Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Convert between fractions, decimals, and percentages.
• Solve problems involving finding a percentage of a quantity.
• Order fractions, decimals, and percentages.
• Apply these concepts to solve problems involving discounts.

Lesson summary

Fractions, decimals, and percentages are fundamental concepts in mathematics that are interconnected and essential for everyday life. This week, we will be focusing on strengthening your understanding of how these three concepts relate to each other and how to convert between them. Imagine you're at a local market in Johannesburg, bargaining for a discount on some fresh fruit. Knowing how to calculate percentages quickly can help you secure the best deal. Or, consider splitting a bill equally amongst friends after enjoying bunny chow in Durban; understanding fractions makes this task straightforward.

Lesson notes

Understanding the Relationship: Fractions, decimals, and percentages are different ways of representing the same value – a part of a whole.

Fraction: Represents a part of a whole. It is written as a/b, where 'a' is the numerator and 'b' is the denominator. The denominator represents the total number of equal parts, and the numerator represents the number of those parts we are considering. For example, 1/4 means one part out of four equal parts.

Decimal: Represents a part of a whole using a base-10 system. It is written with a decimal point separating the whole number part from the fractional part. For example, 0.25 means twenty-five hundredths, which is the same as one-quarter.

Percentage: Represents a part of a whole as a fraction of

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0. The word "percent" means "out of one hundred." It is written with a "%" symbol after the number. For example, 25% means 25 out of 100, which is the same as one-quarter or 0.

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5. Conversions: Fraction to Decimal: Divide the numerator by the denominator.

Example: Convert 3/8 to a decimal. 3 ÷ 8 = 0.375 Decimal to Fraction: Write the decimal as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places. Then, simplify the fraction to its simplest form.

Example: Convert 0.6 to a fraction. 0.6 = 6/10 = 3/5 Fraction to Percentage: Convert the fraction to a decimal (divide the numerator by the denominator). Then, multiply the decimal by 100 and add the "%" symbol.

Example: Convert 1/5 to a percentage. 1 ÷ 5 = 0.2. 0.2 × 100 = 20%.

Therefore, 1/5 = 20%.

Percentage to Fraction: Write the percentage as a fraction with a denominator of

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0. Then, simplify the fraction to its simplest form.

Example: Convert 75% to a fraction. 75/100 = 3/4 Decimal to Percentage: Multiply the decimal by 100 and add the "%" symbol.

Example: Convert 0.85 to a percentage. 0.85 × 100 = 85%.

Therefore, 0.85 = 85%.

Percentage to Decimal: Divide the percentage by

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0. Example: Convert 12% to a decimal. 12 ÷ 100 = 0.12 Finding a Percentage of a Quantity: To find a percentage of a quantity, convert the percentage to a decimal or a fraction and then multiply it by the quantity.

Example: Find 20% of

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0. Method 1: Convert 20% to a decimal: 20 ÷ 100 = 0.

2. Then, multiply: 0.2 × 150 =

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0. Method 2: Convert 20% to a fraction: 20/100 = 1/

5. Then, multiply: (1/5) × 150 =

3

0. Therefore, 20% of 150 is

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0. Ordering Fractions, Decimals, and Percentages: To order fractions, decimals, and percentages, first convert them all to the same form (either all fractions, all decimals, or all percentages). Then, compare the values.

Example: Order the following from smallest to largest: 1/2, 0.6, 40%.

Convert all to decimals: 1/2 = 0.5, 0.6 = 0.6, 40% = 0.

4. Ordering from smallest to largest: 0.4, 0.5, 0.

6. Therefore, the original values ordered from smallest to largest are: 40%, 1/2, 0.

6. Guided Practice (With Solutions)

Question 1: Convert 3/5 to a decimal and a percentage.

Solution: To convert 3/5 to a decimal, divide 3 by 5: 3 ÷ 5 = 0.

6. To convert 0.6 to a percentage, multiply by 100: 0.6 × 100 = 60%.

Therefore, 3/5 = 0.6 = 60%.

Commentary:* This question directly applies the fundamental conversion rules between fractions, decimals and percentages. Remember to perform the division accurately for the fraction to decimal conversion.

Question 2: A shop in Cape Town is having a 25% off sale on all T-shirts. If a T-shirt originally costs R80, what is the discount amount?

Solution: Convert 25% to a decimal: 25 ÷ 100 = 0.

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5. Multiply the original price by the decimal: 0.25 × R80 = R

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0. Therefore, the discount amount is R

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0. Commentary: This question applies percentage concepts to a real-life scenario of discounts. Make sure to understand that the discount is a part of the original price.

Question 3: Arrange the following in ascending order: 0.7, 65%, 4/5 Solution: Convert all to decimals: 7 remains 0.7 65% = 65/100 = 0.65 4/5 = 4 ÷ 5 = 0.8 Ascending order means smallest to largest. So, 0.65 < 0.7 < 0.8 Therefore, the original order is 65%, 0.7, 4/5

Commentary:* This question tests the ability to compare and order values expressed in different formats. Converting to a common format (decimals in this case) simplifies the comparison.

Question 4: What is 15% of 200?

Solution: Convert 15% to a decimal: 15 ÷ 100 = 0.

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5. Multiply the decimal by 200: 0.15 200 = 30 Therefore, 15% of 200 is

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0. Commentary:* This is another application of finding a percentage of a whole. It is important to be careful in converting the percentage into the decimal form correctly. Independent Practice (Questions Only) Convert 7/10 to a decimal and a percentage. Convert 0.35 to a fraction and a percentage. Convert 80% to a fraction and a decimal. What is 30% of 250? A pair of shoes in a shop costs R

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0. There is a sale of 15% off. What is the sale price? Arrange the following from largest to smallest: 0.2, 1/8, 15%. Express 1/3 as a decimal and percentage (round the percentage to two decimal places). What percentage of 60 is 12?