Two fractions are equivalent (e-quiv-a-lent) if their area models have the same shape and have the same shaded area.
For example, let's take a look at the fractions below.
Notice that
both models have the same shape, and
they have the same shaded area.
Therefore, these fractions are equivalent. This means they represent the same number, and we can put an "equals" sign between them.
We have the following equivalent fractions:
Let's use this to write down an equation with numbers.
For the shape on the left:
There are parts of the shape in total. Of them, parts are shaded. So, of the shape is shaded.
For the shape on the right:
There are parts of the shape in total. Of them, part is shaded. So, of the shape is shaded.
Since the two fractions are equivalent, they represent the same number, and we can write down the following equation:
What number is missing from the statement below?
Let's compare the two shapes.
For the shape on the left:
There are parts of the shape in total. Of them, parts are shaded. So, of the shape is shaded.
For the shape on the right:
There are parts of the shape in total. Of them, parts are shaded. So, of the shape is shaded.
Both shaded regions have the same area. Therefore, the two fractions are equivalent, and we obtain the following:
Therefore, the missing value is
What number is missing from the statement below? \[ \dfrac{2}{6} = \dfrac{\fbox{$\phantom{\,0\,}$}}{3} \]
|
a
|
$3$ |
|
b
|
$1$ |
|
c
|
$4$ |
|
d
|
$2$ |
|
e
|
$6$ |
What number is missing from the statement below? \[ \dfrac{3}{4} = \dfrac{6}{\fbox{$\phantom{\,0\,}$}} \]
|
a
|
$3$ |
|
b
|
$9$ |
|
c
|
$8$ |
|
d
|
$5$ |
|
e
|
$6$ |
Given the picture above, what fraction is equivalent to
Let's compare the two shapes.
For the shape on the left:
There are parts of the shape in total. Of them, parts are shaded. So, of the shape is shaded.
For the shape on the right:
There are parts of the shape in total. Of them, parts are shaded. So, of the shape is shaded.
Both shaded regions have the same area. Therefore, the two fractions are equivalent, and we obtain the following:
Given the picture above, what fraction is equivalent to $\dfrac{2}{3}?$
|
a
|
$\dfrac{4}{6}$ |
|
b
|
$\dfrac{3}{2}$ |
|
c
|
$\dfrac{4}{3}$ |
|
d
|
$\dfrac{2}{6}$ |
|
e
|
$\dfrac{1}{2}$ |
Given the picture above, what fraction is equivalent to $\dfrac{6}{8}?$
|
a
|
$\dfrac{4}{4}$ |
|
b
|
$\dfrac{4}{2}$ |
|
c
|
$\dfrac{1}{4}$ |
|
d
|
$\dfrac{2}{4}$ |
|
e
|
$\dfrac{3}{4}$ |
The following fraction model represents
We can generate equivalent fractions by splitting the shape into more equal parts.
For example, if we draw a horizontal line, we get the following model representing
We can continue to split the fraction into equal parts to generate more equivalent fractions.
For example, if we draw two more horizontal lines, we get a model representing
Therefore, the following fractions are all equivalent:
Watch Out! Whenever we split a fraction model into more equal parts to generate equivalent fractions, all parts must have the same area!
We can also create equivalent fractions by removing some parts, where possible.
For example, let's look at the following fraction, representing
If we remove the horizontal line, we'll generate an equivalent fraction representing
Therefore, we conclude once again that the following fractions are equivalent:
The fraction given below is equivalent to the fraction shown in the picture. What number is missing?
There are equal parts in the given shape in total. Of them, parts are shaded. So, of the shape is shaded.
Since we are looking for a fraction of the form , we now draw another shape that has the same shaded area but is divided into equal parts. To do that, we subdivide each part into equal pieces:
The shape on the right is divided into equal parts. Of them, parts are shaded. So, of the shape is shaded.
Hence, we obtain
Therefore, the missing number is
The fraction given below is equivalent to the fraction shown in the picture. What number is missing? \[ \dfrac{\fbox{$\,\phantom{0}\,$}}{9} \]
|
a
|
$1$ |
|
b
|
$2$ |
|
c
|
$3$ |
|
d
|
$4$ |
|
e
|
$5$ |
The fraction given below is equivalent to the fraction represented in the picture. What number is missing? \[ \dfrac{\fbox{$\,\phantom{0}\,$}}{3}. \]
Hint: Create an equivalent fraction with fewer equal parts.
|
a
|
$4$ |
|
b
|
$6$ |
|
c
|
$3$ |
|
d
|
$9$ |
|
e
|
$2$ |
