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

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Some possible values are:

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Let's call the number we are looking for

Write an inequality to match the information.

A number, divided by

Multiply both sides by

Remember that the inequality sign must change if you multiply or divide by a negative value,

The number can be any value which is less than

They can be integers or fractions.

Some possible values are:

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

For example, you could choose

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**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.

Multiply both sides of the inequality by

The

**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

**Let's try -8**, just to convince ourselves it works:

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Any rational number less than -7.5.

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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.

This can also be written as

To simplify, multiply by

Now divide by 2 to isolate x.

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

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