Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Convert between fractions, decimals, and percentages.
• Find a percentage of a quantity.
• Increase or decrease a quantity by a percentage.
• Express one quantity as a percentage of another.
• Solve real-world problems using these concepts.

Lesson summary

Fractions, decimals, and percentages are fundamental mathematical concepts that are interconnected and essential for understanding and navigating everyday life in South Africa. From calculating discounts at Shoprite or Pick n Pay, understanding loan interest rates for buying a house in Soweto, to interpreting statistics about unemployment rates in South Africa, these skills are invaluable. They allow us to compare quantities, make informed financial decisions, and critically analyse data presented in various forms. This week, we will focus on solidifying our understanding of these concepts and exploring the relationships between them.

Lesson notes

Fractions: A fraction represents a part of a whole. It consists of a numerator (the number of parts we have) and a denominator (the total number of equal parts the whole is divided into). For example, 3/4 represents 3 parts out of 4 equal parts. A proper fraction has a numerator smaller than the denominator (e.g., 2/5), while an improper fraction has a numerator greater than or equal to the denominator (e.g., 7/3). A mixed number consists of a whole number and a proper fraction (e.g., 2 1/3).

Decimals: A decimal is another way of representing a fraction, where the denominator is a power of 10 (e.g., 10, 100, 1000). Decimal numbers are written using a decimal point to separate the whole number part from the fractional part. For example, 0.75 represents 75/100, which is the same as 3/

4. The position of a digit after the decimal point determines its value (tenths, hundredths, thousandths, etc.).

Percentages: A percentage is a way of expressing a number as a fraction of

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0. The word "percent" means "out of one hundred." The symbol for percent is %. For example, 60% means 60 out of 100, or 60/

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0. Converting Between Fractions, Decimals, and Percentages: Fraction to Decimal: Divide the numerator by the denominator. For example, 1/4 = 1 ÷ 4 = 0.25 Decimal to Fraction: Write the decimal as a fraction with a denominator that is a power of

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0. Simplify the fraction if possible. For example, 0.6 = 6/10 = 3/5 Fraction to Percentage: Convert the fraction to a decimal by dividing the numerator by the denominator, then multiply by

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0. For example, 3/5 = 0.6 = 0.6 x 100 = 60% Percentage to Fraction: Write the percentage as a fraction with a denominator of

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0. Simplify the fraction if possible. For example, 75% = 75/100 = 3/4 Decimal to Percentage: Multiply the decimal by

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0. For example, 0.85 = 0.85 x 100 = 85% Percentage to Decimal: Divide the percentage by

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0. For example, 40% = 40/100 = 0.4 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 by the quantity.

Example 1: What is 25% of 80 Rand?

Method 1 (Decimal): 25% = 0.25. 0.25 x 80 = 20 Rand Method 2 (Fraction): 25% = 25/100 = 1/4. (1/4) x 80 = 20 Rand Increasing or Decreasing a Quantity by a Given Percentage: Increase: Calculate the percentage increase and add it to the original quantity.

Decrease: Calculate the percentage decrease and subtract it from the original quantity.

Example 2: Increase 150 by 20%. 20% of 150 = (20/100) x 150 = 30 Increased value = 150 + 30 = 180 Example 3: Decrease 200 by 15%. 15% of 200 = (15/100) x 200 = 30 Decreased value = 200 - 30 = 170 Expressing One Quantity as a Percentage of Another: Divide the first quantity by the second quantity and multiply by

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0. Example 4: What percentage is 12 of 40? (12/40) x 100 = 0.3 x 100 = 30% Guided Practice (With Solutions)

Question 1: Convert 3/8 to a decimal and a percentage.

Solution: Decimal: 3 ÷ 8 = 0.375 Percentage: 0.375 x 100 = 37.5%

Commentary: We first divided the numerator by the denominator to get the decimal. Then we multiplied the decimal by 100 to get the percentage.

Question 2: What is 30% of 120 chickens?

Solution: 30% = 30/100 = 0.3 0.3 x 120 = 36 chickens

Commentary: Here, we converted the percentage into a decimal. Multiplying the decimal with the number of chickens gives us the required answer.

Question 3: A shop sells a soccer ball for R

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0. They offer a discount of 15%. What is the sale price of the soccer ball?

Solution: 15% of R150 = (15/100) x 150 = R22.50 Sale price = R150 - R22.50 = R127.50

Commentary: We calculated the discount amount first by finding 15% of the original price. Then we subtracted the discount from the original price to get the sale price.

Question 4: In a class of 40 learners, 28 learners passed their Mathematics test. What percentage of learners passed the test?

Solution: (28/40) x 100 = 0.7 x 100 = 70%

Commentary: Divide the number of learners who passed by the total number of learners, then multiply by 100 to express the result as a percentage.

Question 5: Increase 250 kg of mielies by 8%.

Solution: 8% of 250 = (8/100) x 250 = 20 New amount = 250 + 20 = 270 kg

Commentary: We first calculate 8% of 250 kg. Adding that amount to the original amount will give us the increased amount. Independent Practice (Questions Only)

Question 1: Convert 7/20 to a decimal and a percentage.

Question 2: What is 65% of 300 sheep?

Question 3: A store is selling a television for R

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0. They offer a discount of 20%. What is the sale price of the television?

Question 4: Express 18 out of 25 as a percentage.

Question 5: Decrease 400 litres of water by 35%.

Question 6: What is 12.5% of 160 apples?

Question 7: Convert 0.45 to a fraction in its simplest form.

Question 8: Increase R650 by 12%.

Question 9: In a survey, 72 out of 200 people preferred pap to rice. What percentage of people preferred pap?

Question 10: What is 150% of 80?