# 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.