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

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Answer 1 · 2017-05-10T22:21:31

See a solution process below:

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#