So there are several ways of going about writing a fraction as a mixed number. This question asks how to write a quotient as a mixed number. A quotient is the result of dividing one number by another. This can just be a fraction, which, in this case we will look at, for it will make this process simpler. First of all, let's look at the quotient that results when we divide 19 by 8:
A mixed number is just like a number with a decimal that results from dividing two numbers, but instead of decimals, we use fractions to represent it. So to figure out what the whole number is going to be, we have to determine how many times the denominator can go into the numerator, and then the amount that is leftover is the amount that will be in the fraction:` `
`8/8 + 8/8 + 3/8 = 19/8 `
`1+1+3/8 = 19/8`
`2 3/8 = 19/8 `
We have to be careful when we write fractions in this way because we do not want to think that this is saying "2 times 3/8" but instead this is saying that we have "2 and then 3/8ths of something."
We can also think about this problem using long division. If we set up this problem as a long division problem, then we will have the 8 on the outside and the 19 on the inside. We would determine how many times 8 goes into 19, which would be 2 (since 2*8 is 16). Then there should be a remainder of 3.
We can then take the remainder and put that over the original number we were dividing 19 by:
`2 R 3 `
`2 3/8 `