It's straightforward to find the sum of a whole number and a proper fraction when we want the final answer to be a mixed number.
For instance, we can add and as follows:
Okay, that was pretty easy. And notice that we didn't need a fraction model to do it.
There are other ways to add whole numbers and fractions, which we'll discuss shortly. But first, let's see a few examples of this idea.
is equivalent to which mixed number?
The number is a whole number, and is a proper fraction. Therefore, their sum is a mixed number:
$12+\dfrac{1}{3}$ is equivalent to
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a
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$13\,\dfrac{1}{3}$ |
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b
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$12\,\dfrac{1}{3}$ |
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c
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$12\,\dfrac{2}{3}$ |
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d
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$\dfrac{12}{3}$ |
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e
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$\dfrac{17}{3}$ |
$\dfrac{2}{9}+6$ is equivalent to
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a
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$\dfrac{12}{15}$ |
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b
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$6\,\dfrac{2}{9}$ |
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c
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$\dfrac{8}{9}$ |
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d
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$\dfrac{2}{15}$ |
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e
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$2\,\dfrac{6}{9}$ |
Suppose that we want to add a whole number and a fraction. If we want the final answer to be an improper fraction, then we can proceed by turning the whole number into an improper fraction.
For example, let's find as an improper fraction.
We start by writing as an improper fraction with in the denominator:
Then, we put this fraction over a denominator of by multiplying the numerator and denominator by :
Now, we can add the two numbers:
And we're done!
To use some math jargon, we put the numbers and over a common denominator of before adding them.
Notice that this process is very similar to using fraction models.
To add to using a model, we split each whole into equal parts. When we do, we see that there are shaded parts in total. So we arrive at the same answer:
Sophia walked of a mile and then ran another miles. Expressing the result as an improper fraction, how many miles did Sophia travel?
To find out how many miles Sophia traveled, we have to calculate the sum:
To add and , we need to express the whole number as an equivalent fraction with a denominator of
First, we write as an improper fraction:
Then, we put this fraction over a denominator of by multiplying the numerator and denominator by :
So now, we have to find the following sum:
To add two fractions with like denominators, we add the numerators and keep the denominators the same:
Therefore, Sophia traveled miles.
What is $5+\dfrac{2}{3}$ written as an improper fraction?
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a
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$\dfrac{22}{3}$ |
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b
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$\dfrac{19}{3}$ |
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c
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$\dfrac{17}{3}$ |
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d
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$\dfrac{20}{3}$ |
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e
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$\dfrac{18}{3}$ |
What is $\dfrac{2}{5} + 13$ expressed as an improper fraction?
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a
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$\dfrac{76}{5}$ |
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b
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$\dfrac{61}{5}$ |
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c
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$\dfrac{67}{5}$ |
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d
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$\dfrac{71}{5}$ |
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e
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$\dfrac{7}{5}$ |
How do we write as a mixed number?
Notice that we cannot write because is an improper fraction. Instead, let's find this sum using the same method as before.
First, we write as an improper fraction:
Then, we put this fraction over a denominator of by multiplying the numerator and denominator by :
So now, we have to find the following sum:
To add two fractions with like denominators, we add the numerators and keep the denominators the same:
Finally, we convert this to a mixed number:
Tom and Margaret went to a fruit store to buy apples and pears. Tom bought kilograms of apples while Margaret bought kilograms of pears. Expressing the result as a mixed number, how many kilograms of fruit did they buy together?
To know how many kilograms they bought, we have to calculate the sum:
To add , we need to express the whole number as an equivalent fraction with a denominator of
First, we write as an improper fraction:
Then, we put this fraction over a denominator of by multiplying the numerator and denominator by :
So now, we have to find the following sum:
To add two fractions with like denominators, we add the numerators and keep the denominators the same.
Finally, we convert this to a mixed number:
Thus, Tom and Margaret bought kilograms of fruit.
What is $\dfrac{7}{4}+3$ expressed as an improper fraction?
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a
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$\dfrac{19}{4}$ |
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b
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$\dfrac{23}{4}$ |
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c
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$\dfrac{21}{4}$ |
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d
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$\dfrac{17}{4}$ |
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e
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$\dfrac{25}{4}$ |
What is $8 + \dfrac{4}{3}$ expressed as a mixed number?
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a
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$9 \, \dfrac{2}{3}$ |
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b
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$8 \, \dfrac{3}{4}$ |
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c
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$9 \, \dfrac{1}{3}$ |
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d
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$10 \, \dfrac{4}{5}$ |
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e
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$10 \, \dfrac{3}{4}$ |