Converting mixed numbers to improper fractions

Today we are going to learn how to convert a mixed number into an improper fraction. We’ve prepared some examples, it’s a piece of cake.

Content:

• Example 1
• Steps for writing a mixed number as an improper fraction
• Example 2
• Example 3
• Videos
• References

1) Rewrite 1²/₃ as an improper fraction

First, to get the numerator of the improper fraction, we multiply the denominator (3) by the whole number (1), then we add the result to the numerator (2). Finally, we keep the denominator (3).

When we convert a mixed number into a fraction, we always get an improper fraction. Recall that an improper fraction is a fraction whose numerator is greater than or equal to its denominator.

Steps for writing a mixed number as an improper fraction

To convert from a mixed number into an improper fraction, follow these steps:

1. Multiply the denominator by the whole number.
2. Add this result to the numerator.
3. Keep the denominator.

2) Rewrite 2³/₄ as an improper fraction

To find the numerator of the improper fraction, we multiply the denominator (4) by the whole number (2), and then we add the result (8) to the numerator (3). Finally, we keep the denominator the same.

There is another method to convert a mixed number into an improper fraction. First, we need to model the mixed number. In the image below, we have the model of 2³/₄. Finally we just need to count how many fourths we have in the model. As you can see, we took eleven fourths, and that is the improper fraction we are looking for.

3) Write the mixed number 10²/₇ as an improper fraction

First, we need to find the numerator of the improper fraction, so we multiply the denominator (7) by the whole number (10). Then we add the result (70) to the numerator (2). Finally, the denominator (7) stays the same.

Videos

In the following video, I’ll show you more examples.

And here you will find more examples.

References

We have used these books for today’s lesson:

• Tussy, K., Gustafson, D. y Koenig, D. (2013). Prealgebra (4th ed.; pp. 361-362). Cengage Learning.
• Bittinger, M., Beecher, J. and Johnson, B. (2019). Basic College Mathematics (11th ed.; pp. 168-169). Pearson.