Ian drinks 3/4 cups of water for every half-mile that he runs. In cups, how much water should Ian take along for a 31/2 mile run?

I assume you mean a 3 1/2-mile run.

3 1/2 miles = 7/2

7 * (3/4) = 21/4 = 5 1/4 cups

(3 1/2 mi)×(3/4 cups)/(1/2 mi) =

7/2 × 3/4 × 2/1 = 21/4 cups

To find out how much water Ian should take along for a 3 1/2 mile run, we need to determine the amount of water he drinks per mile and then multiply it by the number of miles he will run.

It is given that Ian drinks 3/4 cups of water for every 1/2 mile that he runs. To find the amount of water he drinks per mile, we can set up a ratio:

(3/4 cups) / (1/2 mile) = x cups / 1 mile

Simplifying the left side of the ratio, we get:

(3/4) / (1/2) = x

To calculate this, we can invert the divisor and multiply:

(3/4) * (2/1) = x

Multiplying the numerators and denominators, we get:

6/4 = x

Simplifying the fraction, we get:

3/2 = x

So, Ian drinks 3/2 cups of water per mile.

To find how much water he should take along for a 3 1/2 mile run, we can multiply the amount of water per mile by the number of miles:

(3/2 cups) * (3 1/2 miles) = x cups

To multiply the fraction by the whole number, we need to convert the whole number to an improper fraction:

3 1/2 = (2*3 + 1) / 2 = 7/2

Now, we can multiply the fractions:

(3/2) * (7/2) = 21/4

Simplifying the fraction, we get:

21/4 = 5 1/4

Therefore, Ian should take along 5 1/4 cups of water for a 3 1/2 mile run.