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
2x2
: 5x2
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} >>
7x2
: 3x2 2x3
: 5x3
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
More Questions
1. The ratio of the number of P5 pupils taking part in a game is 2:1. All the P5 pupils taking part in the games are girls. Among the P6 pupils taking part in the game, the ratio of the girls to the boys are 4:3. There are 30 more P5 girls than P6 girls taking part in the game. How many girls are taking part in the game?
Step 1: Write/working on given information
P5 : P6 P6 - Girls : Boy
2 : 1 4 : 3
All P5 are girls, P5 girls has + 30 than P6 girls
Step 2: link the information
(Remember: ratio is comparing portion, not the units or the actual quantity)
< link with P6's girl unit to P6 information >
P6 - Girl : Boy
4 : 3 (Ratio)
4U : 3U (The number of units in the ratio portion)
P5 : P6
2 : 1
: 7U (total of P6 = 4U + 3U)
14U : 7U (value in ratio portion)
P5 are all girls, and 30 more than P6 girls
P5 girls = 4U + 30
Step 3 : Compute : Draw model / algebra , use formula
10U = 30
U = 3
Total number of girls = 4U + 4U + 30
= 8U + 30 = 8x3 + 30
= 24 + 30
= 54 girls
2. The figure below shows a square that is divided into 4 parts, A, B, C and D.
The line PQ divides the square into 2 equal parts. The ratio of Area A to Area B is 2:3, and the ratio of Area A to Area C is 2: 1. Area D is 113.4 cm2. What is the length of one
side of the square?
Area of square = PR x RQ. Step 1 : Write information
Area of triangle = 1/2 x base x height
D = 113.4 cm2
A : B B : C
2 : 3 2 : 1
all triangle base = side of square, the ratio -> the height
A : B B : C Step 2 : Link
2x2 : 3x2 2x3 : 1 x 3 B - 3, 2 -> 6
4 : 6 6 : 3
A : B : C
4 : 6 : 3
Area PQR = Area PQS. Step 3 : Compute
A : B : C
4U: 6U : 2U
Area A+ B = 10U, Area C + D = 10U
Area D = 10U - 3U
= 7U
= 113.4 cm2
U = 113.4 / 7
= 16.2cm2
Area of PQR = 16.2 x 10 = 162cm2
Area of square = 162 x 2 = 324 cm2
Side = 18cm
3. The figure below shows a rectangle with its corners cut off. Each of the 4 identical corners that bas been cut off is a quarter circle. 
The ratio of the length of the rectangle to its breadth is 12:5. The length of AB is 17cm and the length of CD is 3cm.
a. What is the radius of each quarter circle?
b. What is the perimeter of the shaded part? (take = 3.14)
(Give your answer correct to 1 decimal place)
a.
L : B Step 1: Write Information
12 : 5
17 + 2u : 3 + 2u
Area of Rectangle = length x breadth
Area of circle = π r2
Step 2: Link information
Step 3: Compute(model/algebra) with formula
7 parts -> 14,
1 part -> 14/7 = 2
Using breadth, 3 + 2u = 5 parts = 5 x 2 =10
3 + 2u = 10
u = 3.5cm
b.
Perimeter = add all sides Step 1: Write information
P = 17 + 17 + 3 + 3 + 4 (1/4 circumference) Step 2: Link
4 of 1/4 = circumference. Step 3: Compute
= 2 π r
= 2 x 3.14 x 3.5 = 32.97
= 33 cm (to nearest 1 decimal)
4. The ratio of water to oil is 5 : 1 in container A and 6 : 1 in another container B. Both containers have the same volume of mixture, and are poured together into container C. What is the ratio of water to oil in container C?
w : o w : o. Step 1 : Write information/formula
5 : 1 6 : 1
Step 2: Link Information
A -> 6 portion, B -> 7 portion Step 3: Compute
Common factor = 6 x 7 = 42
water parts = 5x7 + 6x6 = 35 + 36 = 71
oil parts = 6 + 7 = 13
Ratio of water to oil is 71 : 13
~~~~ END ~~~~ :)
