Of course, there are always exceptions. You can’t use this operation on zero. Zero has no inverse. No one knows why—it just is.
The inverse of a number is obtained by reversing the number. That means that if you want to divide a fraction by 5, you simply multiply the fraction by the inverse of 5, which is 1/5. You can understand this process more easily if you remember that 5 is the same thing as 5/1. In other words, 5 divided by 1 equals 5 (that is, 5 ÷ 1 = 5).
And the inverse of 5/1 is 1/5. To come up with the inverse of a number, simply stand the number on its head.So to divide a fraction, use the inverse of the number that follows the division symbol and substitute a multiplication symbol for the division symbol. Therefore,
is expressed as
and then you can simply multiply the fractions.
Now, try the following practice question.
Practice question
- Solve the following:
Answer and explanation
- The correct answer choice is D.
First, change the mixed numbers to fractions:
Flip or invert the second fraction and change the symbol to multiplication:
Cross-reduce (cross-cancel) by using the greatest common factor:
Convert back to a mixed number: