Question

Diego said that the awnser to the question “How many groups of 5/6 are in 1?” Is 6/5 or 1 1/5.Do you agree with his statement? Explain or show your reasoning.

Answer 1

Diego is correct.

There can be
`(6)/(5)` or
`1(1)/(5)` groups in 1.

Explanation:

From the question statement given we find that we need to divide 1 into groups of
`\\frac{5}{6}`.

When we form groups from a given total, we divided the total size by the size of the group.

If we are dividing
`P` number of people in groups of
`n` number of people, then the expression to find the number of groups formed can be given as:

⇒
`(P)/(n)`

For this question the data given is:

`P=1`

`n=(5)/(6)`

So, the number of groups formed can be given as:

⇒
`(1)/((5)/(6))`

When divisor is a fraction, then we multiply the reciprocal of the divisor with the dividend.

⇒
`1*(6)/(5)`

⇒
`(6)/(5)`

In order to convert fraction to mixed number we will divide numerator with denominator and then write the quotient as whole number, remainder as numerator and the denominator remains as it is.

On dividing 6 by 5, the quotient =1 and remainder =1. Thus the mixed number is:

⇒
`1(1)/(5)`

Thus, there are
`(6)/(5)` or
`1(1)/(5)` groups in 1. This matches with Diego's answer and hence he is correct.