Writing Ratios as Fractions
Learning Outcomes
 Given a ratio of two integers, write it as a fraction
 Given a ratio of two decimals, write it as a fraction
 Given a ratio of two mixed numbers, write it as a fraction
When you apply for a mortgage, the loan officer will compare your total debt to your total income to decide if you qualify for the loan. This comparison is called the debttoincome ratio. A ratio compares two quantities that are measured with the same unit. If we compare
$a$
and $b$
, the ratio is written as $a\text{ to }b,\frac{a}{b},\text{or}\mathit{\text{a}}\text{:}\mathit{\text{b}}\text{.}$
Ratios
A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of$a$
to $b$
is written $a\text{ to }b,\frac{a}{b},\text{or}\mathit{\text{a}}\text{:}\mathit{\text{b}}\text{.}$
In this section, we will use the fraction notation. When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number. Because a ratio compares two quantities, we would leave a ratio as
$\frac{4}{1}$
instead of simplifying it to $4$
so that we can see the two parts of the ratio.example
Write each ratio as a fraction: ⓐ$15\text{ to }27$
ⓑ $45\text{ to }18$
.Solution
ⓐ  
$\text{15 to 27}$ 

Write as a fraction with the first number in the numerator and the second in the denominator.  $\frac{15}{27}$ 
Simplify the fraction.  $\frac{5}{9}$ 
ⓑ  
$\text{45 to 18}$ 

Write as a fraction with the first number in the numerator and the second in the denominator.  $\frac{45}{18}$ 
Simplify.  $\frac{5}{2}$ 
try it
Ratios Involving Decimals
We will often work with ratios of decimals, especially when we have ratios involving money. In these cases, we can eliminate the decimals by using the Equivalent Fractions Property to convert the ratio to a fraction with whole numbers in the numerator and denominator.For example, consider the ratio
$0.8\text{ to }0.05$
. We can write it as a fraction with decimals and then multiply the numerator and denominator by $100$
to eliminate the decimals.Do you see a shortcut to find the equivalent fraction? Notice that
$0.8=\frac{8}{10}$
and $0.05=\frac{5}{100}$
. The least common denominator of $\frac{8}{10}$
and $\frac{5}{100}$
is $100$
. By multiplying the numerator and denominator of $\frac{0.8}{0.05}$
by $100$
, we ‘moved’ the decimal two places to the right to get the equivalent fraction with no decimals. Now that we understand the math behind the process, we can find the fraction with no decimals like this:"Move" the decimal 2 places.  $\frac{80}{5}$ 
Simplify.  $\frac{16}{1}$ 
example
Write each ratio as a fraction of whole numbers:ⓐ
$4.8\text{ to }11.2$
ⓑ
$2.7\text{ to }0.54$
Show Solution
Solution
ⓐ $\text{4.8 to 11.2}$ 

Write as a fraction.  $\frac{4.8}{11.2}$ 
Rewrite as an equivalent fraction without decimals, by moving both decimal points $1$ place to the right. 
$\frac{48}{112}$ 
Simplify.  $\frac{3}{7}$ 
$4.8\text{ to }11.2$
is equivalent to $\frac{3}{7}$
.ⓑ The numerator has one decimal place and the denominator has $2$ . To clear both decimals we need to move the decimal $2$ places to the right.$2.7\text{ to }0.54$ 

Write as a fraction.  $\frac{2.7}{0.54}$ 
Move both decimals right two places.  $\frac{270}{54}$ 
Simplify.  $\frac{5}{1}$ 
$2.7\text{ to }0.54$
is equivalent to $\frac{5}{1}$
.try it
Some ratios compare two mixed numbers. Remember that to divide mixed numbers, you first rewrite them as improper fractions.
example
Write the ratio of$1\frac{1}{4}\text{ to }2\frac{3}{8}$
as a fraction.Show Solution
Solution
$1\frac{1}{4}\text{ to }2\frac{3}{8}$ 

Write as a fraction.  $\frac{1\frac{1}{4}}{2\frac{3}{8}}$ 
Convert the numerator and denominator to improper fractions.  $\frac{\frac{5}{4}}{\frac{19}{8}}$ 
Rewrite as a division of fractions.  $\frac{5}{4}\div \frac{19}{8}$ 
Invert the divisor and multiply.  $\frac{5}{4}\cdot \frac{8}{19}$ 
Simplify.  $\frac{10}{19}$ 