R5 Ratio:Overlap/Common-Part Ratio Word Problems

Ratios 

RATIO WITH OVERLAPPING/COMMON PARTS

The question gives the ratio of two objects that overlap each other.

Spotting the sentence pattern:

Example

The figure is made up of rectangle and a square. The ratio of the square to the rectangle is 2:5. If ¼ of the square is shaded, what fraction of the figure is unshaded?

Method (Split-Common-Link)

Step 1: Circle/Underline keywords/pattern. Split up the objects and write ratio

             

                    2         :                   5

Step 2: Find Ratio to Common Overlap-value.

              (Overlap-value is the ‘common unit’ between the 2 objects)

            -> ¼ of square is to 2:5 , ¼ of square is also to 4:10

                               2_x2   :   5_x2                                                

                                4  :  10                                      

            -> ¼ is 1 part of 4 for square and 1 part of 10 for rectangle

             

Step 3: Solve: Link units

            Total = 13,

            Unshaded = 3+9 = 12

            Fraction = 12/13

Example:

The ratio of rectangle X to the shaded part is 7:3. The ratio of the rectangle Y to the shaded part is 5:2. What is the ratio of the area of Rectangle X to Rectangle Y?

           

Method

Step 1: Circle/Underline keywords/pattern. Split up the objects and write ratio

        

Step 2: Find Ratio to Common Overlap-value.

<Use the two sets of ratio with 3 objects to write the ratio>

Area of X to Shaded   Area of shaded Y to Y

    7     : 3                    2     : 5    << common item{shaded area} >>

     7_x2 : 3_x2                  2_x3  : 5_x3

    14  : 6                       6  :  15

Step 3: Solve: Link units

            Area X = 14+ 6 = 20 u

            Area Y = 6 + 15 = 21u

            Ratio of Area X to Y is 20:21

              ~~~~ END ~~~~ :)