How do you evaluate #\frac { 7} { 3} \cdot \frac { 15} { 14}#?
1 Answer
Explanation:
There are 2 possible approaches to evaluating this product.
#• color(red)" Simplify then multiply"larr" preferable method"# To simplify consider
#color(blue)"common factors"# of the values on the numerators with values on the denominators and#color(blue)"cancel"# In this case 7 and 14 can be divided by 7 and 3 and 15 by 3
#rArrcancelcolor(red)(7)^1/cancelcolor(magenta)(3)^1xxcancelcolor(magenta)(15)^5/cancelcolor(red)(14)^2larr" cancelling"#
#=(1xx5)/(1xx2)#
#=5/2larrcolor(purple)" in simplest form"#
#• color(red)" Multiply then simplify"#
#7/3xx15/14=(7xx15)/(3xx14)=105/42# If you see that 21 is the
#color(blue)"highest common factor"# then straight to the simplification.
#105/42=cancel(105)^5/cancel(42)^2=5/2# If not then simplify in steps using 3 then 7, for example.
#rArrcancel(105)^(35)/cancel(42)^(14)=cancel(35)^5/cancel(14)^2=5/2larrcolor(purple)" in simplest form"# A fraction is in
#color(purple)"simplest form"# when no other factor but 1 will divide into the numerator/denominator.
