How do you evaluate #(1\frac { 7} { 8} - \frac { 3} { 4} ) \cdot \frac { 2} { 3}#?

1 Answer
smendyka
Jul 29, 2017

See a solution process below:

Explanation:

First, convert the mixed number into an improper fraction:

#(color(red)(1 7/8) - 3/4) * 2/3 => #

#(color(red)(1 + 7/8) - 3/4) * 2/3 =>#

#(color(red)((8/8 xx 1) + 7/8) - 3/4) * 2/3 =>#

#(color(red)(8/8 + 7/8) - 3/4) * 2/3 =>#

#(color(red)(15/8) - 3/4) * 2/3#

Next, we can subtract the two fractions within the parenthesis. However, before doing this we need to put the fractions over a common denominator:

#(color(red)(15/8) - color(blue)((2/2 xx 3/4))) * 2/3 =>#

#(color(red)(15/8) - color(blue)(6/8)) * 2/3 =>#

#(color(red)(15) - color(blue)(6))/8 * 2/3 =>#

#9/8 * 2/3#

Now, we can factor and cancel common terms before multiplying the fractions:

#9/8 * 2/3 =>#

#(3 * 3)/(2 * 4) * 2/3 =>#

#(color(red)(cancel(color(black)(3))) * 3)/(color(blue)(cancel(color(blue)(2))) * 4) * color(blue)(cancel(color(blue)(2)))/color(red)(cancel(color(black)(3))) =>#

#3/4#

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