Numeracy 1 (MATI3006) Portfolio: Number Operations and Proportions

This portfolio provides solutions to numeracy problems involving number sentences, fractions, percentages, and proportions. It includes creating number sentences with multiple operations, comparing fractions, and applying percentage increase, decrease, and change in real-life scenarios. The portfolio also covers reverse percentages, direct and indirect proportions with real-world examples, and data analysis from tables and graphs. Desklib offers a range of solved assignments and past papers to aid students in their studies.

Section 1
Q1) Choose any number between 30 and 100. Can you create at least two different number sentences
that equal to this number? (for example : 75−(2+3)2=50∧2∗4+7+ 5× 7=50 ¿
You must use at least three separate operations.
i. 23 * 3 + 18 + 52*2 = 80
ii. 15 – 5*(5-2)2 + 30 + 5*22 + (8÷ 2¿2 *15 ÷ 4 = 80
iii. 25 * 2 + 5 *6 = 80
iv. 100 ÷ 2 + 7*22 = 80
v. 23 + 32 + 32 + 5 = 80
vi. (2 + 3)2 + 5 + 10 * 5 = 80
Q2) Choose any two fractions with different denominators (e.g
2
5 ∧3
7 ¿.Which one is larger? Show
your calculations, do not convert them as decimals or percentages.
3
8 and 2
3
L.C.M of 8 and 3
3 8
3 1 8
8 1 1
L.C.M = 3 *8 = 24
Multiply each fraction by the L.C.M
3
8∗24=9

2
3∗24=16
Choosing between 9 and 16, the value of 16 is
Larger; therefore the fraction 2
3 is larger than 3
8
(ii) Convert both fractions you have used above into decimal and percentages.
3
8 = 0.375
3
8 *100 = 37.5%
2
3 = 0.6667
2
3 * 100 = 66.67%
Q3
Provide one real life example for each of the following
>Percentage increase
>Percentage decrease
> Percentage change
Show step by step calculations for each of your examples (questions)
A)
% increase
The cost of a piece of land in the year 2014 was £300,000 but the cost of the piece of land in
2018 was £520,000, what is the percentage increase.
Solution
Determine the difference between the two costs to the find the amount it was hiked by
£520,000 - £300,000 = £220, 000
% increase = difference∈cost
initial cost ∗100

= £ 220,000
£ 300,000∗100 = 73.33%
% decrease
The cost of a piece of land in the year 2014 was £520,000 but the cost of the piece of land in
2018 was £300,000, what is the percentage decrease.
Solution
Determine the difference between the two costs to the find the amount it was reduced by
£520,000 - £300,000 = £220, 000
% Decrease = difference∈cost
initial cost ∗100
= £ 220,000
£ 520 ,000 ∗100 = 42.31%
% change
A pair of shoes went from £5 to £6, what is the percentage change?
Finding the amount it rise with = £6 - £5 = £1
Dividing the value by the initial cost = 1/5 = 0.2
Converting the value to percentage = 0.2 * 100 = 20%
The percentage change = 20% rise
B)
Give one real- world example (question) of reverse percentages and show your calculations to find the
answer?

A sales profit of 10% was added to the original selling price to make it £200
Solution
Convert it to decimal = 10/100 = 0.1
Adding 1 to the decimal
1 + 0.1 = 1.1
Divide the amount by the decimal
£220/1.1 = £200
The amount added was = £220 - £200 = £20
C) Give one real- world examples each (question) of Direct and Indirect Proportions and show your
calculations to find the answer?
Direct proportion
i) If 3 pen costs £1.50, how many pens can be bought by £9.00
Solution
The number of pens is directly proportion to the cost
3/1.5 = x/9
1.5x = 27
X = 18
18 pens
Indirect Proportions
ii) It takes 3 men 5 hours to dig a borehole, how long will it take 10 men to do the job if the rate
of working is same
Solution
The number of men is directly proportional to the time taken to do the job

Let x be time taken for 10 men to finish the job
3 * 5 = 10x
X = 1.5 hours
Section 4
Q4.1)
2015 2016 2017 Mean 2018 predicted
400 500 600 500 560
300 200 400 300 336
250 350 600 400 448
c) Range
Under 25 => 400 – 600
25 – 35 => 200 – 400
Over 35 => 250 – 600
d)
2015 2016 2017 2018
0
200
400
600
800
1000
1200
1400
1600
1800
over 35
25 - 35
Under 25
years
Studen counts

The total number of student per every count were dramatically increasing and dropping, the
highest value at under 25 years was 600 in 2017, while the highest value at 25 to 35 years was
400 in 2017 and the highest value at over 35 years was 600 in 2017.
e)
Total number enrolled in 2015 was 400
Let assume in 2014 the enrollment was x
Therefore increasing by 15% the value in 2014 to determine the value in 2015
1.15 * x = 400
X = 348 students were enrolled in 2014
f) 2016 the enrollment was 350 students
2017 the enrollment was 600 students
Difference = 600 – 350 = 250
% change = 250/350 * 100 = 71.43% increment
g) Let x be male students
Female = 100 + 20 = 120% =120/100
Female = 1.2x
Total = x + 1.2x = 200
2.2x = 200
X = 200/2.2
X = 91 male student
h) Total student under 25 = 2060
Total population in 2017 = 1600
Ratio = 2060: 1600
= 1: 0.777
Q4.2)
Graph 1

The number of students was gradually increasing from 2004 to 2012, but slightly dropped from
2012 to 2014, this happened for undergraduates’ ≤ 20 years
The number of students was gradually increasing from 2004 to 2009, but it highly increased from
2009 – 2010 and continued gradually for undergraduates with 21 - 24 years.
The number of students gradually decreased from 2004 to 2012 but further decreased from 2012
to 2014 for undergraduates with 40 years and over
The number of students gradually decreased from 2004 to 2012 but further decreased from 2012
to 2014 for undergraduate with 30 - 39 years
The number of students gradually decreased from 2004 to 2012 but further decreased from 2012
to 2014 for undergraduate with 25 - 29 years
Graph 2
The number post graduate student within the years 21 – 24 year dramatically increased from
2004 to 2008, but highly increased from 2008 to 2010, the number again dramatically increased
from 2010 – 2012 but dropped from 2012 to 2013, then rose from 2013 to 2014
The number post graduate student within the years 30 – 39 year dramatically decreased from
2004 to 2008, then drastically increased from 2008 to 2011, then the number dropped from 2012
to 2013, then rose from 2013 to 2014
The number post graduate student within the years 25 – 29 year dramatically increased from
2004 to 2011, then dropped from 2011 to 2013 and rose from 2013 to 2014.
The number post graduate student within the 40 years and over there were gradual increase
from 2004 to 2007, then the number dropped from 2007 to 2008, then rose from 2008 to 2011,
the number then decreased from 2011 to 2013, and finally the number rose from 2013 to 2014
Q4.3)
Time (T) in
minutes
Mid-point
x
Frequency Cumulative
frequency
Fx
5 ≤ t <10 7.5 9 9 67.5
10 ≤ t < 15 12.5 5 14 62.5
15 ≤ t < 20 17.5 6 20 105
∑ f =20 235

b) Average = ∑ fx
∑ f =¿235/20 = 11.75
Median = L +
n
2 −B
G ∗W
= 10 +
20
2 −9
5 ∗5
= 11