Numbers, Fractions, Decimals, and Percents

The Joy of the Teacher is the Success of the Students. – Samuel Chukwuemeka

Welcome to Our Site

I greet you this day,
These are the solutions to the NSSCO past questions on Numbers, Fractions, Decimals, and Percents.
The TI-84 Plus CE shall be used for applicable questions.
If time permits and there is sufficient interest, video solutions may be provided. Please subscribe to the YouTube channel to be notified of upcoming livestreams. You are welcome to ask questions during the video livestreams.
If you find these resources valuable and if any of these resources were helpful in your passing the Mathematics exams of NSSCO, please consider making a donation:

Cash App: $ExamsSuccess or
cash.app/ExamsSuccess

PayPal: @ExamsSuccess or
PayPal.me/ExamsSuccess

Venmo: @ExamsSuccess or
Venmo.com/u/ExamsSuccess

Your donation is appreciated.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome.
Feel free to contact me. Please be positive in your message.
I wish you the best.
Thank you.

Percent Applications

$ \underline{\text{Change and Percent of Change}} \\[3ex] (1.)\:\: change = new - initial \\[5ex] (2.)\:\: \%\;\;of\;\;change = \dfrac{change}{initial} * 100 \\[5ex] (3.)\;\; \text{If A is p% more than B, then A = (100 + p)% of B} \\[3ex] (4.)\;\; \text{If A is p% less than B, then A = (100 – p)% of B} \\[5ex] \underline{\text{Percent:Proportion}} \\[3ex] (5.)\;\; \dfrac{is}{of} = \dfrac{\%}{100} \\[5ex] (6.)\;\;\underline{\text{Percent:Equation}} \\[3ex] is \rightarrow equal\;\;to \\[3ex] of\;\; \rightarrow multiply \\[3ex] what \;\; \rightarrow variable \\[5ex] \underline{\text{Wholesale and Retail}} \\[3ex] (7.)\:\: \text{Sale Price } = \text{Initial Price } - \text{Discount} \\[5ex] (8.)\:\: \%\;Discount = \dfrac{Discount}{\text{Initial Price}} * 100 \\[5ex] (9.)\;\; \text{Profit } = \text{Selling Price } - \text{Cost Price} \\[3ex] (10.)\;\; \%\;Profit = \dfrac{Profit}{\text{Cost Price}} * 100 \\[5ex] (11.)\;\; \text{Loss } = \text{Cost Price } - \text{Selling Price} \\[3ex] (12.)\;\; \%\;Loss = \dfrac{Loss}{\text{Cost Price}} * 100 $

(1.) Mwelezi has 456 cupcakes to distribute among the learners in her school.
Each learner receives a cupcake.
Junior primary learners get a $\dfrac{1}{3}$ of the cupcakes.
Senior primary learners get $\dfrac{3}{4}$ of the remaining cupcakes and secondary learners get the rest.
(a.) Work out
(i.) the number of junior primary learners.
(ii.) the number of cupcakes given to the secondary learners.

(b.) Express the answer to part (a.)(ii.) as a percentage of the total number of learners.

Because each learner gets a cupcake, this implies that the number of cupcakes given to each category is the number of learners in that category.
Also, the total number of cupcakes is the total number of learners.

Number of cupcakes = 456
(a.)(i.)
Number of junior primary learners
= Number of cupcakes given to junior primary learners
= $\dfrac{1}{3} * 456 = 152$ learners

Remaining cupcakes = 456 − 152 = 304 cupcakes

Number of cupcakes given to senior primary learners
= $\dfrac{3}{4} * 304 = 228$ cupcakes

Remaining cupcakes = 304 − 228 = 76 cupcakes

(ii.)
Number of cupcakes given to the secondary learners
= Remaining cupcakes
= 76 cupcakes.

(b.)
We can rephrase the question as:
What percent of the total number of learners is the number of cupcakes given to the secondary learners?
In other words, what percent of 456 is 76?

$ \underline{\text{Percent : Proportion}} \\[3ex] \dfrac{is}{of} = \dfrac{\%}{100} \\[5ex] \dfrac{76}{456} = \dfrac{what}{100} \\[5ex] what = \dfrac{76 * 100}{456} \\[5ex] what = 16.66666667 \\[3ex] what \approx 16.7\%\quad\dots\text{to 3 significant figures} $

(2.) Write down the place value of 9 in 348.593

The place value of 9 is: Nine-hundredth (hundredths place)

Number and Place Value
Number	Place Value
3	Three hundred (hundreds place)
4	Forty (tens place)
8	Eight (ones/units place)
$\bullet$	Decimal
5	Five-tenth (tenths place)
9	Nine-hundredth (hundredths place)
3	Three-thousandth (thousandths place)

(8.) Using a calculator, work out $\dfrac{4 \times (\sin 100^\circ) - 3}{5}$
Write down your answer correct to 2 decimal places.

$ \dfrac{4 \times (\sin 100^\circ) - 3}{5} \\[5ex] = \dfrac{4 \times 0.984807753 - 3}{5} \\[5ex] = \dfrac{3.939231012 - 3}{5} \\[5ex] = \dfrac{0.939231012}{5} \\[5ex] = 0.1878462024 \\[3ex] \approx 0.19\quad\dots\text{to 2 decimal places} $

Top