# How do you solve W/9 = 9 ?

Dec 14, 2015

$W = 81$

#### Explanation:

$\frac{W}{9} = 9$

Multiply both sides by $9$.

$\frac{W}{\cancel{9}} \times \cancel{9} = 9 \times 9$

$W = 81$

Dec 14, 2015

$\textcolor{g r e e n}{\text{An expansion on the solution method to deepen understanding of}}$ $\textcolor{g r e e n}{\text{what is going on.}}$

#### Explanation:

$\textcolor{b l u e}{\text{Short cut method}}$
For add or subtract move to the other side of the equals and do the opposite: change its sign.

For divide or multiply move it to the other side of the equals and do the opposite: if originally divide then you multiply when on the other side. If originally multiply then you divide when on the other side.

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$\textcolor{red}{\text{Why the shortcuts work}}$

The key to manipulation of equations and moving something to the other side of the equals sign:

$\textcolor{g r e e n}{\text{For multiply or divide you change it to 1}}$
$\textcolor{p u r p \le}{\text{For add or subtract you change it to 0.}}$

Let me demonstrate:

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$\textcolor{b l u e}{\text{Example 1}}$

Suppose we had $\textcolor{b r o w n}{x + 2 = 3}$ and we whish to find the value of $x$

To end up with $x$ on its own we need to remove the $+ 2$

Subtract $\textcolor{b l u e}{2}$ from both sides:

color(brown)((x+2)color(blue)(-2) = ( 3 )color(blue)(-2)

$x + \left(2 - 2\right) = 3 - 2$

$x + 0 = 1$

$x = 1$
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$\textcolor{b l u e}{\text{Example 2}}$

Suppose we had $\textcolor{b r o w n}{2 x = 3}$

Divide both sides by $\textcolor{b l u e}{2}$
But divide by 2 is the same as multiply by $\textcolor{g r e e n}{\frac{1}{2}}$

$\textcolor{b r o w n}{2 x \textcolor{g r e e n}{\times \frac{1}{2}} = 3 \textcolor{g r e e n}{\times \frac{1}{2}}}$

color(brown)( (2color(green)(xx1))/(color(green)(2)) xx x= (3color(green)(xx1))/(color(green)(2))

color(brown)(2/(color(green)(2)) xx x=3/(color(green)(2))

But $\frac{2}{2} = 1$ so we have:

$1 \times x = \frac{3}{2}$

$x = \frac{3}{2}$
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$\textcolor{b l u e}{\text{For your question:}}$

Multiply both sides by 9 giving:

$\frac{W}{9} \times 9 = 9 \times 9$

$W \times \frac{9}{9} = 81$

$W = 81$