When we divide a whole number by a non-unit fraction, the answer is often not a whole number.
In this lesson, we'll learn how to solve division problems in these cases using models. The process is similar to cases when the answer is a whole number (we saw this in a previous lesson). The difference now is that we have to deal with a remainder.
To demonstrate, let's use a model to solve the following division problem:
We start with a model that represents whole:
We need to determine how many times fits into whole. So, we proceed as follows:
First, we split our whole into thirds (the denominator of our fraction):
Next, we break this into groups of :
Note the following:
We have full group. This is the whole number part of our answer.
We see that there is piece left over out of a possible group of So, the fractional part of our answer is
Therefore, the solution to our division problem is as follows:
Let's see another example.
Use the model above to determine the missing fraction in the following division problem.
Let's start by interpreting our model:
The model shows wholes split into sixths.
There are sixths in each group, with remaining.
Note the following:
There are full groups.
There are sixths left over out of a possible group of So the fractional part of our answer is
Therefore,
Use the model above to determine the missing fraction in the following division problem. \[ 2 \div \dfrac{3}{4} = 2 \, \dfrac{ \fbox{$\,\phantom{0}\,$} }{ \fbox{$\,\phantom{0}\,$} } \]
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a
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$\dfrac13$ |
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b
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$\dfrac23$ |
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c
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$\dfrac12$ |
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d
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$\dfrac14$ |
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e
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$\dfrac34$ |
Use the model above to determine the missing fraction in the following division problem. \[ 3 \div \dfrac{2}{5} = 7 \, \dfrac{ \fbox{$\,\phantom{0}\,$} }{ \fbox{$\,\phantom{0}\,$} } \]
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$\dfrac23$ |
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b
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$\dfrac15$ |
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c
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$\dfrac13$ |
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d
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$\dfrac35$ |
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e
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$\dfrac12$ |
Use the model above to calculate the value of
To calculate , we first need to divide each of the wholes into equal parts.
Next, we break this into groups of :
Note the following:
We got full groups.
There are pieces left over out of a possible group of So the fractional part of our answer is
Therefore,
If the model above represents $1$ whole, use the model to solve the following division problem. Express your answer as a mixed number in its simplest form.
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If the model above represents $2$ wholes, use the model to solve the following division problem. Express your answer as a mixed number in its simplest form.
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If the model above represents $4$ wholes, use the model to solve the following division problem. Express your answer as a mixed number in its simplest form.
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