Question

Question #d9b10

Answer 1

A fraction "of" can be written as the fraction times.

Explanation:

`1/2` of `8/10` is the same as

`1/2 xx 8/10`.

Multiplying fraction is nice! it's the easier thing to do because we just multiply top times top and bottom times bottom. (For adding or subtracting we need the same denominator -- for multiplying we don't.)

`1/2 xx 8/10 = (1 xx 8)/(2 xx 10) = 8/20`.

Usually we would reduce this answer to lowest terms. We'll remove factors that are common to the top and bottom.

`8/20 = (2 xx 4)/(2 xx 10)`. Removing the `2` that is common we get

`8/20 = (4)/(10)`. But we still have a common factor, so we'll get rid of it.

`4/10 = (2 xx 2)/(2 xx 5) = 2/5`

`2` and `5` do not have any factors in common, so we are finished.

Answer 2

`2/5`

Explanation:

We will use three concepts:

• Given a number `x`, half of `x` is the same as `x xx 1/2`.
  For example, half of `22` is `22xx1/2 = 11`
• The product of two fractions `a/b` and `c/d` is `a/bxxc/d = (ab)/(cd)`
• If the numerator and denominator of a fraction share a factor, we may cancel that factor. `(acancel(c))/(bcancel(c))=a/b`

Using the first concept, we have that half of `8/10` is `8/10xx1/2`.

Using the second, we have

`8/10xx1/2 = (8xx1)/(10xx2) = 8/20`

Using the third, we get our final result:

`8/20 = (2xxcancel(4))/(5xxcancel(4)) = 2/5`