify the fractions. 24 and 6 have a common factor of 6. 15 and and 35 have a common factor of 5.

`15/6 div 35/24 ->`

`15/6*24/35 ->`

`3/1*4/7 ->`

`12/7`

Now let's finish up the expression by multiplying by `17/2`. 12 and 2 have a common factor of 2. I will give the proper and improper fractions as answers.

`12/7 * 17/2 ->`

`6/7*17/1`

`102/7` OR `14 4/7`

Answer 2

`102/7 = 14 4/7`

Explanation:

As we are are working with only multiplication and division, this is all one term and can work with all the factors at the same time.
Multiplication and division can be done in any order.

Change the division to multiplication by the reciprocal and the mixed number to an improper fraction.

`15/6 div 35/24 xx 8 1/2`

`= 15/6 xx 24/35 xx17/2" "larr`cancel wherever possible

`rarr 15 and 35` by 5
`rarr 6 and 24` by 6

`= cancel15^3/cancel6 xx cancel24^4 /cancel35^7 xx17/2`

`rarr 2 and 4` by 2

`= 3/1 xxcancel4^2/7 xx 17/cancel2`

`= 102/7`

`= 14 4/7`