What is a fraction?
A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To figure out what fraction of the toys are blue, we need to convert all of the fractions to have a common denominator.
What is a common denominator?
A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
Looking at the fractions, we can see that there are 3 fractions,
and
.
To solve for the common denominator between
and
, we first multiply the denominators, 8 and 5.
We now know that the denominator is going to be 40.
To get the numerators, we can use these equations:
The new fractions look like this:
To easily convert the last fraction (
) we can multiply the numerator and denominator by 10.
Why do we multiply by 10?
We multiply by 10 because the denominator, which is 4, can be multiplied by 10 to get our common denominator of 40.
Now, we have our 3 fractions converted to have common denominators.
(
and
)
(Yellow, red, and green)
We can now add these up and see what fraction of blue is remaining.
Therefore, the fraction of blue toys compared to the total amount is
.
If there are 100 green toys resulting in
of all the toys, we can divide 100 by 10 to get the number of blue toys.
Why do we divide by 10?
We divide by 10 because
is only
of
, meaning we divide by 10.
Therefore, there are 10 blue toys.