Question

Fractions greather than 1/2

Answer 1

`(6)/(10), (7)/(10), (8)/(10),(9)/(10)` (in general, the numerator has to be greater than half the denominator)

Explanation:

There are an infinite number of fractions greater than 1/2, but we can generally form a rule to figure out whether a fraction is greater than 1/2, which will help us find those fractions!

Forming a Rule:

Let's first just express a fraction in the form:
`(a)/(b)`, and we have to ask our self, what determines whether this is 1/2? Well we know if we have 1/2, and multiply it by two, then we have a whole, or one, but the only case where we have a whole, or one, in fraction form, is where the numerator and denominator are equal.

This means, multiplying the numerator "a" by 2, will result in it being equal to the denominator "b". From here, it can be determined that for the fraction:
`(a)/(b)`, to be 1/2, then the numerator "a" has to be half the denominator "b". But this is just telling us what "a" and "b" need to be, for the fraction to be equal to 1/2, not greater than 1/2. This is still useful, since in general the following is true:
`(a+1)/(b)`, if we add one to the numerator, the fraction becomes bigger. So if we want the fraction to be bigger than 1/2, the numerator "a" just needs to be bigger or larger than the half the denominator "b".

Examples:

Let's select a denominator, and from there find numerators that make the fraction bigger than 1/2. For this example let's just select "9". In this case, for a fraction to be 1/2, the numerator just has to be larger than 9/2 or 4.5, but since we can't have decimals in fractions, or at least proper fractions, we just need the numerator to be greater than or equal to 5 (5 is included, since it's still bigger than 4.5)

`(4)/(5)` is actually the only proper fraction, since 5/5 would just simplify to one.

Let's do another example, in this case let the denominator be 10. For the fraction to be considered greater than 1/2, the numerator, has to be greater than half the denominator, 10/2 = 5.

`(6)/(10), (7)/(10), (8)/(10),(9)/(10)` would all be valid answers (although some do simplify further). But all of them represent fractions which have a greater value than 1/2