How do you use order of operations to simplify #9/4 times 2/3 + 4/5 times 5/3#?

1 Answer
Apr 11, 2018

Answer:

See a solution process below:

Explanation:

Using the PEDMAS order of operation, first execute the Multiplication operations:

#color(red)(9)/color(red)(4) xx color(red)(2)/color(red)(3) + color(blue)(4)/color(blue)(5) xx color(blue)(5)/color(blue)(3) =>#

#(color(red)(9) xx color(red)(2))/(color(red)(4) xx color(red)(3)) + (color(blue)(4) xx color(blue)(5))/(color(blue)(5) xx color(blue)(3)) =>#

#18/12 + 20/15 =>#

#(6 xx 3)/(6 xx 2) + (5 xx 4)/(5 xx 3) =>#

#(color(red)(cancel(color(black)(6))) xx 3)/(color(red)(cancel(color(black)(6))) xx 2) + (color(blue)(cancel(color(black)(5))) xx 4)/(color(blue)(cancel(color(black)(5))) xx 3) =>#

#3/2 + 4/3#

Now, after putting each fraction over a common denominator we can add the fractions:

#(3/3 xx 3/2) + (2/2 xx 4/3) =>#

#(3 xx 3)/(3 xx 2) + (2 xx 4)/(2 xx 3) =>#

#9/6 + 8/6 =>#

#(9 + 8)/6 =>#

#17/6#