# Question: Minimum Number of Marbles

## Comment on Minimum Number of Marbles

### How can I know that 15:12:16

How can I know that 15:12:16 is the minimum numbers? ### Ratios behave the same way

Ratios behave the same way that fractions do.

So, for example, we know that the fraction 3/7 is in its simplest form, because there are no integers (greater than 1) that will divide into BOTH 3 and 7.
Likewise, we can say that the ratio 3:7 is in simplest terms.

Conversely, we know that the fraction 15/20 is NOT in its simplest form, because 5 will divide into BOTH 15 and 20 to get 3/4

Using the same approach, we know that the ratio 15:12:16 is in simplest terms, since there are no integers (greater than 1) that will divide into 15, 12 and 16

Does that help?

Cheers,
Brent

### So this mean that for a

So this mean that for a number to be expressed in it's simplest terms it must be divided by the same integer? Cuz 5 can divide 15. 3 and 8 can divide 12 and 16 respectively but since the integer differs it cant be expressed in it's lowest terms? ### A ratio is expressed in

A ratio is expressed in simplest terms if we cannot find an integer that will divide into ALL of the terms in the ratio.

So, for example, the ratio 30:70:120 is NOT expressed in simplest terms, because we can divide all three terms by 10 to get the EQUIVALENT ratio of 3:7:12

At this point, we know that 3:7:12 IS expressed in simplest terms, because there is no integer that will divide into all three terms.

Likewise, 15:12:16 IS expressed in simplest terms, because there is no integer that will divide into ALL three terms.

Does that help?

Cheers,
Brent