Question

How do you solve `28\div ( 2^ { 2} + 3) \times 2\frac { 4} { 5} - 3`?

Answer 1

See a solution process below:

Explanation:

First, convert the mixed fraction to an improper fraction:

`28 -: (2^2 + 3) xx color(red)(2 4/5) - 3 =>`

`28 -: (2^2 + 3) xx (color(red)(2 + 4/5)) - 3 =>`

`28 -: (2^2 + 3) xx (color(red)((5/5 xx 2) + 4/5)) - 3 =>`

`28 -: (2^2 + 3) xx (color(red)(10/5 + 4/5)) - 3 =>`

`28 -: (2^2 + 3) xx 14/5 - 3`

Next, process the exponent term within the parenthesis:

`28 -: (color(red)(2^2) + 3) xx 14/5 - 3 =>`

`28 -: (4 + 3) xx 14/5 - 3`

Next, execute the addition operation within the parenthesis:

`28 -: (color(red)(4 + 3)) xx 14/5 - 3 =>`

`28 -: 7 xx 14/5 - 3`

Then, execute the division and multiplication from left to right:

`color(red)(28 -: 7) xx 14/5 - 3 =>`

`4 xx 14/5 - 3 =>`

`color(red)(4 xx 14/5) - 3 =>`

`56/5 - 3`

Now, execute the subtraction operation:

`56/5 - 3 =>`

`56/5 - (5/5 xx 3) =>`

`56/5 - 15/5 =>`

`41/5`

If necessary, we can lastly convert this result to a mixed faction:

`41/5 => (40 + 1)/5 => 40/5 + 1/5 => 8 + 1/5 => 8 1/5`