When adding fractions using models, we join the shaded parts that refer to the same whole.
Let's consider the following addition problem:
We start by representing this problem using an area model:
We have shaded parts. To add these fractions, we combine the shaded parts into one whole, as follows:
Therefore, we have
Use the model above to find the value of
The shape to the left of the addition sign shows and the shape to the right shows
Combined, both shapes give us shaded parts in total.
Therefore, we have
Finally, we can simplify this fraction by dividing the numerator and denominator by
Therefore, we conclude that
Use the model above to determine the missing number in the statement below. \[ \dfrac{1}{5} + \dfrac{2}{5} = \dfrac{\fbox{$\,\phantom{0}\,$}}{5} \]
|
a
|
$4$ |
|
b
|
$1$ |
|
c
|
$2$ |
|
d
|
$5$ |
|
e
|
$3$ |
Use the model above to find the value of $\dfrac{2}{9} + \dfrac{5}{9}.$
|
a
|
$\dfrac{2}{9}$ |
|
b
|
$\dfrac{7}{5}$ |
|
c
|
$\dfrac{5}{9}$ |
|
d
|
$\dfrac{9}{5}$ |
|
e
|
$\dfrac{7}{9}$ |
Fraction subtraction works similarly to addition. However, this time, we remove shaded parts that refer to the same whole.
Let's consider the following subtraction problem:
We start by representing this problem using an area model:
To subtract the fractions, we count the number of shaded parts in the right shape and remove the number of parts shown in the left shape. This leave us with shaded parts:
Therefore, we have
Finally, we can simplify this fraction by dividing the numerator and denominator by
Therefore, we conclude that
Use the model above to find the value of
The shape to the left of the minus sign shows and the shape to the right shows
We subtract the number of shaded parts on the right from the number of the shaded parts on the left:
Therefore, we have
Use the model above to find the value of $\dfrac{3}{5} - \dfrac{2}{5}.$
|
a
|
$\dfrac{5}{5}$ |
|
b
|
$\dfrac{4}{5}$ |
|
c
|
$\dfrac{3}{5}$ |
|
d
|
$\dfrac{1}{5}$ |
|
e
|
$\dfrac{2}{5}$ |
Use the model above to find a fraction that is equivalent to $\dfrac{4}{8} - \dfrac{2}{8}.$
|
a
|
$\dfrac{3}{4}$ |
|
b
|
$\dfrac{1}{2}$ |
|
c
|
$\dfrac{5}{8}$ |
|
d
|
$\dfrac{3}{8}$ |
|
e
|
$\dfrac{1}{4}$ |
Number line models give us another way to add and subtract fractions.
Let's demonstrate by considering the following addition problem:
Each fraction has a denominator of So, we create a number line where the segment between and is split into equal parts. Each part represents of a whole.
Then, we mark on our number line.
We want to add So, we need to move spaces to the right.
We have landed on Therefore,
To subtract one fraction from another using number lines, we use the same method, except we move to the left. Let's see an example.
Use the number line above to find the value of
The line segment between and is split into equal parts. So, each part gives of a whole.
To find we start at the point and move steps to the left:
We have landed on Therefore,
Given the number line above, find the value of $\dfrac{3}{7}+\dfrac{1}{7}.$
|
a
|
$\dfrac{4}{7}$ |
|
b
|
$\dfrac{5}{7}$ |
|
c
|
$\dfrac{3}{7}$ |
|
d
|
$\dfrac{4}{8}$ |
|
e
|
$\dfrac{6}{7}$ |
Use the number line above to find the value of $\dfrac{3}{5} - \dfrac{1}{5}.$
|
a
|
$\dfrac{2}{5}$ |
|
b
|
$\dfrac{1}{5}$ |
|
c
|
$\dfrac{4}{5}$ |
|
d
|
$\dfrac{3}{5}$ |
|
e
|
$\dfrac{5}{5}$ |
