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.
• Express a quantity as a percentage of another.
• Increase or decrease a quantity by a percentage.
• Solve real-life word problems.

Lesson summary

Fractions, decimals, and percentages are interconnected concepts that are fundamental to everyday life. In South Africa, understanding these concepts is crucial for various applications, from budgeting and managing personal finances (calculating discounts at Shoprite or Pick n Pay) to interpreting data related to economic growth, population demographics, and even sports statistics. This week, we will focus on solidifying our understanding of how to convert between these three forms, solve problems involving them, and apply them to practical scenarios. Being competent with these concepts allows you to make informed decisions in your daily lives and participate more effectively in the economy.

Lesson notes

2. 1.

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

Example: 3/4 means we have 3 parts out of a total of 4 parts. 2.

2. Decimals: A decimal is another way to represent a part of a whole, using a base-10 system. The decimal point separates the whole number part from the fractional part.

Example: 0.75 represents seventy-five hundredths. The first digit after the decimal point represents tenths, the second represents hundredths, the third represents thousandths, and so on. 2.

3. 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" and is represented by the symbol %.

Example: 75% means 75 out of 100. 2.

4. Converting Between Fractions, Decimals, and Percentages: Fraction to Decimal: Divide the numerator by the denominator.

Example: To convert 1/2 to a decimal, divide 1 by 2, which equals 0.

5. 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.

Example: To convert 0.25 to a fraction, write it as 25/100, which simplifies to 1/

4. Fraction to Percentage: First, convert the fraction to a decimal (divide numerator by denominator). Then, multiply the decimal by 100 and add the % symbol.

Example: To convert 3/4 to a percentage, divide 3 by 4 to get 0.

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5. Multiply 0.75 by 100 to get 75%.

Therefore, 3/4 = 75%.

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

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0. Then, simplify the fraction.

Example: To convert 60% to a fraction, write it as 60/100, which simplifies to 3/

5. Percentage to Decimal: Divide the percentage by

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0. Example: To convert 45% to a decimal, divide 45 by 100, which equals 0.45. 2.

5. Finding a Percentage of a Quantity: To find a percentage of a quantity, convert the percentage to a decimal (divide by 100) and then multiply the decimal by the quantity.

Example: Find 20% of

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0. Convert 20% to a decimal: 20/100 = 0.20 Multiply the decimal by the quantity: 0.20 80 = 16 Therefore, 20% of 80 is 16. 2.

6. Expressing a Quantity as a Percentage of Another Quantity: Divide the first quantity by the second quantity and then multiply the result by

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0. Example: What percentage is 15 of 50?

Divide 15 by 50: 15 / 50 = 0.3 Multiply the result by 100: 0.3 100 = 30% Therefore, 15 is 30% of 50. 2.

7. Increasing or Decreasing a Quantity by a Given Percentage: Increase: Calculate the percentage increase and add it to the original quantity.

Example: Increase 50 by 10%. Calculate 10% of 50: (10/100) 50 = 5 Add the increase to the original quantity: 50 + 5 = 55 Therefore, increasing 50 by 10% gives

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

Example: Decrease 80 by 25%. Calculate 25% of 80: (25/100) 80 = 20 Subtract the decrease from the original quantity: 80 - 20 = 60 Therefore, decreasing 80 by 25% gives

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0. Guided Practice (With Solutions)

Question 1: Convert 0.65 to a fraction in its simplest form.

Solution: 0.65 can be written as 65/

1

0

0. To simplify, find the greatest common factor (GCF) of 65 and 100, which is

5. Divide both the numerator and denominator by 5: (65 ÷ 5) / (100 ÷ 5) = 13/

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0. Therefore, 0.65 = 13/

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0. Question 2: A shop is offering a 15% discount on a pair of shoes that originally cost R

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0. What is the discount amount in Rands?

Solution: Convert 15% to a decimal: 15/100 = 0.15 Multiply the decimal by the original price: 0.15 R400 = R60 Therefore, the discount amount is R

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0. Question 3: In a class of 40 students, 24 are girls. What percentage of the class are girls?

Solution: Divide the number of girls by the total number of students: 24 / 40 = 0.6 Multiply the result by 100: 0.6 100 = 60% Therefore, 60% of the class are girls.

Question 4: Increase 120 by 30%.

Solution: Calculate 30% of 120: (30/100) 120 = 36 Add the increase to the original quantity: 120 + 36 = 156 Therefore, increasing 120 by 30% gives

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6. Question 5: What is 7/8 expressed as a percentage?

Solution: Divide 7 by 8: 7 / 8 = 0.875 Multiply the result by 100: 0.875 100 = 87.5% Therefore, 7/8 is equal to 87.5%. Independent Practice (Questions Only) Convert 7/20 to a decimal and a percentage. Convert 0.8 to a fraction in its simplest form and a percentage. Convert 35% to a fraction in its simplest form and a decimal. Calculate 45% of

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0. What percentage is 36 of 120? Increase 75 by 20%. Decrease 150 by 35%. A shirt costs R180, and there is a sale with a 25% discount. What is the sale price of the shirt? A school has 600 learners. If 12% of the learners are in Grade 7, how many Grade 7 learners are there? John earns R4000 per month. He saves 15% of his salary. How much money does he save each month?