The discussion centers on the algebraic manipulation of fractions, specifically how to rearrange the expression \(\frac{x \cdot \frac{1}{z}}{y}\) into the form \(\frac{x}{y \cdot \frac{1}{z}}\). It is established that these two expressions are not equivalent, as demonstrated by substituting values for \(x\), \(y\), and \(z\). The key takeaway is that multiplying in the numerator can be interpreted as multiplying the entire fraction, leading to the simplified form \(\frac{x}{yz}\).
PREREQUISITESStudents learning algebra, educators teaching fraction manipulation, and anyone seeking to improve their understanding of algebraic expressions.
Well, you can't make it look exactly like that- they are not the same values, as you can see by putting in some values: if x, y, and z are all equal to 2, for example, the first fraction would have value \frac{2\frac{1}{2}}{2}= \frac{1}{2} while the second would be \frac{2}{2\frac{1}{2}}= 2.daigo said:Say I have:
\frac{x \cdot \frac{1}{z}}{y}
How can I make it look like:
\frac{x}{y \cdot \frac{1}{z}}
I'm trying to figure out the algebraic rule(s) for this