We can use fraction models to divide fractions that have a common denominator.
For example, suppose we wish to compute the fraction division
Let's start by writing down a fraction model to represent this division.
We can break down our division problem as follows:
Computing means we want to determine how many times fits into
Since both fractions have a common denominator, this is the same as determining how many times fits into
Therefore, instead of , we can simply compute
So, we have
Therefore, we conclude that
Finally, looking at our fraction model again, we can see that the shaded parts on the right of the division sign fit exactly twice into the shaded parts on the left. So, our result makes sense.
Use the model above to find the value of
We can break down our division problem as follows:
Computing means we want to determine how many times fits into
Since both fractions have a common denominator, this is the same as determining how many times fits into
Therefore, instead of , we can simply compute
So, we have
Therefore, we conclude that
Use the model above to find the value of $\dfrac{1}{4} \div \dfrac{3}{4}.$
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$ \dfrac{1}{3}$ |
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b
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$ \dfrac{3}{4}$ |
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c
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$ \dfrac{3}{16}$ |
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d
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$ \dfrac{4}{3}$ |
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e
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$ \dfrac{1}{4}$ |
Use the model above to compute the following result. Express your answer as an improper fraction in its lowest terms.
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We can use similar reasoning to divide fractions with different denominators. The only difference is that we must put the fractions over a common denominator before dividing them.
To illustrate, let's consider the following division problem:
A fraction model for this problem is shown below.
Our fractions have the denominators and Therefore, we can make a common denominator of
To create our common denominator, we split the shape on the left of the division sign into parts vertically, and we split the shape on the right into parts horizontally:
So, our division problem now is
Since the denominators are equal, this is equivalent to
Therefore, we conclude that
Use the model above to determine the missing number in the equation below.
The denominators are and We can make a common denominator of by splitting the shape on the left into parts vertically:
So, our division problem now is
Since the denominators are equal, this is equivalent to
Therefore, we conclude that
Hence, the missing number is
Use the model above to determine the missing number in the equation below.
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Use the model above to determine the missing number in the equation below.
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Calculate using the model above.
The denominators are and We can make a common denominator of
We split the shape on the left of the division sign into parts vertically, and we split the shape on the right into parts horizontally:
So, our division problem now is
Since the denominators are equal, this is equivalent to
Therefore, we conclude that
Use the model above to compute the following result. Express your answer as a fraction in its lowest terms.
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Find the value of $\dfrac{1}{2} \div \dfrac{2}{3}$ given the model above.
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$\dfrac{2}{6}$ |
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b
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$\dfrac{3}{4}$ |
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c
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$\dfrac{4}{3}$ |
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d
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$\dfrac{3}{2}$ |
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$\dfrac{6}{2}$ |
Use the model above to find the value of
The denominators are and We can make a common denominator of
We split the shape on the right of the division sign into parts horizontally:
So, our division problem now is
Since the denominators are equal, this is equivalent to
Therefore, we conclude that
Use the model above to compute the following result. Express your answer as a mixed number in its lowest terms.
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Calculate $\dfrac{3}{5} \div \dfrac{1}{2}$ using the model above.
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$1 \, \dfrac{3}{4}$ |
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b
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$\dfrac{3}{4}$ |
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$1 \, \dfrac{1}{5}$ |
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d
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$\dfrac{5}{6}$ |
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$1 \, \dfrac{1}{3}$ |
