According to the meaning of the question, set the whole cup of juice as "1".

Halfway through the first cup,

Then 1- 1/2= 1/2,

When filled with water, there are 1/2 juice and 1/2 water.

And drank half, that is, drank 1/4 water and 1/4 juice.

Fill it up again, that is, add 1/2 water.

Finish it,

Then drink fruit juice14 and water 3/4.

The total amount of fruit juice is1/2+1/4+1/4 =1.

The total amount of water is 1/2+ 1/4+3/4=3/2.

3/2 > 1

So Xiaoming drinks more water.

Extended data:

This kind of problem belongs to the score problem in mathematical application problems, and the ideas to solve the score problem are as follows:

An object, a figure and a unit of measurement can all be regarded as the unit "1". Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction. In the fraction, the denominator indicates how many shares the unit "1" is divided into, and the numerator indicates how many shares there are; One of them is called fractional unit.

Method of comparing scores:

1, isomorphic method

First, the scores of two different molecules are converted into the same scores of two molecules, and then compared according to "the scores of two molecules are the same, and the scores with smaller denominator are larger".

2. Decimal method

Decimate the two fractions first and then compare them.

3. Bridging method

Between the two scores to be compared, find an intermediate score and compare according to the relationship between the two scores.

4. Law of Difference.

According to "the difference between numerator and denominator is equal to two true fractions, and the sum of numerator plus mother is larger;" For two false scores with the same difference between numerator and denominator, the score obtained by adding the numerator to the mother is large and small. "

5. Cross multiplication

The product of the numerator of the first fraction multiplied by the denominator of the second fraction is regarded as the relative value of the first fraction; Take the product of the numerator of the second fraction multiplied by the denominator of the first fraction as the relative value of the second fraction, and the greater the relative value, the greater the score.

6. Comparative reciprocal method

Compare the sizes of two scores by comparing their reciprocal sizes. The smaller the reciprocal score, the greater the original score; The higher the reciprocal score, the smaller the original score.

Step 7 separate

Divide the first score by the second score. If the quotient is less than 1, the first score is small. If the quotient is greater than 1, the first score is large; If the quotient is equal to 1, then the two fractions are equal.

8, the overall method

Multiply two fractions by the denominator of a fraction at the same time, turn a fraction into an integer, and then compare it.

9. Reduction method

Before comparing two scores, divide the two scores and then compare them.