How do you evaluate #4\frac { 4} { 7} \div \frac { 4} { 9} #?

1 Answer
Mar 4, 2017

#10 2/7#

Explanation:

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way a number looks without changing its inherent value.

#4 -> color(green)(4color(red)(xx1)" " =" " 4color(red)(xx7/7)" "=" "28/7#

so #4 4/7" "#is the same as #4+4/7" "=" "28/7+4/7" "=" "32/7#

Putting this all together we have:

#32/7-:4/9#

The short cut approach is to turn #4/9# upside down and multiply

#color(green)(32/7)xxcolor(red)(9/4)#

This is the same as

#color(green)(32/(color(red)(4))xx(color(red)(9))/7)#

#(cancel(32)^8)/(cancel(4)^1)xx9/7" "=" "72/7" "=" "10 2/7#