‘REMAINING’ – Fraction of a fraction/Value
Words problem involving fractions can be wordy and confusing for learners.
Solve the question by 'spotting' keywords / patterns and using step-by-step method to answer the question.
Solving ‘Remaining’ – Fraction of a fraction
(a) Sentence Construction
Words Problem with ‘remaining’ or ‘remainder’ are usually constructed as
(b) Relationship between the numbers in the sentence.
There is usually the First Fraction/Number object (who/what) and Second fraction/number object (who/what) in the remaining fractions.
Example:
In a basket, 2/5 of the fruits are apples. 2/3 of the remaining fruits are bananas.
The first fraction(number)’s object(what) is apple, and the remaining two others are bananas and other fruits.
((c) Solve the Word Problems
((c) Solve the Word Problems
Model Method:
Step 1: Keywords/Draw Model with First Fraction/Value
- Use the DENOMINATOR of the First Fraction/Value to draw model
- Shade the MAIN object’s unit (the numerator);
Step 2: Complete Model with Second Fractions
- label ‘remaining’ or ‘remainder’ for unshaded part
- Divide/’Split’ the Unshaded part as a ‘Whole’ (2nd fraction denominator),
- shade the second fraction ‘Part’ (using numerator) and the rest.
Step 3: Solve Problem with the model (1 part = 1 U)
Example1:
<< Read the sentence carefully and spot the word patterns>>
In a basket, 2/5 of the fruits are apples. 2/3 of the remaining fruits are bananas. There are 20 fruits. How many bananas is in the basket?
Step 1: Keywords/Draw Model with First Fraction/Value
{Underline/Circle keywords/Draw model with first fraction}
[First = Apple, 2/5, Second = bananas 2/3 remaining]
- Draw Model of First Fraction DENOMINATOR (total 5 of Apple)
- Shade the firs fraction(the numerator);
Step 2: Complete Model with second fractions
- Label ‘remaining’ or ‘remainder’ for unshaded part
- ‘Split’/divide unshaded parts to 3 parts (2nd fraction denominator)
- Shade 2/3 of the remaining fruits are bananas.
Step 3: Solve Problem with Model (1 equal part = 1 U)
(To make U of standard/same portion: U is already ‘same size’)
There are 20 fruits.
Total = 5u
5u = 20.
U = 20/5 = 4.
U = 20/5 = 4.
There are 4x2 = 8 bananas.
Example 2
John gave 3/8 of his money to his parents. He gave 1/10 of the remainder to his sister. What fraction of his money did he give his sister?
Step 1: Keywords/Draw Model with First Fraction/Value
{Circle Number, underline keywords}
[Write key values: Parents = 3/8, Sis = 1/10 R]
- Draw Model total (whole) of 8 parts
- Shade 3 parts (the first fraction’s numerator)
Step 2: Complete Model with second fraction
- label ‘remainder’
- Split/Divide the unshaded parts to 10 parts (denominator of second fraction)
- Shade 1 part for the sister (numerator 1/10)
Step 3: Solve Problem with Model (1 equal part = 1 U)
- Model to equal parts : Split each of the 3/8 to 2 parts
Total (Whole) = 20, Sister (part) = 1
He gave 1/20 of his money to his sister.
Example 3
A shop had
a number of mobile phones for sales. After selling
32 of them in the morning and 5/8 of the remainder in the
afternoon, it was left with ¼ of the mobile phones. How many mobile phones were sold altogether?
<<
Read the sentence carefully and spot the word patterns>>
Step 1: Underline
keywords and MAIN and Remaining Fraction. Who/What?
There is no fraction but 32 mobile phone
Step 2a: Draw Model : Shade/Label the MAIN who’s unit
Label ‘remaining’
or ‘remainder’ for unshaded part
Step 2b: ‘Unshaded part’ as
a whole (2nd
who denominator), divide into 2nd
who portion (using denominator) and the rest.
Step 3: Solve (with
uniform U)
(To make U of standard/same portion: U is
already ‘same size’)
¼ portion -> 3U
Total portion = 12u
32 + 5u = ¾ x 12u
4u = 32
u = 8
Total mobile phone sold =
32 + 8 x 8 = 96 mobile phones.
VIDEOS
<< Branching method can also be used>>
Branching Method
The branching method is useful for remainder-type of questions.
The branching method is useful for remainder-type of questions.
Example
In a basket, 2/5 of the fruits are apples. 2/3 of the remaining fruits are bananas. There are 20 fruits. How many bananas?
HOW TO DRAW and USE THE BRANCH DIAGRAM
Same Example
In a basket, 2/5 of the fruits are apples. 2/3 of the remaining fruits are bananas. There are 20 fruits. How many bananas?
In a basket, 2/5 of the fruits are apples. 2/3 of the remaining fruits are bananas. There are 20 fruits. How many bananas?
Step1: Draw the first branch with given fraction.
Step3: Continue Step1 write and Step2: draw for all the rest of the conditions.
Link and Solve
There are 20 fruits
There are 20 x 3/5 x 2/5 = 8 bananas
Additional question:
What is the fraction of the other fruits?
(a) locate others on diagram
(b) Compute Required fraction:
Multiply fractions along the branch to others (the green arrows)
others -> 3/5x 1/3 = 1/5
NOTE for Fraction Branch Diagram:
The SUM (adding the fractions) of the branches at the same level is 1.
~~~~ END ~~~~ :)
