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.
• Express one quantity as a percentage of another.
• Apply these concepts to solve real-life problems.

Lesson summary

Fractions, decimals, and percentages are different ways of representing the same thing: a part of a whole. Understanding the relationship between these representations is crucial for everyday life, from calculating discounts at a store to understanding statistics about employment in South Africa. This week, we will deepen our understanding of how to convert between fractions, decimals, and percentages and apply this knowledge to solve problems. Knowing how to work with these different forms allows us to make informed decisions about our finances, understand proportions in recipes, and interpret data presented in various formats.

Lesson notes

2. 1.

Fractions: A fraction represents a part of a whole. It has a numerator (the number on top) and a denominator (the number on the bottom). The denominator tells you how many equal parts the whole is divided into, and the numerator tells you how many of those parts you have.

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

2. Decimals: A decimal is another way of representing a part of a whole, using a base-10 system. The decimal point separates the whole number part from the fractional part. Each place value to the right of the decimal point represents a power of ten: tenths, hundredths, thousandths, and so on.

Example: 0.75 means 75 hundredths. 2.

3. Percentages: A percentage is a fraction out of

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0. The word "percent" means "out of one hundred." The symbol for percent is %.

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

4. Converting Fractions to Decimals: To convert a fraction to a decimal, divide the numerator by the denominator.

Example: Convert 3/4 to a decimal. 3 ÷ 4 = 0.75 2.

5. Converting Decimals to Fractions: To convert a decimal to a fraction: Write the decimal as a fraction with a denominator of 1 (e.g., 0.75 = 0.75/1). Multiply both the numerator and denominator by 10, 100, 1000, etc., depending on the number of decimal places, to eliminate the decimal (e.g., 0.75/1 * 100/100 = 75/100). Simplify the fraction to its lowest terms (e.g., 75/100 = 3/4).

Example: Convert 0.625 to a fraction. 625/1 * 1000/1000 = 625/

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0

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0. Simplifying: 625/1000 = 5/8 (Dividing both numerator and denominator by 125). 2.

6. Converting Fractions to Percentages: To convert a fraction to a percentage: Convert the fraction to a decimal (divide the numerator by the denominator). Multiply the decimal by 100 and add the % symbol.

Example: Convert 1/5 to a percentage. 1 ÷ 5 = 0.2 2 * 100 = 20% 2.

7. Converting Percentages to Fractions: To convert a percentage to a fraction: Write the percentage as a fraction with a denominator of

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0. Simplify the fraction to its lowest terms.

Example: Convert 40% to a fraction. 40/100 = 2/5 (Dividing both numerator and denominator by 20). 2.

8. Converting Percentages to Decimals: To convert a percentage to a decimal, divide the percentage by

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0. Example: Convert 65% to a decimal. 65 ÷ 100 = 0.65 2.

9. Finding a Percentage of a Quantity: To find a percentage of a quantity: Convert the percentage to a decimal. Multiply the decimal by the quantity.

Example: Find 25% of 80. 25% = 0.25 25 * 80 = 20 2.

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0. Expressing One Quantity as a Percentage of Another: To express one quantity as a percentage of another: Write the quantities as a fraction, with the first quantity as the numerator and the second quantity as the denominator. Convert the fraction to a percentage (multiply by 100 and add the % symbol).

Example: What percentage is 15 of 60? 15/60 = 1/4 1/4 = 0.25 25 * 100 = 25% Guided Practice (With Solutions)

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

Solution: Decimal: 7 ÷ 20 = 0.35 Percentage: 0.35 100 = 35%

Commentary: We first divide the numerator by the denominator to find the decimal equivalent. Then, we multiply the decimal by 100 to get the percentage.

Question 2: What is 15% of 120?

Solution: Convert 15% to a decimal: 15 ÷ 100 = 0.15 Multiply the decimal by 120: 0.15 120 = 18

Commentary: We convert the percentage to a decimal first, which allows us to easily multiply by the quantity.

Question 3: Express 24 as a percentage of

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0. Solution: Write the quantities as a fraction: 24/80 Simplify the fraction (optional but helpful): 24/80 = 3/10 Convert the fraction to a decimal: 3 ÷ 10 = 0.3 Convert the decimal to a percentage: 0.3 100 = 30%

Commentary: Simplifying the fraction makes the division easier. The key is to remember to put the "part" (24) over the "whole" (80) to form the fraction.

Question 4: Convert 0.8 to a fraction and a percentage.

Solution: Fraction: 0.8 = 8/10 = 4/5 Percentage: 0.8 100 = 80%

Commentary: Remember to simplify the fraction to its lowest terms.

Question 5: Convert 72% to a fraction in its simplest form and a decimal.

Solution: Fraction: 72/100 = 36/50 = 18/25 Decimal: 72/100 = 0.72

Commentary: Dividing both numerator and denominator by 2 twice, we reach the simplest form 18/

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5. Dividing 72 by 100 yields 0.72 Independent Practice (Questions Only) Convert 9/25 to a decimal and a percentage. What is 32% of 250? Express 45 as a percentage of

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5. Convert 0.375 to a fraction in its simplest form and a percentage. Convert 12.5% to a fraction in its simplest form and a decimal. A shop is offering a 15% discount on a shirt that originally costs R

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0. What is the discount amount in Rands? In a class of 40 students, 28 are girls. What percentage of the class are girls? If you scored 42 out of 60 on a test, what percentage did you get? Write 11/8 as a decimal and a percentage. A farmer plants 45 hectares of his 150 hectare farm with maize. What percentage of the farm is planted with maize?