UWS 700137 Mathematical Patterns and Relationships Class Test V3

This document provides detailed solutions to a mathematics class test covering a range of topics including fractions, decimals, percentages, and their conversions. The solutions include simplifying fractions, identifying proper and improper fractions, finding equivalent fractions, and converting between mixed and improper fractions. The test also assesses the ability to perform arithmetic operations with fractions and solve related word problems involving topics like salary calculations, time zone conversions, and calculating discounts, GST, and commissions. Furthermore, the solutions provide answers to questions on measurements and the concept of leap years. The solutions are presented in a clear and concise manner, demonstrating each step of the calculation and providing the final answers in their simplest forms.

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Question 1(13

Marks
a) State the fraction for each shaded diagram below. [2]
(i) (ii)
b) Put each fraction below in the correct column: [2]
108 ,19 , 157 , 5511 , 491 , 23 1 , 56
51 19 399 18 84 28 316
Proper Fraction Improper Fraction Equal to 1 Mixed number
c) Find an equivalent fraction for the following. [2]
3
=
7 42
8 96
=
5
d) Simplify the following fractions. [2]
= 10/13 = 77/105
e) Convert the following mixed numbers to improper fractions. [2]
7 = 15 =

© UWS and UWS Enterprises Pty Ltd 2021.1 700137 Mathematical Patterns and Relationships Class Test 2 V3 Page 1 of 7

f) Complete the following table, expressing your answers in its simplest forms.
(0.5 mark each) [3]
Common Fraction
(in its simplest form)
Decimal Fraction Percentage
88/100 0.88 88%
56/100
0.56
56%
0.52 52%
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Marks
Question 2(12
a) Evaluate the following, giving your answers in simplest form. (2 marks each) [8]
(i) +7
= 389/684
(ii) 9 +4
=516/4324
=129/1081
(iii) −
=3/30
=1/10
(iv)
=
-
93/4000
5 −2
b) Last fortnight, of Tim’s salary was spent on taxes. Also of his salary was used on
bills. How much savings did Tim gain, assuming the remainder was on
savings? [2]
Let total salary be x.
x- (3x/10 + 19x/50)
16/50 = 8/25
c) Loraine’s resides in Adelaide, Australia and her son Dermot lives in London, UK.
Adelaide is 8 hours ahead of London. Loraine decides to have a Zoom meeting
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Marks
with Dermot on Friday 7:13am Adelaide time. Explain how Dermot should figure out what
London time will be then. [2]Question 3 (12 marks)
Answer: 10.43 pm in London and 7.13 am in Adelaide will be the proper time of meeting.
a) Evaluate the following, giving your answers in simplest form. (2 marks each) [8]
(i)  (ii) 4 
(iii)  (iv) ÷6
b) A Zoom class meeting had 28 students present.
(i) If of the students were female, how many females were there? [1]
10 females.
(ii) How many males were in the Zoom class meeting? [1]
18 males
c) A large eight kilogram bucket of fried chicken was shared at a birthday party. If this was
equally shared with kilograms portions each. How many portions can
be obtained? Show all working out. [2] Question 4(13
a) Complete the following
Page 4 of 7

Marks
(i) 0.0981 km = ____98.1________ m [1]
(ii) 6752m2 = ______0.006752________ km2 [1]
b) A tennis racquet was originally marked at $315. If Silvia received a 31% discount,
how much did she pay? [2]
$217.35
c) Adriana purchased a mid-range smartphone for $495. GST (Good and services tax) is
mandatory for consumers products in Australia.
(i) If Adriana’s purchase did not include GST, how much GST must be added? [1]
10% GST must be added in Australia.
This is $49.5.
(ii) If Adriana’s purchase on the flip side did include GST, calculate the
smartphone cost excluding GST? [2]
The cost excluding GST is 445.5
Page 5 of 7

d) Stuart is a sales employee at the electronics store Harvey Norman. He is paid on a
monthly basis and earns 12% commission of the total sales, on top of his monthly salary.
(i) If he sold electrical goods worth $52,500 last month, how much commission
would Stuart have earned? [2]
The commission is $6,300.
(ii) If Stuart’s monthly salary is $4300, how much would he have earned last
month including commission? [1]
= $4,300 + $6,300 = $10,600
e) Within the solar system, it takes three hundred and sixty-five and twenty-five hundredth
days for Earth to make one revolution around the sun. A calendar year has 365 days and
a leap year (every 4 years) with 366 days.
(i) After four years, calculate how many days it takes for Earth to make one
revolution around the sun? [2]
1461 days.
(ii) Hence using part (i) or otherwise, explain why a leap year has 366 days? [1]
This is observed that the Earth takes 365.25 days to orbit the sun but after every 4 years the
month of February has 29 days instead of 28. So, there are 366 days in the same year which
is called as Leap Year. The earth completed the complete one revolution around Sun in 365
days and 6 hours. So after 4 years, the 6 hours is added 4 times to become 24 hours which is
an addition of complete 1 day.
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