Evaluate the expression `\frac{3mn}{-2p}` when `m\ =\ \frac{1}{3},` `n\ =-3,`and `p=3.`
To evaluate the expression, we substitute the given values of m, n, and p into the expression.
Given \(m = \frac{1}{3}\), \(n = -3\), and \(p = 3\), the expression becomes:
\[
\frac{3mn}{-2p} = \frac{3\left(\frac{1}{3}\right)(-3)}{-2(3)}
\]
Simplifying the expression within the brackets, we have:
\[
\frac{3\left(\frac{1}{3}\right)(-3)}{-2(3)} = \frac{1(-3)(3)}{-2(3)}
\]
Further simplifying, we get:
\[
\frac{1(-3)(3)}{-2(3)} = \frac{-9}{-6}
\]
Dividing -9 by -6 gives:
\[
\frac{-9}{-6} = \frac{3}{2}
\]
Therefore, the value of the expression \(\frac{3mn}{-2p}\) when \(m = \frac{1}{3}\), \(n = -3\), and \(p = 3\) is \(\frac{3}{2}\).
To evaluate the expression
\(\frac{3mn}{-2p}\)
when \(m = \frac{1}{3}, n = -3,\) and \(p = 3,\) we substitute the given values into the expression.
Substituting the values of \(m,\) \(n,\) and \(p,\) we get
\(\frac{3 \cdot \left(\frac{1}{3}\right) \cdot (-3)}{-2 \cdot 3}\)
Simplifying further,
\(\frac{-3}{-6}\)
Dividing both the numerator and denominator by \(-3,\) we get
\(\frac{1}{2}\)
So the value of the expression \(\frac{3mn}{-2p}\) when \(m = \frac{1}{3}, n = -3,\) and \(p = 3\) is \(\frac{1}{2}\).
Match the inequality to the graph of its solution.(2 points)
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A number line between negative 10 and 10 is shown. A blue open circle is shown at 10, and a blue ray is drawn to the left of 10.
A number line between negative 10 and 10 is shown. A blue closed circle is shown at negative 4, and a blue ray is drawn to the left of negative 4.
A number line is labeled from negative 10 to 10. There is an open circle on 4 and the line is shaded to the right.
To evaluate the expression `\frac{3mn}{-2p}` when `m\ =\ \frac{1}{3},` `n\ =-3,`and `p=3,` follow these steps:
Step 1: Substitute the given values of `m,` `n,` and `p` into the expression.
`\frac{3(\frac{1}{3})(-3)}{-2(3)}`
Step 2: Simplify the expression inside the parentheses.
`\frac{3(\frac{-1}{1})(-3)}{-2(3)}`
Step 3: Simplify the numerator and denominator separately.
`\frac{3(\frac{-1}{1})(-3)}{(-2)(3)}`
`\frac{3(-1)(-3)}{-2(3)}`
Step 4: Calculate the numerator and denominator.
`\frac{9}{-6}`
Step 5: Simplify the fraction, if possible.
The fraction `\frac{9}{-6}` can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which in this case is 3. Therefore,
`\frac{9}{-6} = \frac{9/3}{-6/3} = \frac{3}{-2} = -\frac{3}{2}`
Thus, the evaluated expression `\frac{3mn}{-2p}` with `m\ =\ \frac{1}{3},` `n\ =-3,`and `p=3` is equal to `-3/2`.