Question

during a bike challenge, riders have to collect various colored ribbons. each 1/2 mile they collect a red ribbon, each 1/8 mile they collect a green ribbon, and each 1/4 mile they collect a blue ribbon. which colors of ribbons will be collected at the 3/4 mile marker?

Answer 1

Answer: Hello there!

As we know, each 1/2 mile there is a red ribbon, each 1/8 mile there is a green ribbon, and each 1/4 mile there is a blue ribbon.

We want to know which color of ribbons is in the 3/4 mile marker.

then we need to see if 3/4 is a multiple of some of the previous numbers.

Start with the red ribbons, we need to see the quotient between 3/4 and 1/2, if the result is a whole number, then 3/4 is a multiple of 1/2

this is q = (3/4)/(1/2) = (3/4)*2 = 6/4

here we haven't a whole number, then there is no red ribbon at the 3/4 mile marker.

now with the green ones:

(3/4)/(1/8) = (3/4)*8 = 24/4 = 6

there we have a whole number, this means that at the 3/4 mile marker, we will see the sixth green ribbon, then we have a green ribbon in this marker.

now with the blue:

(3/4)/(1/4) = (3/4)*4 = 3

At the 3/4 mile marker, we will see the third blue ribbon, then there is a blue ribbon in this marker.

Then we know that in the 3/4 mile marker, there are a green and a blue ribbon.

Answer 2

The correct answer is:
green and blue.

Step-by-step explanation:
We want to see which fractions
`(3)/(4)` is a multiple of. We know that
`(3)/(4)` is a multiple of
`(1)/(4)`, because
`(1)/(4)`*3=
`(3)/(4)`.

We can divide fractions to determine if
`(3)/(4)` is a multiple of
`(1)/(2)`:

`( (3)/(4))/( (1)/(2))`;

in order to divide fractions, flip the second one and multiply:

`(3)/(4)`)*
`(2)/(1)`=
`(6)/(4)`=1
`(1)/(2)`.
This did not divide evenly, so
`(3)/(4)` is not a multiple of 1/2.

Checking to see if
`(3)/(4)` is a multiple of
`(1)/(8)`,
`( (3)/(4))/( (1)/(8))`;

flip the second one and multiply:

`(3)/(4)`*
`(8)/(1)`=
`(24)/(4)`=6.
This divided evenly, so
`(3)/(4)` is a multiple of
`(1)/(8)`.