EVERYDAY ARITHMETIC 2
LEARNING OBJECTIVES:
By the end of the lesson, students will be able to:
(i) calculate problems on percentages.
(ii) solve problems involving fractions
WHAT IS A FRACTION?
A fraction is a number that represents a part of a whole or a part of a group.
It is written in the form:
\frac{a}{b}
where:
-
a (numerator) shows the number of parts taken
-
b (denominator) shows the total number of equal parts
Example:
\frac{3}{4} means 3 parts out of 4 equal parts.
Types of Fractions
1. Proper Fraction
A fraction in which the numerator is less than the denominator.
Examples:
\frac{2}{5}, \frac{3}{8}, \frac{7}{10}
2. Improper Fraction
A fraction in which the numerator is greater than or equal to the denominator.
Examples:
\frac{7}{4}, \frac{9}{5}, \frac{6}{6}
3. Mixed Fraction (Mixed Number)
A number made up of a whole number and a proper fraction.
Examples:
2\frac{1}{3}, 4\frac{2}{5}, 1\frac{3}{4}
PERCENTAGES
Percentage means “per hundred” and is used to express a number as a fraction of 100.
The symbol for percentage is %.
Formula
Percentage = PartWhole×100%\text{Percentage}
Example
If a student scores 45 marks out of 60:
45/60×100%=75%
Answer: The student scored 75%.
Percentage Increase
Percentage Increase shows how much a quantity has increased compared to its original value.
Formula
Percentage Increase = Increase/Original Value×100%
Where:
Increase = New Value − Original Value
Example
The price of a book increased from ₦2,000 to ₦2,500.
Increase = ₦2,500 − ₦2,000 = ₦500
500/2000×100%=25%
Answer: The price increased by 25%.
Percentage Decrease
Percentage Decrease shows how much a quantity has reduced compared to its original value.
Formula
Percentage Decrease = Decrease/Original Value×100%
Where:
Decrease = Original Value − New Value
Example
A shirt was reduced in price from ₦4,000 to ₦3,200.
Decrease = ₦4,000 − ₦3,200 = ₦800
800/4000×100%=20%
Answer: The price decreased by 20%.
ACTIVITY
Answer the following questions on Fractions, Percentage increase and Percentage decrease:
A. FRACTIONS
(1) Simplify <span class="katex"><span class="katex-mathml">12/18 (2) Convert <span class="katex"><span class="katex-mathml">3/5 to a decimal. (3) Convert </span><span class="katex" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif"><span class="katex-mathml">7/4 to a mixed number (4) Add 2/3+1/6 (5) Subtract </span><span class="katex" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif"><span class="katex-mathml">5/8−1/4 (6) Multiply </span><span class="katex" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif"><span class="katex-mathml">3/4×2/5 (7) Divide </span><span class="katex" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif"><span class="katex-mathml">6/7÷3/7 (8) Find </span><span class="katex" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif"><span class="katex-mathml">2/3 of 24 (9) Arrange in ascending order: </span><span class="katex" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif"><span class="katex-mathml">3/4, 2/5, 5/8 (10) Express </span><span class="katex" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif"><span class="katex-mathml">9/20 as a percentage.
B. PERCENTAGE INCREASE
(11) A bag costs ₦2,000 and later increases to ₦2,500. Find the percentage increase.
(12) The population of a town increased from 4,000 to 4,800. Find the percentage increase.
(13) A student’s score increased from 60 to 75. Find the percentage increase.
(14) A shirt priced at ₦3,000 was increased to ₦3,600. Find the percentage increase.
(15) The length of a rope increased from 20 m to 25 m. Find the percentage increase.
(16) The price of rice increased from ₦18,000 to ₦21,600. Find the percentage increase.
(17) A company’s profit increased from ₦500,000 to ₦650,000. Find the percentage increase.
(18) The number of pupils in a class increased from 30 to 36. Find the percentage increase.
(19) A worker’s salary increased from ₦80,000 to ₦100,000. Find the percentage increase.
(20) The price of fuel increased from ₦650 to ₦780 per litre. Find the percentage increase.
C. PERCENTAGE DECREASE
(21) A phone priced at ₦120,000 was reduced to ₦96,000. Find the percentage decrease.
(22) The number of students reduced from 50 to 40. Find the percentage decrease.
(23) A bag of cement reduced in price from ₦9,000 to ₦7,200. Find the percentage decrease.
(24) A shirt was reduced from ₦4,000 to ₦3,000. Find the percentage decrease.
(25) The weight of a substance reduced from 80 kg to 60 kg. Find the percentage decrease.
(26) The price of a book reduced from ₦2,500 to ₦2,000. Find the percentage decrease.
(27) The population of a village reduced from 10,000 to 9,500. Find the percentage decrease.
(28) A worker’s salary reduced from ₦100,000 to ₦85,000. Find the percentage decrease.
(29) The distance travelled reduced from 200 km to 150 km. Find the percentage decrease.
(30) The price of a TV reduced from ₦250,000 to ₦200,000. Find the percentage decrease.
FINAL ANSWERS
(1) 2/3 (2) 0.6 (3) </span><span class="katex-mathml" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif">1\frac{3} (4) </span><span class="katex-mathml" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif">5/6 (5) </span><span class="katex-mathml" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif">3/8 (6) </span><span class="katex-mathml" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif">3/10
2 (8) 16 (9) </span><span class="katex-mathml" style="font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif">2/5, 5/8, 3/4 (10) 45% (11) 25%
(12) 20% (13) 25% (14) 20% (15) 25% (16) 20%
(17) 30% (18) 20% (19) 25% (20) 20% (21) 20% (22) 20% (23) 20% (24) 25% (25) 25% (26) 20%
(27) 5% (28) 15% (29) 25% (30) 20%