Roy is going to increase the size of his patio to make room for a new BBQ grill. The ratio oof 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.

The issue here is to express fractions more easily:

2 1/4: 6 3/4

lets simplify fractions:

2 1/4 = 8/4 + 1/4 = 9/4

6 3/4 = 24/6 + 3/4 = 27/6

So the ratio can also be expressed as:

9/4 : 27/6

lets find a common denominator:

54/24 : 108/24

are also equivalent, so we can reduce:

54 : 108

and finally

1 : 2