Adding Fractions Practice

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Question 2

What is the resulting fraction when we add:

Add 2 1/3 with 3/4

Give the answer in the simplest form.


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Select and check your answer...

A. 3 1/12
B. 1 3/12
C. 3 1/3
D. 1 1/4

Step by Step Solution

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    Step 1

    Notice that, 2 1/3 is a mixed fraction? It is advisable change it to an improper fraction before adding. This is shown in the steps below:

    converting mixed to improper fraction
    1. Multiply the denominator 3 with the whole number 2. This gives 6.
    2. Now, add 6 with the numerator 1. This gives 7.
    3. This 7 will becomes the improper fraction's numerator. The resulting fraction is 7/3.
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    Step 2

    After conversion, we have:

    add 7/3 with 3/4

    Realize that, the denominators are not the same? We need to make the denominators the same before we can add them. To do so, we can use the ideas behind Equivalent Fractions.

    First, we multiply 7/7 with the other fraction's denominator. Next we multiply 3/4 with the other fraction's denominator. By doing so, both fractions will have like denominators. This is shown below:

    Using equivalent fractions
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    Step 3

    Now, with both fractions have like denominators. We can proceed by adding these fractions. This will result in the fraction 37/12.

    Adding 28/12 with 9/12 gives 37/12
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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 it into 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, 3 1/12. Clearly, the answer is A.