Lee drank 1 2/3 quarts of water today. He drank 2/5 quarts less water than Sonia. How many quarts of water did Sonia drink today?

Sonia drank 31/15 qt. of water (2 1/15 qt. as a mixed number, or approximately 20.07 qt. as a decimal).

Step-by-step explanation:

To add and subtract fractions, a least common denominator needs to be found. But first, to make it easier, mixed numbers should be replaced with improper fractions. So, Lee drank 5/3 qt. of water.

Now to find the LCD (least common denominator), the denominators of each fraction should be multiplied by 1, then 2, then 3, etc until a product of one fraction is the same as that of another (as shown):

For 2/5, the denominator is 5, so 5*1 = 5, 5*2 = 10, 5*3 = 15 ...

For 5/3, the denominator is 3, so 3*1 = 3, 3*2 = 6, 3*3 = 9, 3*3 = 4, 3*5 = 15 ...

15 is the LCD, since both denominators can be multiplied by a whole number for a product of 15.

Now, each fraction is multiplied by 1, by multiplying each fractions numerators and denominators by the number found previously that causes the denominator to equal 15:

For 2/5, 5*3 = 15, so both 2 and 5 are multiplied by 3

2 * 3 = 6, 5 * 3 = 15, so 2/5 = 6/15

For 5/3, 3*5 = 15, so both 5 and 3 are multiplied by 5

5 * 5 = 25, 3 * 5 = 15, so 5/3 = 25/15

Now these fractions can easily be added or subtracted by performing these operations on their numerators. Sonia drank 6/15 qt. more than Lee, so she drank 6/15 + 25/15 qt. of water, or 31/15 qt.