# How do you solve 3.25 = a/2.5?

Apr 24, 2017

A slightly different way of thinking about the multiplication

#### Explanation:

$\textcolor{red}{\text{Step 1}}$

Write as $\text{ } 3.25 = \frac{1}{2.5} \times a$

Multiply both sides by $2.5$

$3.25 \times 2.5 = \frac{2.5}{2.5} \times a$

But $\frac{2.5}{25} = 1$ so the right hand side ends up as just $a$

$3.25 \times 2.5 = a$

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$\textcolor{red}{\text{Step 2}}$

Write $2.5$ as $\text{ } \textcolor{g r e e n}{2} \textcolor{b l u e}{+ \frac{1}{2}}$

$3.25 \times 2.5 \text{ "->" "color(brown)(3.25)(color(green)(2)" "+" "color(blue)(1/2))" } = a$

$\text{ "6.5" "+" } 1.5 + 0.125 = a$

Note that:
$\text{ } \textcolor{b r o w n}{3.25} \textcolor{g r e e n}{\times 2} = \textcolor{m a \ge n t a}{6.5}$

$\text{ } \textcolor{b r o w n}{3.25 \textcolor{b l u e}{\times \frac{1}{2}} \to \left(3 + 0.25\right) \textcolor{b l u e}{\frac{1}{2}}} \to \textcolor{m a \ge n t a}{1.5 + 0.125}$

$a = \textcolor{m a \ge n t a}{6.5 + 1.5 + 0.125} = 8.125$