Let's remind ourselves of the symbols we use to compare numbers:
the symbol "" means "is greater than"
the symbol "" means "is less than"
the symbol "" means "is equal to"
We can also use these symbols to compare fractions.
For example, let's compare the following fractions:
The area models for these fractions are shown below:
To compare these fractions, we note the following:
The fractions have the same number of parts (thirds). This means we only need to compare the number of shaded parts.
Since the fraction on the left has fewer shaded parts, it must be smaller than the fraction on the right.
To express the fact that is smaller than we use a "less than" symbol, as follows:
Finally, expressing this comparison using numbers only, we get the following:
Which symbols could replace the empty box above to make the statement true?
Let's start by drawing the area models:
Notice that
the two fractions have the same number of parts, and
the fraction on the left has more shaded parts.
Therefore, the fraction on the left must be greater than the fraction on the right.
Therefore, the correct statement is the following:
So, the correct answer is "III only."
\[ \dfrac{3}{5} \,\square \,\dfrac{1}{5} \]
Which symbols could replace the empty box above to make the statement true?
- $=$
- $< $
- $>$
|
a
|
II only |
|
b
|
I and II only |
|
c
|
I only |
|
d
|
III only |
|
e
|
I and III only |
\[ \dfrac 1 7 \,\square \,\dfrac 2 7 \]
Which symbols could replace the empty box above to make the statement true?
- $>$
- $< $
- $=$
|
a
|
II and III only |
|
b
|
I only |
|
c
|
II only |
|
d
|
I and III only |
|
e
|
III only |
When two fraction models have the same number of shaded parts, we compare the size of the parts.
For example, let's compare the following fractions:
We start by drawing the fraction models.
Notice that
both fractions have one shaded part, and
the fraction on the left has larger parts (halves) than the fraction on the right (thirds).
This means that the fraction on the left is larger than the fraction on the right. Let's add a "greater than" symbol to show this.
Writing this inequality using numbers only, we have
Which symbols could replace the empty box above to make the statement true?
Let's start by drawing the area models:
Both fractions have the same number of shaded parts. However, the parts are of different sizes.
The fraction on the left has a smaller shaded part (one-fifth) than the fraction on the right (one-quarter). Therefore, the fraction on the left is smaller.
Therefore, the correct statement is the following:
So, the correct answer is "III only."
\[ \dfrac 1 4 \,\square \,\dfrac 1 8 \]
Which symbols could replace the empty box above to make the statement true?
- $>$
- $< $
- $=$
|
a
|
II and III only |
|
b
|
III only |
|
c
|
I and II only |
|
d
|
II only |
|
e
|
I only |
\[ \dfrac{1}{7} \,\square \,\dfrac{1}{6} \]
Which symbols could replace the empty box above to make the statement true?
- $=$
- $>$
- $< $
|
a
|
II only |
|
b
|
I only |
|
c
|
I and III only |
|
d
|
I and II only |
|
e
|
III only |
Which symbols could replace the empty box above to make the statement true?
Let's start by drawing the area models:
Both fractions have the same number of shaded parts. However, the parts are of different sizes.
The fraction on the left has larger parts (quarters) than the fraction on the right (eighths). Therefore, the fraction on the left is larger.
Therefore, the correct statement is the following:
So, the correct answer is "III only."
\[ \dfrac{2}{3} \,\square \,\dfrac{2}{5} \]
Which symbols could replace the empty box above to make the statement true?
- $=$
- $< $
- $>$
|
a
|
I and III only |
|
b
|
II only |
|
c
|
I and II only |
|
d
|
I only |
|
e
|
III only |
\[ \dfrac{4}{7} \,\square \,\dfrac{4}{6} \]
Which symbols could replace the empty box above to make the statement true?
- $=$
- $< $
- $>$
|
a
|
I and II only |
|
b
|
II only |
|
c
|
III only |
|
d
|
I and III only |
|
e
|
I only |
