Question

`3 3/4` is bigger than `1 19/21`. How many times bigger?

Answer 1

`3 3/4` is roughly 2 times bigger than `1 19/21`

Explanation:

So we have to fractions,

`3 3/4` and `1 19/21`

which are equivalent to,

`15/4` and `40/21`

to find how many times bigger `3 3/4` is we equate the fractions and multiply one side by a variable.

`15/4=x*40/21`

`15*21=x*40*4`

`315=160x`

`x=63/32`

`x~~ 2`

So `3 3/4` is roughly 2 times bigger than `1 19/21`

Answer 2

This is a division problem: you're trying to find the ratio between the two numbers.

Explanation:

`x=(3 3/4)div(1 19/21)`

We first convert from mixed fractions:
`(3*4/4+3/4)div(1*21/21+19/21)=15/4div40/21`

Division by a fraction equals multiplying by its inverse:

`15/4xx21/40=(15*21)/(4*40)`

We can only cancel out a `5` from both `15` and `40`:

`(3*cancel5*21)/(4*cancel5*8)=63/32=1 31/32`

So the higher number is almost (but not quite) twice as big as the smaller, or `31//32`th bigger.