A Tip on Multiplying Mixed Fractions by Whole Numbers

One of the common mistakes in multiplying mixed fractions by whole numbers is converting the mixed fraction into improper fractions immediately. What is more difficult is that if the teacher requires the answer to be in mixed fraction. This means that you have to convert it back to mixed fraction. Below is a common scenario of this mistake.

Question:  Multiply  8 ¼ × 3 the and show your answer in mixed form.

Common Steps

Step 1: Convert the mixed fraction to improper fraction.

\displaystyle \frac {4 \times 8 + 1}{4} = \frac{33}{4}

Step 2: Multiply the impproper fraction to the whole number.

\displaystyle \frac {33}{4} \times 3 = \frac{99}{4}

Step 3: Convert the product back to mixed fraction.

By manual division, the answer is 24 ¾ .  

Instead of doing these steps, there is however a much easier strategy in multiplying the numbers above.

Multiply the whole number:

8 \times 3 = 24

Multiply the fraction:

\frac{1}{4} \times 3 = \frac{3}{4}

So, the correct answer is 24 and ¾.

Most of the time, you can do this strategy especially if the answer required is a mixed fraction. This is also a lot faster if the product of the whole number and the fraction is a proper fraction. In case of improper fraction, however, you will still need to convert the product into mixed fraction. This is however, shorter and the numbers are smaller.  Here is an example.

18 \frac{2}{5} \times 3

Multiply the whole number:

18 \times 3 = 54

Multiply the fraction:

\frac{2}{5} \times 3 = \frac{6}{5}

Now, latex 6/5 is the same as 1 and 1/5, so the answer is 55 1/5.

Although this process is longer, it saves you by converting 18 2/5 to improper fraction which requires multiplication of larger numbers. The larger the number you multiply, the higher is the probability of having mistakes in calculation.

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