roy is going to increase the size of his patio to make room for a new bbq grill. The ratio of the area of the old patio to the area of the new patio is 2 1/4 : 6 3/4. Convert this ratio to a unit rate and explain what this unit rate means in the context of this problem.

We are going to rewrite the ratio.
 We have:
 2 1/4: 6 3/4
 = (2 + 1/4) / (6 + 3/4)
 = (2.25) / (6.75)
 = (225/100) / (675/100)
 = (45/20) / (135/20)
 = (9/4) / (27/4)
 = 9/27
 = 3/9
 = 1/3
 Therefore, we have:
 A1 / A2 = 1/3
 A2 = 3A1
 A1: old patio
 A2: new patio
 Answer:
 The area of the new patio is three times larger than the area of the old patio.