# What is 1.638 -: .35?

Apr 16, 2016

In fraction form $\to 4 \frac{17}{25}$

In decimal form $\to 4.68$

#### Explanation:

Write as $\textcolor{b r o w n}{\frac{1.638}{0.35}}$

Multiply the given expression by 1 but in the form of $1 = \frac{1000}{1000}$

$\frac{1.638}{0.35} \times \frac{1000}{1000} \text{ " =" } \frac{1.638 \times 1000}{0.35 \times 1000}$

$\text{ "color(brown)(=1638/350)" }$

This looks different to $\frac{1.638}{0.35}$ but if you divide them both out you end up with the same answer. So they are 'equivalent'.

'~~~~~~~~~~~~ For reference ~~~~~~~~~~~~
$1 \times 350 = 350$
$2 \times 350 = 700$
$3 \times 350 = 1050$
$4 \times 350 = 1400$
$5 \times 350 = 1750$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Calculating the division into 1638}}$

5 lots of 350 is too big a number so we chose 4

$\textcolor{b r o w n}{\text{So the first number of our division is 4}}$

We have 4 + the remainder of $1638 - 1400 = 238$

So we write $4 + \frac{238}{350}$

$\textcolor{b r o w n}{\implies 4 \frac{238}{350}} \text{ }$ which simplifies to $\textcolor{b r o w n}{\text{ } 4 \frac{17}{25}}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This means that

$\left(1.638 \div 0.35\right) = 1638 \div 350 = 4 \frac{17}{25} \text{ }$

As a decimal this is 4.68