Ratio Fractions

For example, if we were told that John owned 15 cats and 3 dogs, this could be expressed in a ratio form. It can be written as $15:3$. This literally means that there are 15 cats to 3 dogs available.

Now this can also be written in a fraction form, $\frac{15}{3}$.

Ratios are not to be taken as quantities available. They express how many dogs there are to every cat owned. This makes them extremely valid if we have to simplify them.

We can find the greatest common divisor for both figures and divide them by it. Here, we realize that 3 can divide both 15 and 3 to leave us with $5:1$ or $\frac{5}{1}$.

It is at this point that the concept of ratios becomes vivid. However, now we are talking about how many cats there are to every dog. So though there are 15 cats and 3 dogs, the ratio for that is best written as $5:1$ because for every 5 cats, there is one dog.

We are making a cake, the recipe sometimes says mix flour with water in the ratio 2 part 1. That means that if you use 2 cups of flour, mix it with 1 cup of water. Both numbers should be non-zero in order to make meaning out of the comparison.

What is the ratio of native French speakers to native English speakers if there were 16 native English speakers in a class of 40 students given that the rest of the class are native French speakers?

Solution

We can first note the figures given in the question.

$Totalnumberofstudents=40$

$NumberofnativeEnglishspeakers=16$

If we want to find the number of English speakers in class, we subtract the number of native French speakers from the total number of students to get,

$NumberofnativeFrenchspeakers=40-16=24$

The ratio for this can therefore be expressed as $24:16$ or $\frac{24}{16}$.

However, this can further be simplified using the greatest common divisor 8. It divides 24 to give us 3, and divides 16 to give us 2. And hence, the appropriate ratio for boys to girls in the class can be expressed as $3:2$ or $\frac{3}{2}$.

A university in London organizes a graduation for students, and the people present include 120 graduates and 80 parents. Express the ratio of the number of graduates to parents.

Solution

This can be expressed as a ratio as $120:80$.

However, we can simplify this even more. We now find the greatest common factor for both values; 80 and 120m which is 40. We will now divide each of them by the 40 to simplify them,

For example, the Austrian flag possesses a ratio of 2 parts in red and a ratio of 1 part in white. This means that there are 3 parts in all.

The fraction for the red part is written as,

$\frac{2}{2+1}=\frac{2}{3}$

The fraction for the white part is also written as

As mentioned earlier, the number of parts in all with regards to the flag is found by summing $a$ and $b$.

John and Mike share cupcakes in the ratio $3:4$. What is the fraction of the cupcake Mike gets?

Solution

We are asked to give the fraction of Mike from the whole cupcake and so, Mike's portion is in the fraction $\frac{b}{a+b}$, where $a=3$ and$b=4$.

Thus, Mike's portion is

$\frac{b}{a+b}=\frac{4}{3+4}=\frac{4}{7}$

Mike gets $\frac{4}{7}$ of the cake.

In a YouTube video, a recipe for cakes was outlined as 4 cups of flour and a cup of milk. What fraction of the cake is the flour?

Solution

The flour's part is given by$\frac{a}{a+b}$where$a=4$ and $b=1$, hence

$\frac{a}{a+b}=\frac{4}{4+1}=\frac{4}{5}$

The fraction of the flour is $\frac{4}{5}$.

Bernard's dog gives birth to 8 female puppies and 4 male ones. What fraction of the puppies are female?

Solution

The female fraction of the puppies is given as $\frac{a}{a+b}$ where $a=8$and $b=4$, thus we have

$\frac{a}{a+b}=\frac{8}{8+4}=\frac{8}{12}$

We notice here that the resulting fraction can be simplified further. Both the denominator and the numerator can be divided by 4, so we will divide both by 4.

$\frac{8÷4}{12÷4}=\frac{2}{3}$

The fraction of the female puppies is $\frac{2}{3}$.

For example, if we were given the fraction of female puppies born to be $\frac{4}{5}$, what we can make from this, is that with the part of the total number of puppies that were born, 4 out of 5 of them were female.

On the other hand, if we are given the ratio of female puppies to male puppies born are $4:1$, then we know that for every 4 female puppies born, one is male.