How do you evaluate #\frac { 1} { 4} \times \frac { 2} { 3} - \frac { 2} { 3} \div \frac { 3} { 5}#?

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Answer 1 · 2017-08-14T13:25:25

#-17/18#

In a calculation which involves different operations, identify the number of terms first. (Terms are separated by #+ and -# signs)

#color(blue)(1/4 xx2/3)color(red)( -2/3 div 3/5)" "larr# there are 2 terms.

Simplify each term to a single answer and then subtract them in the final step.

To divide is the same as multiplying by the reciprocal

#=color(blue)(1/cancel4^2 xxcancel2/3)color(red)( -2/3 xx5/3)" "(" cancel where possible" /"then multiply straight across")#

#=" "color(blue)(1/6)" "-" "color(red)(10/9)#

#=color(blue)(1/6)xx3/3 color(red)(-10/9)xx2/2" "larr# convert to a common denominator

#=(3-20)/18#

#=-17/18#

Answer 2 · 2017-08-14T13:38:55

See the explanation

#1/4**2/3-2/3-:3/5#

#a/b**c/d=>(ac)/(bd)#
#a/b-:c/d=>a/b*d/c=>(ad)/(bc)#

From this,

#=>1/4**2/3-2/3-:3/5#

#=>(1*2)/(4*3)-2/3*5/3#

#=>2/12-(2*5)/(3*3)#

#=>2/12-10/9#

#a/b-c/d=>((a*d)-(b*c))/(b*d)#

From this,

#=>2/12-10/9#

#=>((2*9)-(12*10))/(12*9)#

#=>(18-120)/108#

#=>(-102)/108#

#=>-102/108#

#=>-(6*17)/(6*18)#

#=>-(cancelcolor(red)6*17)/(cancelcolor(red)6*18)#

#=>-17/18#