Ratio
ONE SET OF RATIO AND QUANTITY OF ONE ITEM
Example 1
The ratio of the number of textbooks to the number
of magazines in a box is 3:8. If there are 15 textbooks fewer than magazines,
how many magazines are there?
Method:
Step 1 – Circle Who/What, Ratio and number (books and
magazines,3:8, 15)
textbooks 3
Magazines 8
Step 2 – Draw Model for Ratio
Step 3 – Link and Solve
- 15 books fewer
5
u -> 15
1
u -> 15 ÷ 5 = 3
Answer:
how many magazines are there?
Magazines
-> 8u -> 8 x 3 = 24
There
are 24 magazines
Example
Frank, Grace and Aaron shared 60 posters in the
ratio 3:5:2. How many more posters did Grace receive than Frank?
Step 1: Circle/Underline Object(Who)/Ratio/Number
(Frank Grace, Aaron, 3:5:2, 60)
Frank 3
Grace 5
Aaron 2
Step 2 – Draw Model
for numbers
Step 3 – Link
and Solve
- Total numbers = 60 -> = total
number of boxes
- Let U be 1 unit
10u
-> 60
1u
-> 60 ÷ 10 = 6
<Question - How many more posters did Grace
receive than Frank?>
Grace receive more than Frank -> 2u -> 2 x
6 = 12
Grace received 12 more posters than Frank.
Using Ratio to solve
Frank, Grace and Aaron shared 60 posters in the
ratio 3:5:2. How many more posters did Grace receive than Frank?
Total units = Total ratios = 3+ 5 + 2 = 10
1 unit = 60 / 10 = 6 posters
Grace receives 5 – 3 = 2 units more than Frank
= 2 x 6 =
12
Grace received 12 more posters than Frank.
(2) 1 set of Ratio and a Fraction
The question gives a set of ratio and a fraction
related to the items.
Example
At a fan fair, ¼ of the visitors were men. The
remaining visitors were women and children in the ratio of 1:3. If there were
120 children than men, how many visitors were at the fan fair?
Method
Step 1: Read the question, Circle/Underline keywords/pattern.(1/4;
remaining, men, women, children; 1:3; 120 children
At a
fan fair, ¼ of the visitors were men. The remaining visitors were women and children in the ratio
of 1:3.
If there were 120
children more than men, how many
visitors were at the fan fair?
Step 2: Draw the model: Convert the ratio to fraction
and complete the model
Men Women Children
For
ratio 1:3, total unit is 4.
Fraction
of women is ¼ and children is ¾
{Convert
3parts to units divisible by 4 => 12 parts}
-
Women = ¼ x 12 = 3 units, children = ¾ x 12 = 9 unit
-
split men part to 4unit
Men
women children
4u 3u 9u
Step 3: Solve: Link units to value
There
were 120 children more than men
=>
9u – 4u = 5u
5u
= 120
u
= 24
Total
= 16u. There were 16 x 24 = 384 visitors.
(3) 1 set of Ratio and Value of Items
The question gives a set of ratio and the values
related to the items.
Example
The ratio of the number of cars to vans to motorbikes is 5:1:4
in the carpark. Given that there is a total of 640
wheels. find the number of motorbikes and
vans in the carpark.
Method
Step 1: Circle/Underline keywords/pattern.
Write the ratio
Car Van Bike
5u
1u 4u
Step 2: Write/Draw Model or
working of item values
Car Van
Bike
5u 1u 4u
wheel
x4 x4 x2
Step 3: Solve: Link ratio to value
Car Van
Bike
5u 1u
4u
wheel
x4 x4 x2
20u + 4u + 8u
= 32u
32u = 640 ,
u= 640/32 = 20
Number of motorbikes = 4x20 = 80, and number of
van = 1x20 = 20
Example
A football costs $50. A basketball cost $20 less
than the football. A total of $2700 is paid for a number of footballs and
basketballs. The ratio of the football to basketball is 3:4.
How many basketballs did the school buy?
Step 1: Circle/Underline keywords/pattern.
Write the ratio
Football Basketball
3u 4u
Step 2: Write/Draw model or
working with Values of the item/s
Football Basketball
3u 4u
Cost $50 $40
Step 3: Solve: Link ratio to value
Football Basketball
3u 4u
Cost $50 $40 -> $2700
(3u
x 50) + (4u x 30) = 270u
270u
= 2700
u=
10.
The school bought 10x4 = 40 basketballs
Example
The carpark has cars and motorcycles. There are
altogether 120 wheels. How many cars and motorcycles are there?
Step 1: Circle/Underline keywords/pattern.
Write the ratio
Car
wheel Motorcycle wheel
4
2
Step 2: Write working/Draw
model of associated item value
Car
wheel Motorcycle wheel
4u 2u
Total = 120 wheels
Step 3: Solve: Link ratio
to value
6u
= 120
u=
20
There are 4x20 = 80 wheels for cars. Thus 80/4 =
20 cars
There are 2x20 = 40 wheels motorcycles and 40/2
= 20 motorcycle
~~~ END ~~~
