Consider the following decimal fraction:
Let's use an area model to convert this fraction into a decimal fraction with a denominator of
First, we draw the area model corresponding to six-tenths:
We are looking for a fraction of the form
So, we need to find another shape with the same shaded area 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.
Therefore, we obtain
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
What number is missing from the statement below? \[ \dfrac{3}{10} = \dfrac{\fbox{$\phantom{\,0\,}$}}{100} \]
|
a
|
$30$ |
|
b
|
$24$ |
|
c
|
$300$ |
|
d
|
$10$ |
|
e
|
$3$ |
Given the picture above, what fraction is equivalent to $\dfrac{2}{10}?$
|
a
|
$\dfrac{20}{100}$ |
|
b
|
$\dfrac{200}{100}$ |
|
c
|
$\dfrac{12}{100}$ |
|
d
|
$\dfrac{2}{100}$ |
|
e
|
$\dfrac{210}{100}$ |
We can convert between equivalent decimal fractions without drawing area models.
For example, we can make a denominator of in if we multiply the numerator and denominator of the fraction by
Therefore,
Similarly, to make an equivalent decimal fraction, we can divide the numerator and denominator by Let's see an example.
Find a decimal fraction with a denominator of that's equivalent to
To make a denominator of we divide the numerator and the denominator of by
Therefore, is equivalent to
What is the missing number in the following equality?
\[\dfrac{3}{10}=\dfrac{\,\fbox{$\phantom{0}$}}{100}\]
|
a
|
$13$ |
|
b
|
$30$ |
|
c
|
$3$ |
|
d
|
$10$ |
|
e
|
$31$ |
What fraction is equivalent to $\dfrac{20}{100}?$
|
a
|
$\dfrac{2}{10}$ |
|
b
|
$\dfrac{5}{10}$ |
|
c
|
$\dfrac{4}{10}$ |
|
d
|
$\dfrac{12}{10}$ |
|
e
|
$\dfrac{20}{10}$ |
Using what we've learned, we can now add fractions with denominators and
For example, let's find the value of
Note the following:
The denominators of our two fractions are not the same. Therefore, we cannot add these fractions straight off the bat.
However, we can add these fractions if we convert the first fraction to an equivalent decimal fraction with a denominator of before adding.
To put over a denominator of we multiply the numerator and denominator by
We can now add the fractions. We keep the denominator the same, and we add the numerators:
Therefore, we conclude that
Compute
To add the fractions, we need to express each fraction as an equivalent fraction with a denominator of
To put over a denominator of we multiply the numerator and denominator by
We can now add the fractions. We keep the denominator the same, and we add the numerators:
$\dfrac{2}{10} + \dfrac{7}{100} = $
|
a
|
$\dfrac{27}{100}$ |
|
b
|
$\dfrac{9}{100}$ |
|
c
|
$\dfrac{207}{100}$ |
|
d
|
$\dfrac{27}{10}$ |
|
e
|
$\dfrac{9}{10}$ |
$\dfrac{3}{10} + \dfrac{17}{100} = $
|
a
|
$\dfrac{20}{100}$ |
|
b
|
$\dfrac{47}{10}$ |
|
c
|
$\dfrac{37}{10}$ |
|
d
|
$\dfrac{47}{100}$ |
|
e
|
$\dfrac{37}{100}$ |