How do you find the quotient #-9/10div3#?

1 Answer
Nov 4, 2016

#-3/10#

Explaining it takes a lot longer than doing the maths.

Explanation:

#color(blue)("Shortcut method")#

.............................................................
#color(magenta)("Using 2 examples I am explaining a principle I am about to adopt:")#

#2xx3" is the same as "3xx2#

In the same way we have:

#" "color(red)(2/3)xx color(blue)(16/32)#

# = (color(red)(2)xx color(blue)(16))/(color(red)(3)xx color(blue)(32))#

# = (color(red)(2)xx color(blue)(16))/(color(blue)(32)xx color(red)(3)) #

#= (color(red)(2))/(color(blue)(32))xx(color(blue)(16))/(color(red)(3))#
........................................................................

Write the question as:#" "-(9/10-:3/1)#

Invert the divisor (that which you are dividing by) and change divide to multiply.

#-(9/10xx1/3)#

This is the same as:

#-(9/3xx1/10) " "->" "-((cancel(9)^3)/(cancel(3)^1) xx 1/10) #

#=-3/10#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("First principle method")#

A fraction consists of #("count")/("size indicator") ->("numerator")/("denominator")#

You can not directly divide the counts unless the size indicators are the same.

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

#color(green)(-(9/10-:[3/1color(magenta)(xx1)])" "=" "-(9/10-:[3/1color(magenta)(xx10/10)])#

Giving:

#-(9/10-:30/10)#

This gives the same answer as:

#-(9-:30) = -9/30 = -(9-:3)/(30-:3)#

#-(cancel(9)^3)/(cancel(30)^10) = -3/10#