# Tuesday, Nov. 22nd

ws-equationsolving-fractions-2.pdf
ws-mathcounts-20161122-OPLET.docx
In class today students worked on equation solving and mathcounts problems. I notice that generally they are comfortable solving multi-step equations like (equation 1)

$\dpi{300}\inline 72 + 4(5 - 3x) - (x + 3) - (4 - x) - 2(3 - 5x)$

But many students were not sure how to solve (equation 2):

$\dpi{300}\inline \dfrac{3x - 4}{5} = \dfrac{2x - 5}{2}$

So we did this example in class. I showed students that division can be distributed just like multiplication so we can turn the equation into

$\dpi{300}\inline \dfrac{3}{5}x - \dfrac{4}{5} = x - \dfrac{5}{2}$

and then solve it. Or, we can notice that if two fractions are equal, then their cross products are equal. For example, $\dpi{300}\inline \dfrac{\color{red} 3}{\color{blue}4} = \dfrac{\color{blue} 9}{\color{red}12}$ it is also the case that $\dpi{300}\inline {\color{red} 3 \cdot 12} = {\color{blue} 4 \cdot 9}$. This is true for all equivalent fractions and so another way to approach solving equation 2 is to find the cross products and set them equal

$\dpi{300}\inline 2(3x - 4) = 5(2x - 5)$

And solve from there

$\dpi{300}\inline 6x - 8 = 10x - 25$

Subtract $\dpi{300}\inline 6x$ from both sides and add $\dpi{300}\inline 25$ to both sides to get

$\dpi{300}\inline 17 = 4x$

And finally,

$\dpi{300}\inline \dfrac{17}{4} = x$

Assignment [handouts attached]

• Equations worksheet
• Mathcounts worksheet

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