Adding Fractions With Unlike Denominators Practice

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Question 2

What is the resulting fraction when we add 2/3 and 3/5 ? Give the answer in the simplest form.


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Select and check your answer...

A. 15/19
B. 21/15
C. 4 1/5
D. 1 4/15

Step by Step Solution

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    Step 1

    Let's write down these fractions:

    Fractions have unlike denominators

    From here, we can see that these fractions have unlike denominators.

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    Step 2

    Since the denominators are not the same, we must make them the same before we are able to add them. To do so, we can use the ideas behind Equivalent Fractions.

    To find the equivalent fractions, we can multiply 2/3 with the other fraction's denominator and vice versa. By doing so, both fractions will have like denominators. This is shown below:

    Multiply to find equivalent fractions
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    Step 3

    Now, with both fraction have like denominators. We can proceed by adding these fractions. This will result in the fraction 19/15:

    Add the fractions to get 19/15
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    Step 4

    Notice that 19/15 is an improper fraction. Even though there is nothing wrong leaving it like this, it is advisable to change this fraction to a mixed fraction..

    We can do so by performing a long division on 19/15 as shown below:

    convert improper to mixed fraction
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    Step 5

    After conversion, we get the mixed fraction, 1 4/15. Clearly, the answer is D.