Can a positive mixed number be less than 1? What does this tell us?
No, see solution.
Practice makes perfect
A mixed number consists of a non-zero integer number and a fraction whose numerator is less than the denominator. This type of fraction is also known as a proper fraction.
a bc
a ≠0 and bsum of its two components.
a bc = a+b/cTherefore, a positive mixed number is always greater than 1 because a is greater than or equal to 1. We can also rewrite a positive mixed number as an improper fraction.
a bc = a* c+b/c
When we multiply fractions, we can either get a result that is greater than, less than, or equal to the first fraction. If we multiply by a fraction that is greater than 1, the result will be greater than the first fraction. Let's see an example!
1/2 * 2 = 1
1 > 1/2
If the multiplier fraction is less than 1, the result will be less than the original fraction.
1/2 * 1/2 = 1/4 [0.8em]
1/4 < 1/2
Finally, if the fraction is equivalent to 1, the result will be equal to the original fraction.
1/2 * 2/2 = 2/4 [0.8em]
2/4 = 1/2
When we multiply two positive mixed numbers — both of which are are both greater than 1 by definition — the result has to be greater than the first number. Therefore, the result will always be greater than 1 because the both factors are greater than 1.
