Consider how multiplying or dividing the given values could lead to the desired result.
Example Solution: 24y/xz
Practice makes perfect
There are many expressions we can create with the given values of x, y, and z to obtain a result of - 16. We have that x= -3, y= -2, and z= -1. For our expression, we will arbitrarily choose to create a fraction. Now, for example, we can let the numerator of the fraction be 24y.
24y = 24( - 2) = - 48
From here, we can think about what we might divide - 48 by to end with - 16. Since the result needs to be negative, the number we are looking for is positive. The result also is a whole number. Consider a few possibilities.
Possible Number
Division
Result
1
-48 ÷ 1
-48
2
- 48 ÷ 2
-24
3
-48 ÷ 3
-16
4
-48 ÷ 4
- 12
6
-48 ÷ 6
- 8
8
-48 ÷ 8
- 6
12
-48 ÷ 12
- 4
16
-48 ÷ 16
- 3
24
-48 ÷ 24
- 2
48
-48 ÷ 48
- 1
That means that the denominator of our fraction must be 3. Notice that if we multiply x by z we will obtain exactly 3.
x * z = - 3( - 1) = 3
Knowing that, we can complete our expression.
\begin{gathered}
\dfrac {24y}{xz}
\end{gathered}
We can verify that this works by substituting the given values into our expression.
