We can add fractions with unlike denominators using fraction models. To illustrate, let's use the fraction model below to find the value of
We cannot add the fractions at the moment because they are split into different numbers of parts. In other words, they have different denominators.
To get around this, we split the shape on the right into a total of equal parts by drawing a horizontal line. This turns the fraction into the equivalent fraction
Now that both fractions have the same number of parts, we can add them:
So now, we have:
To add fractions, they need a common denominator. Splitting up the second shape meant that the fractions had a common denominator of , which allowed us to add them.
Use the fraction model above to find the value of
We split the shape on the left into equal parts by drawing a horizontal line:
Now that they have the same number of parts, we can add them:
Therefore,
In this case, we made a common denominator of
Use the model above to find the value of $\dfrac{2}{6} + \dfrac{5}{12}.$
|
a
|
$\dfrac{12}{6}$ |
|
b
|
$\dfrac{7}{6}$ |
|
c
|
$\dfrac{12}{12}$ |
|
d
|
$\dfrac{7}{12}$ |
|
e
|
$\dfrac{9}{12}$ |
Use the model above to solve the following addition problem.
|
a
|
|
|
b
|
|
|
c
|
|
|
d
|
|
|
e
|
Use the model below to find the value of
The denominators are and Since is a multiple of , we can make a common denominator of
We split the shape on the right into parts by drawing two vertical lines:
Now that both shapes have a common denominator of , we can add them:
Therefore, we have:
Use the model above to solve the following addition problem.
|
a
|
|
|
b
|
|
|
c
|
|
|
d
|
|
|
e
|
Find the value of $\dfrac{1}{8} + \dfrac{1}{2}$ given the model above.
|
a
|
$\dfrac{3}{8}$ |
|
b
|
$\dfrac{2}{8}$ |
|
c
|
$\dfrac{5}{2}$ |
|
d
|
$\dfrac{5}{8}$ |
|
e
|
$\dfrac{2}{4}$ |
Let's suppose that we want to work out The fraction model for this is given below.
We cannot alter the shape on the left so that it contains equal parts. So what do we do?
The denominators are and . So we can make a common denominator of as follows:
We split the shape on the left into parts vertically.
We split the shape on the right into parts horizontally.
We can now add the two numbers:
Therefore, we have:
Use the model above to determine the number that is missing in the statement below.
The denominators are and So we can make a common denominator of
We split the shape on the left of the addition sign into parts vertically, and we split the shape on the right into parts horizontally:
Now, the shape to the left shows and the shape to the right shows
We add the number of shaded parts and get:
Therefore, we have
So, the missing number is
Use the model above to complete the following addition problem.
|
a
|
|
|
b
|
|
|
c
|
|
|
d
|
|
|
e
|
Use the model above to determine the number that is missing in the statement below. \[ \dfrac{1}{4} + \dfrac{1}{5} = \dfrac{\fbox{$\,\phantom{0}\,$}}{20} \]
|
a
|
$10$ |
|
b
|
$7$ |
|
c
|
$15$ |
|
d
|
$12$ |
|
e
|
$9$ |
