Fractions
Terminology
Fraction : Numerator
Fraction : Numerator
Denominator
There are two numbers in a fraction
n: numerator = how many of the equal parts are shaded
d: denominator = how many equal parts the total is split into
If the fraction
is spelt in words, the numerator Is usually the number and the denominator is
expressed with an additional suffix : -th added to another number.
Example: two-fifth -> 2/5
Fraction of a Whole
=>In Model Representation,
The numerator is the shaded
portion
The
total number
of squares is the denominator
Comparison Terms (With Associated Total Number)
Using Model to solve Words
Problem/Problem Sums
Example:
There are thrice as
many apples as orange.
The word
‘thrice’ is used to describe apples, the nearest object(actor) =>
a. There are 3 apples to every 1 orange
b. When there are 3 apples, there is 1 orange
Example:
There are 3 times more apples
than oranges. There are 8 apples. How many oranges are there?
The word ‘3 times’ is used to describe apples. The
term ‘more’ can be explained as:
adding
3 to the existing number -> 1+3
Method:
Step 1: Who/What and the Numbers?
Underline/Circle and write.
Step 2: What is the story? Draw Model and link
Step 3: (S)olve.
Example
12 fruits are in a basket. There are thrice as many
apples as bananas. How many
apples are there?
Step 1 – Who/What and the Numbers? Underline/Circle and write.. => Apple, Banana
Who/What number
Apple
Banana
Step 2 – What is the story? Draw Model and link
The word ‘thrice’ is used to describe apples.
There are thrice as many
apples as bananas.
Who number
Apple
3u
Banana 1u
Step 3 – Solve
There are 12 fruits
3u + u = 12 ,
4u = 12.
u=3.
There are 3x3 = 9 apples
Example:
Ali had 2/5 as many
stickers as Mary. Ali has 6 stickers.
How many stickers does Mary has?
Step 1 – Who/What and the Numbers? Underline/Circle and write. => Ali, Mary
Who number
Ali
Mary
Step 2 – What is the story? Draw Model and link
Ali has
2/5, Mary has 1 -> Ali has 2, Mary will have 5
Ali
2u
Mary 5u
Step 3: (S)olve.
Step 3: (S)olve.
Ali
has 6 stickers
2u
= 6
u = 3
Therefore, Mary has 5x3 = 15 stickers.
Example
There are 4/7 as many adults
as children on the bus. There are a total of 33 of them on the bus. How
many are children?
Step 1 – Who/What and the Numbers? Underline/Circle and write. => Adult, children
Object number
Adult
Children
Step 2 – What is the story? Draw Model and link
4/7 as many
adults as children=> 4 adults to 7 children
Adult
4u
Chlldren
7u
Step 3: (S)olve.
Total of 33
4u
+ 7u = 33
11u = 33
u = 3
There are 3 x 4 = 12 children on the bus
Practice
Mary
has four times more apples than Peter.
There are 12 apples. How many apples does each has?
Answer : Mary has 10 apples and Peter has 2 apples.
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What is U?
There is usually
a certain fixed quantity ‘bundled’(U)
together for comparison between the different objects.
Example
There are 3 times more apples than oranges. There
are 8 apples. How many oranges are there?
This example can be shown in table form:
Orange
|
Apple
|
Unit
|
1
|
4
|
1
|
2
|
8
|
2
|
3
|
12
|
3
|
4
|
16
|
4
|
The table shows that apples are 3 times more than
orange.
Thus for 1 unit there is 1 orange and 4 apples.
For 2 units, there is 2 oranges and 8 apples, etc.
When U=2, there are 8 apples , oranges = 2.
Thus, U defines the “bundled”
quantity.
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