How do you find the quotient of 5.8 divided by 30.8?

Nov 7, 2015

$\frac{29}{54}$ with KCF

Explanation:

I will explain this using a method known as KCF, or Keep Change Flip.

The first step is to convert each number into a fraction. This is simply done by putting your decimal over $10$, since it's in the "tenths place". You will have $5 \frac{8}{10} \mathmr{and} 30 \frac{8}{10}$. You can simplify them to $5 \frac{4}{5} \mathmr{and} 30 \frac{4}{5}$.

Now you must convert them to improper fractions. You do this by multiplying the denominator by the whole number, and adding the numerator to that. You leave that sum over the denominator. For $5 \frac{4}{5}$, we would do $5 \cdot 5$, (denominator times whole number), and then $25 + 4$, (answer plus numerator). Then you would leave it over the original denominator, $5$. This will leave you with $\frac{29}{5}$, and you can do the same for the other fraction. ($\frac{154}{5}$).

Now you can use KCF. Line your fractions up like you will multiply them. $\frac{29}{5} \div \frac{154}{5}$. Now you will keep the first number, change the division sign to multiplication, and flip the last number.

You're left with $\frac{29}{5} \cdot \frac{5}{154}$. You can multiply like normal fractions at this point. You are left with $\frac{145}{770}$. When you simplify, you get $\frac{29}{154}$. You can divide the top number by the bottom to get the decimal.