Question

Margaret and Adam both get the same amount of pocket money. Margaret saves 1/2 of hers and Adam saves 19/20 of his who saves more?

Answer 1

Adam saves more.

Explanation:

`19/20 = 95%` of his money
`1/2 = 50%` of her money.

Another way of looking at this is to change to a common denominator

`1/2 xx 10/10 = 10/20`

`19/20 xx 1/1 = 19/20`

Clearly 19 is more than 10

Answer 2

Adam saves more

Explanation:

A fraction consists of:

`("count")/("size indicator")" "->" "("numerator")/("denominator")`

You can not directly compare counts unless the size indicators are the same.

Multiply by 1 and you do not change the value. However 1 comes in many forms so you can change the way a fraction looks without changing its actual value.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Approach 1")`

`color(green)([1/2color(red)(xx1)] " compared to "19/20`

`color(green)([1/2color(red)(xx10/10)] " compared to "19/20`

`" "color(green)([10/20] " compared to "19/20`

Now we can directly compare the counts (numerators)

10 is less than 19 which is mathematically written as `10<19`

So `1/2<19/20" " ->" Margaret's savings" < "Adams savings"`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Approach 2")`

We know that `10/20` is `1/2`

and 19 > 10

So Adam saves more