# How do you use cross products to solve 3.6/3=y/14.4?

Apr 16, 2018

$y = 17.28$

#### Explanation:

$\frac{3.6}{3} = \frac{y}{14.4}$ Using the cross-products property, this is also
$\left(3.6\right) \left(14.4\right) = \left(3\right) \left(y\right)$ Distribute terms:
$51.84 = 3 y$ Divide both sides by $3$ to isolate $y$:
$17.28 = y$ or
$y = 17.28$

Apr 16, 2018

$y = 17.28$

#### Explanation:

Here, $\frac{3.6}{3} = \frac{y}{14.4}$
Now, by doing cross multiplication, we get
$\to 3 \times y = 3.6 \times 14.4$
$\to 3 y = 51.84$
$\to y = \frac{51.84}{3}$
$\therefore y = 17.28$

Hope that helped

Apr 16, 2018

Why cross multiply works is explained.

$y = 17.28$

#### Explanation:

The thing about 'cross product' is that it a consequence (end result) derived form first principles. This is quite often not explained.

Once you really understand what it is going on you will use the 'cross product' without giving it much thought. It is much faster than first principles.
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$\textcolor{b l u e}{\text{First principles - why the cross product works}}$

In first principles:

For add or subtract change what you wish to move to the other side of the = into the value of 0. Anything having 0 added or subtracted does not change in value

For multiply or divide change what you wish to move to the other side of the = into the value 1. Anything multiplied by 1 does not change in value

Given: $\frac{3.6}{3} = \frac{y}{14.4}$

The objective is to have just one $y$ and for it to be on its own on one side of the = and everything else on its other side. So we need to 'get rid' of the $14.4$ from $\frac{y}{14.4}$

This is 'multiply or divide' situation so we change the $14.4$ into the value of 1.

$\textcolor{b r o w n}{\text{Multiply BOTH sides by } 14.4}$

$\textcolor{g r e e n}{\frac{3.6}{3} = \frac{y}{14.4} \textcolor{w h i t e}{\text{dddd") ->color(white)("dddd}} \frac{3.6}{3} \textcolor{red}{\times 14.4} = \frac{y}{14.4} \textcolor{red}{\times 14.4}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddd.d") ->color(white)("dddd}} \frac{3.6}{3} \textcolor{red}{\times 14.4} = y \times \underbrace{\frac{\textcolor{red}{14.4}}{14.4}}}$
$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddddddddddddddddddddddd}} \downarrow}$
$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddd.d") ->color(white)("dddd") 3.6/3color(red)(xx14.4)=yxxcolor(white)(".d}} 1}$

$\textcolor{p u r p \le}{\text{See how this end up; the 'divide by 14.4' has been moved to the}}$ $\textcolor{p u r p \le}{\text{other side of the = and changed to multiply}}$

$\textcolor{b r o w n}{\text{Simplifying}}$

$\frac{3.6 \div 3}{3 \div 3} \times 14.4 = y$

$\textcolor{w h i t e}{\text{dd")1.2color(white)("dd}} \times 14.4 = y$

$y = 17.28$
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