We can use fraction models to help us to add fractions and whole numbers.
For example, suppose that we want to find the value of as an improper fraction. Let's solve this problem using a fraction model.
We cannot add these two fractions at the moment, because they are split into different numbers of parts (i.e., they have different denominators). So what do we do?
The first shape is split into equal parts. So, we can split the whole number into equal parts also:
Now, both shapes are split into equal parts, and we have shaded parts in total. Therefore,
And that's our answer!
Learning to add fractions and whole numbers will give us vital clues on how to add fractions with unlike denominators, which is our ultimate goal.
Use the model below to find the value of as an improper fraction.
All three shapes are split into equal parts, and we have parts in total.
Therefore,
Using the fraction model above, find the value of $1+\dfrac 3 7.$
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a
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$\dfrac{17}{14}$ |
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b
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$\dfrac{13}{7}$ |
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c
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$\dfrac{11}{7}$ |
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d
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$\dfrac{10}{14}$ |
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e
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$\dfrac{10}{7}$ |
Use the model above to solve the following addition problem. Express your answer as an improper fraction in its lowest terms.
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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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Use the model above to determine the missing number in the following statement:
The first shape is split into equal parts. We can split the second shape into equal parts, as follows:
There are shaded parts in total. Therefore, the sum of the two fractions is
Hence, the missing number is
Use the model above to determine the missing number in the statement below. \[ 1+\dfrac{7}{9} = \dfrac{\fbox{$\,\phantom{0}\,$}}{9} \]
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a
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$16$ |
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b
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$10$ |
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c
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$11$ |
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d
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$12$ |
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e
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$17$ |
Use the model above to determine the missing number in the statement below. \[ \dfrac{2}{3} + 2 = \dfrac{\fbox{$\,\phantom{0}\,$}}{3} \]
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a
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$8$ |
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b
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$7$ |
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c
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$5$ |
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d
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$9$ |
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e
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$6$ |
Use a visual fraction model to find the value of as an improper fraction.
Writing as a visual fraction model, we get the following:
The shape on the right is split into equal parts. We can split the first and second shapes into equal parts as follows:
There are shaded parts in total. Therefore, their sum is
Use a visual fraction model to find the value of $1+\dfrac 4 9$ as an improper fraction.
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a
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$\dfrac{15}{9}$ |
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b
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$\dfrac{13}{18}$ |
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c
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$\dfrac{13}{9}$ |
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d
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$\dfrac{17}{9}$ |
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e
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$\dfrac{19}{18}$ |
Use a visual fraction model to find the value of $3+\dfrac 1 3$ as an improper fraction.
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a
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$\dfrac{11}{3}$ |
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b
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$\dfrac{10}{3}$ |
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c
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$\dfrac{7}{3}$ |
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d
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$\dfrac{13}{3}$ |
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e
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$\dfrac{11}{6}$ |
