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

Answer 1

#-3/10#

Explaining it takes a lot longer than doing the maths.

#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#
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Answer 2

To find the quotient of (-\frac{9}{10} \div 3), you simply divide (-9) by (10) and then divide the result by (3).

[ \frac{-\frac{9}{10}}{3} = -\frac{9}{10} \times \frac{1}{3} = -\frac{9}{30} = -\frac{3}{10} ]

So, the quotient is (-\frac{3}{10}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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