Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Convert fluently between fractions, decimals, and percentages.
• Solve problems involving finding a percentage of a quantity.
• Express one quantity as a percentage of another.
• Apply these concepts to solve real-life problems.

Lesson summary

Fractions, decimals, and percentages are fundamental mathematical concepts that are heavily intertwined and used in our daily lives. This week, we'll solidify our understanding of these concepts and explore how they relate to each other. Think about shopping at a grocery store (discount percentages), sharing a pizza with friends (fractions of the pizza), or calculating your test scores (decimals representing your percentage). These concepts are not just abstract ideas; they're tools that help us understand and navigate the world around us. Understanding these concepts will enable you to manage your pocket money, understand sales offers, and interpret data effectively.

Lesson notes

2.1 Fractions: A fraction represents a part of a whole. It is written in the form a/b, where 'a' is the numerator (the number of parts we have) and 'b' is the denominator (the total number of equal parts the whole is divided into).

Example: 3/4 means we have 3 parts out of a total of 4 equal parts. 2.2 Decimals: A decimal is another way to represent a part of a whole, using a base-10 number system. The digits to the right of the decimal point represent fractions with denominators that are powers of 10 (tenths, hundredths, thousandths, etc.).

Example: 0.75 means 7 tenths and 5 hundredths, which is equivalent to 75/100. 2.3 Percentages: A percentage means "out of one hundred." It is a way of expressing a number as a fraction of

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0. The symbol for percentage is %.

Example: 50% means 50 out of 100, or 50/100. 2.4 Converting Between Fractions, Decimals, and Percentages: Fraction to Decimal: Divide the numerator by the denominator.

Example:* Convert 1/4 to a decimal. 1 ÷ 4 = 0.25 Decimal to Percentage: Multiply the decimal by

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0. Example:* Convert 0.25 to a percentage. 0.25 x 100 = 25% Percentage to Decimal: Divide the percentage by

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0. Example:* Convert 25% to a decimal. 25 ÷ 100 = 0.25 Percentage to Fraction: Write the percentage as a fraction with a denominator of 100, then simplify if possible.

Example:* Convert 75% to a fraction. 75/100 = 3/4 (simplified)

Fraction to Percentage: Convert the fraction to a decimal (by dividing), and then multiply the decimal by

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0. Alternatively, try to make the denominator

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0. Example:* Convert 2/5 to a percentage. 2 ÷ 5 = 0.4. 0.4 x 100 = 40%. Alternatively, 2/5 = 40/100 = 40% 2.5 Finding a Percentage of a Quantity: To find a percentage of a quantity, convert the percentage to a decimal or fraction and then multiply by the quantity.

Example: Find 20% of 150 ZA

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

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0. Then, 0.20 x 150 = 30 ZA

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

5. Then, (1/5) x 150 = 30 ZAR. 2.6 Expressing One Quantity as a Percentage of Another: To express one quantity as a percentage of another, divide the first quantity by the second quantity and then multiply by

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0. Example: What percentage is 15 of 60? 15 ÷ 60 = 0.

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5. Then, 0.25 x 100 = 25%.

Therefore, 15 is 25% of 60. 2.7 Worked Examples (South African Context): Example 1: A shop in Durban is having a sale offering 15% off all items. If a T-shirt originally costs R80, what is the discount amount and the sale price?

Discount amount: 15% of R80 = (15/100) 80 = R

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2. Sale price: R80 - R12 = R

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8. Example 2: Sarah scored 35 out of 50 on a Mathematics test. What percentage did she score?

Percentage score: (35/50) 100 = 70%.

Example 3: A farmer in Limpopo has a field that is 2/5 planted with maize. What percentage of the field is planted with maize?

Percentage planted with maize: (2/5) 100 = 40%. 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 divided the numerator by the denominator to get the decimal. Then, we multiplied the decimal by 100 to get the percentage.

Question 2: Find 30% of

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0. Solution: Decimal method: 30 ÷ 100 = 0.30. 0.30 x 250 = 75 Fraction method: 30/100 = 3/10. (3/10) x 250 = 75

Commentary:* Both the decimal and fraction methods give the same answer. Choosing the method depends on the numbers involved; sometimes one is easier than the other.

Question 3: What percentage is 24 of 80?

Solution: (24 ÷ 80) x 100 = 0.3 x 100 = 30%

Commentary:* We divided the first quantity (24) by the second quantity (80) and then multiplied by 100 to express the result as a percentage.

Question 4: A cellphone company offers a 25% discount on a new phone that costs R

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0. What is the discounted price?

Solution: Discount: 25% of R2800 = (25/100) R2800 = R700 Discounted Price: R2800 - R700 = R2100

Commentary:* We calculated the discount amount first and then subtracted it from the original price to find the discounted price. Independent Practice (Questions Only) Convert the following fractions to decimals and percentages: 1/5, 7/10, 11/20, 3/

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5. Convert the following decimals to percentages and simplified fractions: 0.6, 0.08, 0.125, 0.

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5. Convert the following percentages to decimals and simplified fractions: 60%, 15%, 22%, 120%. Calculate 45% of

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0. Calculate 12.5% of

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8. What percentage is 36 of 90? What percentage is 12 of 48? A pair of jeans originally cost R450, but are on sale for 20% off. What is the sale price? A school has 800 students. 35% of the students play soccer. How many students play soccer? In a survey, 65 out of 200 people preferred pap and vleis over other traditional meals. What percentage of people preferred pap and vleis?