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

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#### Explanation

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1
Feb 5, 2018

Some possible values are: $7 \frac{1}{3} , 7 \frac{1}{4} , 7 , 6 \frac{1}{2} , 6 \ldots .$

#### Explanation:

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

Write an inequality to match the information.

A number, divided by $- \frac{3}{2}$ must be greater than $5$

$x \div - \frac{3}{2} > 5 \text{ } \leftarrow$ solve for $x$

$\frac{x}{- \frac{3}{2}} > 5$

Multiply both sides by $- \frac{3}{2}$ to cancel the division by $- \frac{3}{2}$.
Remember that the inequality sign must change if you multiply or divide by a negative value,

$\frac{x}{\cancel{- \frac{3}{2}}} \textcolor{b l u e}{\times \cancel{- \frac{3}{2}}} < 5 \textcolor{b l u e}{\times - \frac{3}{2}}$

$x < - \frac{15}{2}$

The number can be any value which is less than $7 \frac{1}{2}$

They can be integers or fractions.

Some possible values are: $7 \frac{1}{3} , 7 \frac{1}{4} , 7 , 6 \frac{1}{2} , 6 \ldots .$

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Nimo N. Share
Feb 4, 2018

The answer to the question is to pick some rational number less than $- \frac{15}{2}$.
For example, you could choose $- \frac{16}{2} = - 8$.

#### 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 $- \frac{3}{2}$, but remember to change the sense of the inequality sign, since we are multiplying by a negative number.

$\frac{R}{- \frac{3}{2}} \cdot \left(- \frac{3}{2}\right) < 5 \cdot \left(- \frac{3}{2}\right)$
The $- \frac{3}{2}$ 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 $- \frac{15}{2}$.

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

Let's try -8, just to convince ourselves it works:
$\frac{- 8}{- \frac{3}{2}} > 5 \text{ ?}$

$\frac{+ 8 \cdot 2}{3} > 5 \text{ ?}$

$\frac{16}{3} > 5 \text{ ?}$

$\frac{16}{3} = 5 \frac{1}{3}$, and
$5 \frac{1}{3} > 5 \text{ YES!}$

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#### Explanation

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vanessa Share
Feb 4, 2018

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.

$x \cdot \frac{2}{-} 3 > 5$

This can also be written as

$\frac{2 x}{-} 3 > 5$

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

$2 x < - 15$

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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