Question

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

Answer 1

`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`