Remember that a unit fraction is a fraction containing in the numerator.
For example, the following fractions are unit fractions since they each contain in the numerator:
However, the following fractions are not unit fractions since they do not contain in the numerator:
In this lesson, we will use models to divide whole numbers by unit fractions.
Let's start with an example. Suppose we divide the pizza below into fifths. How many fifths will there be in total?
Since each part is of a whole, we need to split pizza (whole) into equal parts, as shown below.
So, we get parts in total.
The circles above are divided into halves. How many halves are there in total?
Since each part is of a whole, we need to split each of the circles (wholes) into equal parts, as shown below.
So, we get parts in total.
The pizza above is divided into sixths. How many sixths are there in total?
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a
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$2$ |
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b
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$4$ |
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c
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$6$ |
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d
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$\dfrac16$ |
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e
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$1$ |
If the $2$ circles above are divided into eighths, then there will be
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b
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c
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d
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e
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The $3$ pancakes above are divided into halves. How many halves are there in total?
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a
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$5$ |
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b
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$2$ |
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c
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$8$ |
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d
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$6$ |
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e
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$3$ |
The model below represents wholes. Let's use it to calculate the value of
To calculate , we need to divide each of wholes into equal parts, as shown below.
We get pieces in total.
Therefore,
What model could represent the division problem below?
Consider the following wholes:
To calculate , we need to divide each of wholes into equal parts, as shown below. This gives us the corresponding model for the given division problem.
We get pieces in total.
Which model represents the division problem below? \[ 2 \div \dfrac{1}{5} = 10 \]
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e
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Which model represents the division problem below? \[ 3 \div \dfrac{1}{4} = 12 \]
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b
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c
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Each of the three shapes in the model below represents one whole.
From left to right, what numbers are missing from the division problem below?
In the model, there are shapes. Each shape consists of pieces that each represent of a whole. There are pieces in total.
The model tells us that when we divide wholes into quarters, we will be left with pieces.
Therefore, the division problem is:
So, the missing numbers are and
Each of the five shapes in the model above represents one whole. Insert the missing numbers in the division problem below.
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a
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b
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c
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d
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e
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Each of the two shapes in the model above represents one whole. From left to right, what numbers are missing from the division problem below? \[ \fbox{$\,\phantom{0}\,$} \div \dfrac{1}{4} = \fbox{$\,\phantom{0}\,$} \]
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a
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$2$ and $6$ |
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b
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$4$ and $2$ |
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c
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$3$ and $8$ |
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d
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$3$ and $6$ |
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e
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$2$ and $8$ |
The model above represents wholes. Use this model to calculate the value of
To calculate , we need to divide each of wholes into equal parts, as shown below.
We get pieces in total.
Therefore:
The shape in the model above represents $1$ whole. Using this model, find the value of $1 \div \dfrac{1}{6}.$
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a
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$4$ |
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b
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$8$ |
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c
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$6$ |
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d
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$\dfrac{1}{4}$ |
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e
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$9$ |
The shape in the model above represents $2$ wholes. Use this to solve the following division problem.
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e
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