solve the equation w - 5 2/5 = 3 1/4

To solve the equation w - 5 2/5 = 3 1/4, we need to eliminate fractions and decimals.

First, let's convert the mixed numbers 5 2/5 and 3 1/4 to improper fractions.

5 2/5 = (5 * 5 + 2) / 5 = 27/5

3 1/4 = (3 * 4 + 1) / 4 = 13/4

Now, substitute these values back into the equation:

w - 27/5 = 13/4

To eliminate the fractions, we can multiply through by the least common multiple (LCM) of the denominators, which in this case is 20.

20(w) - 20(27/5) = 20(13/4)

20w - 108 = 65

Now, let's isolate the variable w by adding 108 to both sides:

20w - 108 + 108 = 65 + 108

20w = 173

Finally, divide both sides by 20 to solve for w:

w = 173/20

This fraction can be simplified to a mixed number, so divide the numerator (173) by the denominator (20):

173 ÷ 20 = 8 remainder 13

Therefore, w = 8 13/20.