What rational number could be divided by #-3/2# to have a quotient greater than #5?#

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Feb 5, 2018

Answer:

Some possible values are: # 7 1/3, 7 1/4, 7 , 6 1/2, 6 ....#

Explanation:

Let's call the number we are looking for #x#

Write an inequality to match the information.

A number, divided by #-3/2# must be greater than #5#

#x div -3/2 > 5" "larr# solve for #x#

#x /(-3/2) >5#

Multiply both sides by #-3/2# to cancel the division by #-3/2#.
Remember that the inequality sign must change if you multiply or divide by a negative value,

#x /cancel(-3/2) color(blue)(xxcancel(-3/2)) < 5 color(blue)(xx-3/2)#

#x < -15/2#

The number can be any value which is less than #7 1/2#

They can be integers or fractions.

Some possible values are: # 7 1/3, 7 1/4, 7 , 6 1/2, 6 ....#

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Nimo N. Share
Feb 4, 2018

Answer:

The answer to the question is to pick some rational number less than # -15/2 #.
For example, you could choose # -16/2 = -8 #.

Explanation:

Problem:
What rational number could be divided by -3/2 to have a quotient greater than 5?

Use R to represent the rational number, then translate the statement into math symbols.

# color(blue)( R/(-3/2) > 5 #
Multiply both sides of the inequality by # - 3/2 #, but remember to change the sense of the inequality sign, since we are multiplying by a negative number.

# R/(-3/2) * (-3/2) < 5 * (-3/2) #
The # - 3/2 # in the denominator disappears from the left side of the inequality.
# color(red)( R < -15/2 #

The answer to the question is to pick some rational number less than # -15/2 #.

There are many rational numbers from which to choose. For example, you could choose # -16/2 = -8 #, or even # -70/3 #, since it is smaller than # -15/2 #.

Let's try -8, just to convince ourselves it works:
# (-8)/(-3/2) > 5 " ?"#

# (+8 * 2)/(3) > 5 " ?"#

# (16)/(3) > 5 " ?"#

# (16)/(3) = 5 1/3 #, and
# 5 1/3 > 5 " YES!"#

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vanessa Share
Feb 4, 2018

Answer:

Any rational number less than -7.5.

Explanation:

Dividing by a fraction is the same thing as multiplying by its reciprocal. Using this and the given information, let's write an inequality, with x being equal to the rational number.

#x *2/-3 > 5#

This can also be written as

#(2x)/-3 > 5#

To simplify, multiply by #-3#. When multiplying by a negative number, the sign must be flipped.

#2x < -15#

Now divide by 2 to isolate x.

#x < -7.5#

So, any rational number less than -7.5 would be an answer. Some possible answers are -8, -27, and -85.

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