Assignment 5: 80 marks
Elective to Assignment Two
Contributes 20% to final pass mark
Unique Number:
215087
Student:
68593503
Due date: 4 October 2023
Part 1
1.
2.
3.
4.
5.
B
B
C
A
C
Part 2
1.
A. Divided into 3 Parts
B.
2.
3.
a.
1.
2.
3.
4.
5.
½
5/8
4/4
2/6
3/7
B
i)
4/6 > 1/2
L. 5/5 > 1/2
4.
1. Proper Fraction:
A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the
bottom number).
It represents a part of a whole that is less than one whole.
Proper fractions are typically used when you want to represent a part of something without exceeding the
whole.
Example: 3/4
In the fraction 3/4, the numerator (3) is less than the denominator (4).
It represents three parts out of a total of four equal parts, which can be visualized as three out of four slices
of a pizza.
Mixed Fraction:
2. A mixed fraction is a combination of a whole number and a proper fraction.
It is often used to represent quantities that include both whole parts and fractional parts.
Example: 2 1/3
In the mixed fraction 2 1/3, "2" is the whole number, and "1/3" is the proper fraction.
It represents two whole units and one-third of another unit, such as 2 whole apples and 1/3 of another apple.
Common Fraction:
3. A common fraction is a fraction that is not expressed as a decimal or a percentage.
It is a general term for fractions used in everyday mathematics.
Example: 5/8
The fraction 5/8 is a common fraction.
It represents five parts out of eight equal parts, which could be used, for example, to describe the portion of
a cake eaten
5.
Five and a Third:
The correct representation of "five and a third" as a mixed fraction is 5 1/3.
This means 5 whole units and 1/3 of another unit.
Sixteen Thirds:
The correct representation of "16 thirds" as a fraction is 16/3.
This means 16 parts out of 3 equal parts.
6.
a. If 12 counters represent one-third of a set, you can find the size of the set by multiplying 12 by 3 (the
reciprocal of 1/3, which is 3/1).
Set Size = 12 * 3 = 36
So, the set has 36 counters in total.
b. If 12 counters are three-thirds (or the whole) of a set, it means the set consists of those 12 counters.
So, the full set has 12 counters.
c. If nine counters represent five-sixths of a set, you can find the size of the set by dividing 9 by 5/6, which is
equivalent to multiplying by its reciprocal (6/5).
Set Size = 9 / (5/6) = 9 * (6/5) = 54/5
So, there are 54/5 counters in one set. This can be simplified further:
54/5 = 10 remainder 4/5
So, there are 10 sets of 5 counters each, plus an additional 4/5 of a set. In other words, the set has 10
counters, and there are 4/5 of a counter left.
d. If 18 counters represent one-half of a whole set, you can find the number of counters in a whole set by
multiplying 18 by 2 (the reciprocal of 1/2, which is 2/1).
Set Size = 18 * 2 = 36
So, there are 36 counters in a whole set.
PART 3
Answer the following with true or false. (2x5=10)
1. A partition is something that separates or divides a whole into equal parts.
False
2. the relationship between non interacting partitions and the number of parts in a second is
there non intersecting partitions in the circle can be used to represent and not determine
fractions.
True
3. using manipulatives for fractions operations such as addition, subtraction, multiplication
in division, can help learners with procedural understanding of fractions which are often
considered challenging.
True
4. Various geometric figures like triangles and squares can be used to representing illustrate
the differences between fractions
True
5. A cube it's a special kind of a Polygon.
False
Part 4
1.
2. Use the symbols ˃; ˂, ≈ or = to make the following true.
A. <
B. <
C. =
5. 3/10
7. 1/3 x 18 = (1/3) x 18 = 18/3
=6
8.
9,
PART 5
1.
(3/4) ÷ 2
Multiply by the reciprocal of the divisor (2), which is 1/2:
(3/4) x (1/2)
Multiply the numerators and denominators:
(3 x 1) / (4 x 2) = 3/8
So, each of Shade's two friends will get 3/8 of the pizza.
2 Activity 4.2
a. The GCD of 3 and 12 is 3.
Divide both numbers by the GCD (3):
3÷3=1
12 ÷ 3 = 4
b. GCD of 90 and 30:
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The GCD of 90 and 30 is 30.
Divide both numbers by the GCD (30):
90 ÷ 30 = 3
30 ÷ 30 = 1
E. Convert 30 mm to centimetres by dividing by 10:
30 mm ÷ 10 = 3 cm
The ratio is 6 cm to 3 cm. To simplify it further, divide both parts by their greatest common
divisor, which is 3:
(6 cm ÷ 3): (3 cm ÷ 3) = 2: 1
(7
2. Activity 4.4
(2)
The perimeter of the triangle is given as 72 cm. The perimeter of a triangle is the sum of its side
lengths. equation based on the given ratios:
3x + 4x + 5x = 72
Combine the like terms:
12x = 72
divide both sides by 12 to solve for x:
x = 72 / 12
x=6
with value of x, Is left to find the lengths of the sides:
Shortest side: 3x = 3 * 6 = 18 cm
Middle side: 4x = 4 * 6 = 24 cm
Longest side: 5x = 5 * 6 = 30 cm
4. Activity 4.4 (3)
i)
Bobo's earnings = 5x = 5 * 10 = R50
Thabo's earnings = 9x = 9 * 10 = R90
Thabo's earnings - Bobo's earnings = R90 - R50 = R40
ii)
n the new split, the boys decide to divide their pay in the ratio of 3:4:5, which sums up to 3 + 4
+ 5 = 12 parts. To find out how much each person received in the new split, divide the total
payment (R240) by the sum of the parts (12):
calculate Bobo's new share:
Bobo's new share = (3/12) * 240 = R60
To find out how much more Bobo makes in this new split compared to part (i), you can
subtract Bobo's initial share from his new share:
Bobo's new share - Bobo's initial share = R60 - R50 = R10
5. Activity 4.12 (i) and (iv)
i)
2/5:
Simplify 2/5: divide the numerator and denominator by their greatest common divisor, 1.
So, 2/5 remains 2/5 in its simplest form.
4/10:
To simplify 4/10, divide the numerator and denominator by their greatest common divisor, which
is 2.
4÷2=2
10 ÷ 2 = 5
So, 4/10 simplifies to 2/5.
Since both ratios simplify to 2/5, they are equivalent. Therefore, the pair of ratios 2/5 and 4/10
are indeed proportions.
iv)
To determine whether the pair of ratios 3/4 and 10/14 are in proportion, we can cross-multiply
and see if the products are equal:
Cross-multiply:
(3 * 14) and (10 * 4)
Calculate the products:
42 and 40
The products, 42 and 40, are not equal.
Therefore, the pair of ratios 3/4 and 10/14 are not in proportion because the cross-products are
not equal. In a proportion, the cross-products should be equal.
STUDENT DECLARATION OF ACADEMIC HONESTY
DEPARTMENT OF MATHEMATICS EDUCATION
COLLEGE OF EDUCATION UNIVERSITY OF SOUTH AFRICA
The Department of Mathematics Education places specific emphasis on integrity and ethical
behaviour with regard to the preparation of written work submitted for academic assessment
Although your lecturers can provide you with information about referencing techniques and
guidelines on how to avoid plagiarism, you also have a responsibility to fulfil in this regard.
Should you at any time feel unsure about the requirements, you must consult your lecturer before
you submit an assignment.
You will be guilty of plagiarism when you extract information from a book, an article, a web page
or a fellow student’s work and submit it as your own work, without acknowledging the source. If
you commit plagiarism, you are stealing someone else’s property. You may not use another
student’s work. Nor may you allow anyone to copy or use your work with the intention of
submitting it as his/her work.
Students who are guilty of plagiarism will forfeit all credit for the work in question. Plagiarism is a
serious violation of Unisa’s regulations and may lead to expulsion.
The declaration of academic honesty must accompany all written assignments.
I (full names): _Nathi Booi___
student number: 68593503_
module: __MTE1502
declare that
1. I understand what plagiarism entails and am aware of Unisa’s policy in this regard
2. this assignment is my own, original work
3. in instances where I used someone else’s work, whether a printed source, an internet source or
any other source, I provided the proper acknowledgement; I also included a complete reference
list
3. I did not use the work of another current student or previous student to submit as my work
4. I did not allow and will not allow anyone to copy my work with the intention of submitting it as
his/her work
Signature: _Nathi Booi Date: __03/ October 2023