# Converting mixed numbers to improper fractions | Fractions | Pre-Algebra | Khan Academy | Summary and Q&A

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July 15, 2011
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Converting mixed numbers to improper fractions | Fractions | Pre-Algebra | Khan Academy

## TL;DR

To convert a mixed number like 5 and 1/4 to an improper fraction, multiply the whole number by the denominator and add the numerator to get the new numerator over the original denominator.

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### Q: What is the definition of an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. This means that the absolute value of the numerator is greater than or equal to the absolute value of the denominator.

### Q: How do you convert a mixed number to an improper fraction?

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, and add the numerator. Write the sum as the new numerator over the original denominator.

### Q: Can you provide an example of converting a mixed number to an improper fraction?

Sure! For example, to convert 5 and 1/4 to an improper fraction, you multiply 5 (the whole number) by 4 (the denominator) to get 20. Then, you add 1 (the numerator) to get 21. The resulting improper fraction is 21/4.

### Q: Why does the method of multiplying the whole number by the denominator and adding the numerator work?

This method works because it represents the whole number (5) as a fraction over the original denominator (4). By adding the numerator (1), we are combining the fraction part with the whole number part, resulting in the improper fraction 21/4.

## Summary & Key Takeaways

• An improper fraction has a numerator that is greater than or equal to the denominator.

• Mixed numbers can be written as improper fractions by multiplying the whole number by the denominator and adding the numerator.

• 5 and 1/4 can be written as 21/4 by multiplying 5 by 4 and adding 1.