Problem:
The ratio of 2 to ⅓ is equal to the ratio of what?

Solution:
Multiply each side of the ratio 2 to ⅓ by 3, yielding 6 to 1.

Strategy:
You can also choose to write the ratio 2 to ⅓ as a fraction: 2 ÷ ⅓ which yields 6.

Problem:
150 is what percent of 30?

Solution:
150 / 30 = 5 *100 = 500%

Strategy:
These types of basic percent problems can be set up using the equation:
Is/Of = %/100
In this question: Is = 150; Of = 30; % = unknown
The equation becomes: 150/30 = x/100

Problem:
If the area of a square region having sides of length 6 centimeters is equal to the area of a rectangular region having width 2.5 centimeters, then the length of the rectangle, in centimeters, is what?

Solution:
The area of the square is 6 cm * 6 cm = 36 square-cm.
The area of the rectangle is 2.5 cm * length.
If the areas are equal, then 36 = 2.5 * length.
Therefore, the length = 14.4 cm.

Strategy:
The areas of a square and a rectangle are equal to length * width. For a square, the length and the width are equal. Therefore, the area of a square can be written as side*side.

Also, rather than dividing 36 by 2.5 to get the length, it can be easier to multiply the numerator and denominator by a factor of 1 to eliminate the decimals. Multiplying by 2/2 yields 72 by 5. This can save you valuable time needed for other problems.

Problem:
A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?

Solution:
If half of the rolls were sold by noon, ⅟₂*40 dozen = 20 dozen rolls were sold by noon and 20 dozen rolls remained.
80%, or 0.8 of the remaing rolls = .8*20 dozen = 16 dozen were sold by closing.
Thus, there were 20 dozen – 16 dozen = 4 dozen rolls remaining at closing.

Strategy:
Percents can be written as fractions or decimals. When working with percents, the word “OF” means to multiple. In this problem, half of 40 dozen translates to ⅟₂*40 dozen = 20 dozen. Also, 80% of 20 dozen translates to .8*20 dozen = 16 dozen.

Problem:
A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet.  If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

Solution:
The capacity (volume) of a rectangular box is calculated as length * width * height (l*w*h).
So, the equation is l*w*h = 10. 
Because the new sandbox is twice as long, twice as wide, and twice as high, its capacity is:
 (2*l)*(2*w)*(2*h) = 8*l*w*h.
Substituting 10 for the value of l*w*h gives
 8*l*w*h = 8*10 = 80.

Strategy:
Capacity and volume are interchangeable.  The equation for the volume of a rectangular box is:
Volume = Length*Width*Height or V=L*W*H