# How do write in simplest form given 7/10-2/15?

Oct 29, 2016

$\frac{17}{30}$

#### Explanation:

In order to add or subtract fractions, we have to have common denominators.

1. List multiples of both numbers.

$10 : 10 , 20 , \underline{30} , 40 \ldots .$
$15 : 15 , \underline{30} , 45 , 60 \ldots .$

2. Look for the smallest underlined number (known as the least common multiple, or LCM). This is your common denominator.

Common denominator: $30$

3. Multiply the numerator and denominator by the factor that it would take to get to your common denominator…like this:

$\frac{7}{10} \cdot \frac{3}{3} = \frac{21}{30}$

and, $\frac{2}{15} \cdot \frac{2}{2} = \frac{4}{30}$

Now we have both of our fractions with common denominators, so we can subtract! Remember, in a subtraction problem, the numerators subtract but the denominators stay the same. It looks like this:

$\frac{7}{10} - \frac{2}{15} = \frac{21}{30} - \frac{4}{30} = \frac{17}{30}$

Oct 30, 2016

$\frac{17}{30}$

#### Explanation:

$\textcolor{b l u e}{\text{Initial thoughts}}$

Known: $\text{ "2xx15=30" }$ and $\text{ } 3 \times 10 = 30$ so both the 'denominators' will divide exactly into 30.

A fraction consist of " "("numerator")/("denominator")" "->" "("count")/("size indicator")

You can not directly add or subtract the counts unless the size indicators are the same.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Making the denominators (size indicators) the same}}$

$\textcolor{b r o w n}{\text{Multiply by 1 and you do not change the value. However 1 comes in many forms}}$

$\text{ "[7/10color(red)(xx1)]" " -" } \left[\frac{2}{15} \textcolor{red}{\times 1}\right]$

$\text{ "[7/10color(red)(xx3/3)]" " -" } \left[\frac{2}{15} \textcolor{red}{\times \frac{2}{2}}\right]$

$\text{ "21/30" "-" } \frac{4}{30}$

$\text{ } \frac{17}{30}$