Percentages : Meaning and Conversion of percentages to decimals and fractions

SUBJECT: MATHEMATICS

CLASS: BASIC FIVE / PRIMARY 5

TERM : SECOND TERM

WEEK : WEEK 3

TOPIC : PERCENTAGES : CONVERTING TO DECIMALS AND FRACTIONS AND VICE VERSA

• What is percentage with examples
• What symbol is used to represent percentage
• Changing percentage to fractions and vice versa with examples
• Changing percentage to decimal and vice versa with examples
• Expressing a number as a percentage of other number

Importance

• Percentages are used in calculating discounts on sales of goods
• Percentages are used by banks to calculate interest rates like simple interest and compound interest
• Percentages are used by calculate the rate of interest in the country by Economics analysts
• Percentages are important in calculating and understanding the financial aspects of everyday life
• It helps to interpret monthly financial budgets

Learning Objectives :

Pupils should be able to

• Explain the meaning of percentage
• Calculate the ratio and percentage of numbers
• Solve questions related to real life problems on percentages
• Express a number as the percentage of other

Learning Activities :

• Pupils work in pairs. Work on hundred boxes drawn on a piece of cardboard and then shade out 10 out of the 100 boxes
• The process of percentage has been displayed which is 10%

Embedded Core Skills

• Critical thinking and problem solving skills
• Communication and Collaboration
• Student Leadership skills and Personal Development

Learning Resources

• Counting paper
• Percentage chart
• Sticky notes
• Flash cards
• Eraser
• Whiteboard or blackboard
• Markers or pens
• Calculator
• Rounding worksheets

Content

Percentages : Meaning and Conversion of percentages to decimals and fractions

A percentage is a way to express a number as a fraction of 100. It is often denoted using the symbol “%”. For example, 50% means 50/100, or one half.

Examples:

• 50% of 60 is 30 (50/100 * 60 = 30)
• 20% of $100 is $20 (20/100 * $100 = $20)
• 75% of the students passed the exam (75/100 of the students passed the exam)
• A stock went up by 12%, it’s new value is 112% of the old value

The symbol “%” is used to represent percentage. It is placed after a number to indicate that it is a percentage. For example, 50% means 50 out of 100, or one half.

How to convert percentages to decimals

To convert a percentage to a decimal, divide the percentage by 100. This is because a percentage is a way to express a number as a fraction of 100. For example:

• 50% is the same as 50/100, which can be simplified to 0.5 as a decimal
• 75% is the same as 75/100, which can be simplified to 0.75 as a decimal
• 12.5% is the same as 12.5/100, which can be simplified to 0.125 as a decimal

Examples:

• 50% to decimal: 50/100 = 0.5
• 75% to decimal: 75/100 = 0.75
• 12.5% to decimal: 12.5/100 = 0.125

You can also convert a percentage to a decimal by moving the decimal point two places to the left. For example:

• 50% = 50.0 = 0.50
• 75% = 75.0 = 0.75
• 12.5% = 12.5 = 0.125

In general, to convert a percentage to decimal, you can divide the percentage by 100 or move the decimal point two places to the left.

How to convert decimals to percentages

To convert a decimal to a percentage, multiply the decimal by 100. This is because a percentage is a way to express a number as a fraction of 100. For example:

• 0.5 (decimal) is the same as 50/100, which can be written as 50%
• 0.75 (decimal) is the same as 75/100, which can be written as 75%
• 0.125 (decimal) is the same as 12.5/100, which can be written as 12.5%

Examples:

1. 0.5 (decimal) to percentage: 0.5 * 100 = 50%
2. 0.75 (decimal) to percentage: 0.75 * 100 = 75%
3. 0.25 (decimal) to percentage: 0.25 * 100 = 25%
4. 0.125 (decimal) to percentage: 0.125 * 100 = 12.5%
5. 1 (decimal) to percentage: 1 * 100 = 100%

Another way to convert decimal to percentage is to move the decimal point two places to the right and add % sign.

In general, to convert a decimal to a percentage, you can multiply the decimal by 100 or move the decimal point two places to the right and add % sign.

How to convert percentages to fractions.

To convert a percentage to a fraction, divide the percentage by 100 and simplify the fraction. This is because a percentage is a way to express a number as a fraction of 100. For example:

• 50% is the same as 50/100, which can be simplified to 1/2 as a fraction
• 75% is the same as 75/100, which can be simplified to 3/4 as a fraction
• 12.5% is the same as 12.5/100, which can be simplified to 1/8 as a fraction

Examples:

1. 50% to fraction: 50/100 = 1/2
2. 75% to fraction: 75/100 = 3/4
3. 12.5% to fraction: 12.5/100 = 1/8
4. 25% to fraction: 25/100 = 1/4
5. 100% to fraction: 100/100 = 1

Note that in some cases, the resulting fraction might not be fully simplified.

In general, to convert a percentage to a fraction, divide the percentage by 100 and simplify the fraction.

How to convert fractions to percentages

To convert a fraction to a percentage, multiply the fraction by 100 and add the percentage sign (%). This is because a percentage is a way to express a number as a fraction of 100.

For example:

• 1/2 as a fraction is equivalent to 50/100 or 50% as a percentage
• 3/4 as a fraction is equivalent to 75/100 or 75% as a percentage
• 1/8 as a fraction is equivalent to 12.5/100 or 12.5% as a percentage

Examples:

1. 1/2 (fraction) to percentage: (1/2) * 100 = 50%
2. 3/4 (fraction) to percentage: (3/4) * 100 = 75%
3. 1/8 (fraction) to percentage: (1/8) * 100 = 12.5%
4. 2/3 (fraction) to percentage: (2/3) * 100 = 66.67%
5. 5/6 (fraction) to percentage: (5/6) * 100 = 83.33%
6. 1/4 (fraction) to percentage: (1/4) * 100 = 25%
7. 1 (fraction) to percentage: (1) * 100 = 100%

Note that in some cases, the resulting percentage might not be rounded off.

In general, to convert a fraction to a percentage, multiply the fraction by 100 and add the percentage sign (%).

How to express a number, unit of measurement, time measurement or quantity as a percentage of another.

A percentage can be used to express a number, unit of measurement, time measurement or quantity as a part of a whole. To express a number, unit of measurement, time measurement or quantity as a percentage of another, you can use the following formula:

(part/whole) x 100 = percentage

Examples:

1. A student scored 80 out of 100 on an exam. To express this as a percentage, we can use the formula: (80/100) x 100 = 80%. So the student scored 80% on the exam.
2. A company earned $50,000 out of $100,000 in revenue. To express this as a percentage, we can use the formula: (50000/100000) x 100 = 50%. So the company earned 50% of the revenue target.
3. A basketball player made 8 out of 10 free throws. To express this as a percentage, we can use the formula: (8/10) x 100 = 80%. So the basketball player made 80% of the free throws
4. A car traveled 150 miles out of 200 miles. To express this as a percentage, we can use the formula: (150/200) x 100 = 75%. So the car traveled 75% of the distance.
5. An employee worked 8 hours out of 10 hours. To express this as a percentage, we can use the formula: (8/10) x 100 = 80%. So the employee worked 80% of the working hours.
6. A shipment was delivered on time 8 out of 10 orders. To express this as a percentage, we can use the formula: (8/10) x 100 = 80%. So 80% of the orders were delivered on time.
7. A product was sold in 20 units out of 25 units. To express this as a percentage, we can use the formula: (20/25) x 100 = 80%. So 80% of the units of the product were sold.
8. A project was completed on time 8 out of 10 tasks. To express this as a percentage, we can use the formula: (8/10) x 100 = 80%. So 80% of the tasks in the project were completed on time.

Importance of percentages

Importance

• Percentages are used in calculating discounts on sales of goods
• Percentages are used by banks to calculate interest rates like simple interest and compound interest
• Percentages are used by calculate the rate of interest in the country by Economics analysts
• Percentages are important in calculating and understanding the financial aspects of everyday life
• It helps to interpret monthly financial budgets
• Percentages are used to determine the success rate of a project or task
• Percentages are used to measure the growth of a company or investment
• Percentages are used to calculate taxes, including sales tax and income tax
• Percentages are used to compare and evaluate different options, such as investment opportunities or loan options
• Percentages are used in polls and surveys to represent the opinions or preferences of a population
• Percentages are used to measure the performance of a sports team or individual player
• Percentages are used to calculate the grade point average for students
• Percentages are used to measure inflation and the cost of living
• Percentages are used in cooking recipes

More story problems on percentages

1. If the price of a shirt is $50 and it is on sale for 20% off, how much will it cost? (50 * 20/100 = $10, so the shirt will cost $40)
2. If a car gets 30 miles per gallon and you have traveled 150 miles, what percentage of the gas tank is left? (150/30 = 5, so the gas tank is 50% full)
3. If a company’s revenue is $1,000,000 and its expenses are $800,000, what is the profit margin? (1000000-800000 = 200000, 200000/1000000 = 0.2, so the profit margin is 20%)
4. If a test has 20 questions and a student answered 18 correctly, what is the student’s percentage score? (18/20 = 0.9, so the student’s score is 90%)
5. If a basket contains 8 apples and 2 are rotten, what percentage of the apples are rotten? (2/8 = 0.25, so 25% of the apples are rotten)
6. If a company’s stock price increases from $50 to $60, what is the percentage increase? (60-50 = 10, 10/50 = 0.2, so the stock price increased by 20%)
7. If a company’s sales are $500,000 and it wants to increase its sales by 10%, how much should the sales increase by? (500000*10/100 = 50000, so the sales should increase by $50,000)
8. If you invested $1000 and it grew to $1100 in a year, what is the percentage increase? (1100-1000 = 100, 100/1000 = 0.1, so the investment grew by 10%)
9. If a company’s profits are $100,000 and it wants to increase its profits by 20%, how much should the profits increase by? (100000*20/100 = 20000, so the profits should increase by $20,000)
10. If a pizza is divided into 8 slices and you have eaten 3 slices, what percentage of the pizza have you eaten? (3/8 = 0.375, so 37.5% of the pizza has been eaten)

Evaluation

1. What is the percentage of a number that is equivalent to 25/100? a) 25% b) 50% c) 75% d) 100%
2. If a company’s revenue is $1,000,000 and its expenses are $800,000, what is the profit margin? a) 20% b) 25% c) 30% d) 35%
3. If a test has 20 questions and a student answered 18 correctly, what is the student’s percentage score? a) 80% b) 85% c) 90% d) 95%
4. If a stock price increases from $50 to $60, what is the percentage increase? a) 10% b) 15% c) 20% d) 25%
5. If a company’s sales are $500,000 and it wants to increase its sales by 10%, how much should the sales increase by? a) $50,000 b) $60,000 c) $70,000 d) $80,000
6. To express a number, unit of measurement, time measurement or quantity as a percentage of another, we divide the part by the whole and multiply the result by: a) 50 b) 75 c) 100 d) 150
7. If a basket contains 8 apples and 2 are rotten, what percentage of the apples are rotten? a) 12.5% b) 25% c) 37.5% d) 50%
8. If a company’s profits are $100,000 and it wants to increase its profits by 20%, how much should the profits increase by? a) $20,000 b) $25,000 c) $30,000 d) $35,000
9. If you invested $1000 and it grew to $1100 in a year, what is the percentage increase? a) 5% b) 10% c) 15% d) 20%
10. If a pizza is divided into 8 slices and you have eaten 3 slices, what percentage of the pizza have you eaten? a) 37.5% b) 42.5% c) 47.5% d) 52.5%

Fill in the gaps

1. A number that is equivalent to 25/100 is __________.
2. If a company’s revenue is ₦1,000,000 and its expenses are ₦800,000, the profit margin is __________.
3. If a test has 20 questions and a student answered 18 correctly, the student’s percentage score is __________.
4. If a stock price increases from ₦50 to ₦60, the percentage increase is __________.
5. If a company’s sales are ₦500,000 and it wants to increase its sales by 10%, the sales should increase by __________.
6. To express a number, unit of measurement, time measurement or quantity as a percentage of another, we divide the part by the whole and multiply the result by __________.
7. If a basket contains 8 apples and 2 are rotten, the percentage of the apples that are rotten is __________.
8. If a company’s profits are ₦100,000 and it wants to increase its profits by 20%, the profits should increase by __________.
9. If you invested ₦1000 and it grew to ₦1100 in a year, the percentage increase is __________.
10. If a pizza is divided into 8 slices and you have eaten 3 slices, the percentage of the pizza that you have eaten is __________.

Lesson Presentation

Introduction:

• Begin the lesson by asking students if they have ever heard of the term “percentage” before.
• Write the word “percentage” on the board and ask students to give examples of when they have used or seen percentages before (e.g. discounts, grades, polls).

Direct Instruction:

• Define percentage as “a way of expressing a number as a fraction of 100”.
• Write the formula “part/whole x 100 = percentage” on the board and have students repeat it.
• Provide examples of how to convert fractions, decimals, and whole numbers to percentages and vice versa.
• Use real-life examples to show the importance of understanding percentages in everyday life (e.g. calculating discounts, interest rates, taxes).

Guided Practice:

• Provide students with worksheets that include problems for them to practice converting between fractions, decimals, and percentages.
• Allow students to work in pairs or small groups to complete the worksheets.
• Have students share their answers with the class and discuss any misconceptions or difficulties they had.

Independent Practice:

• Assign a project or homework that requires students to use percentages to solve real-life problems (e.g. calculating discounts at a store, determining the grade point average of a student).

Closure:

• Review the key concepts of the lesson with the students.
• Have students complete a quick quiz or exit slip to assess their understanding of the material.
• Remind students that understanding percentages is an important skill for everyday life and encourage them to continue practicing.