Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Convert between fractions, decimals, and percentages.
• Find the percentage of a whole number.
• Compare and order all three forms.
• Solve real-world problems like discounts.

Lesson summary

Fractions, decimals, and percentages are different ways of representing parts of a whole. Understanding how to work with them is essential for everyday life, from calculating discounts at the shops to figuring out proportions in recipes when you're helping your family cook a delicious potjie. In South Africa, where managing finances and understanding budgeting is crucial, a solid grasp of these concepts is incredibly valuable. This week, we'll deepen our understanding of the relationships between fractions, decimals, and percentages and learn how to convert between them fluently.

Lesson notes

2.1 Understanding Fractions A fraction represents a part of a whole. It is written as a numerator (the top number) divided by a denominator (the bottom number). The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those parts we have. For example, 3/4 means we have 3 out of 4 equal parts of a whole. Fractions can be proper (numerator less than denominator), improper (numerator greater than or equal to denominator), or mixed numbers (a whole number and a proper fraction). 2.2 Understanding Decimals A decimal is another way to represent a part of a whole. It uses a decimal point to separate the whole number part from the fractional part. Each digit after the decimal point represents a power of ten: tenths, hundredths, thousandths, and so on. For example, 0.75 means 75 hundredths, or 75/100. 2.3 Understanding Percentages A percentage means "out of one hundred." The symbol "%" is used to represent percentage. So, 50% means 50 out of 100, or 50/100, which is equal to 0.5 or 1/2. 2.4 Converting Fractions to Decimals To convert a fraction to a decimal, divide the numerator by the denominator.

Example 1: Convert 1/4 to a decimal. 1 ÷ 4 = 0.25 Therefore, 1/4 = 0.25 Example 2: Convert 3/8 to a decimal. 3 ÷ 8 = 0.375 Therefore, 3/8 = 0.375 2.5 Converting Decimals to Fractions To convert a decimal to a 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 1: Convert 0.6 to a fraction. 0.6 = 6/

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0. Simplify by dividing both numerator and denominator by 2: 6/10 = 3/5 Therefore, 0.6 = 3/5 Example 2: Convert 0.75 to a fraction. 0.75 = 75/

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0

0. Simplify by dividing both numerator and denominator by 25: 75/100 = 3/4 Therefore, 0.75 = 3/4 2.6 Converting Fractions to Percentages To convert a fraction to a percentage, first convert the fraction to a decimal (by dividing the numerator by the denominator). Then, multiply the decimal by 100 and add the "%" sign.

Example 1: Convert 1/2 to a percentage. 1 ÷ 2 = 0.5 0.5 x 100 = 50% Therefore, 1/2 = 50% Example 2: Convert 3/5 to a percentage. 3 ÷ 5 = 0.6 0.6 x 100 = 60% Therefore, 3/5 = 60% 2.7 Converting Percentages to Fractions To convert a percentage to a fraction, write the percentage as a fraction with a denominator of

1

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0. Then, simplify the fraction.

Example 1: Convert 25% to a fraction. 25% = 25/

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0. Simplify by dividing both numerator and denominator by 25: 25/100 = 1/4 Therefore, 25% = 1/4 Example 2: Convert 75% to a fraction. 75% = 75/

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0. Simplify by dividing both numerator and denominator by 25: 75/100 = 3/4 Therefore, 75% = 3/4 2.8 Converting Percentages to Decimals To convert a percentage to a decimal, divide the percentage by

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0. Example 1: Convert 40% to a decimal. 40 ÷ 100 = 0.4 Therefore, 40% = 0.4 Example 2: Convert 12.5% to a decimal. 12.5 ÷ 100 = 0.125 Therefore, 12.5% = 0.125 2.9 Finding a Percentage of a Whole Number To find a percentage of a whole number, first convert the percentage to a decimal. Then, multiply the decimal by the whole number.

Example 1: Find 20% of 80. 20% = 0.20 0.20 x 80 = 16 Therefore, 20% of 80 is

1

6. Example 2: Find 15% of 150. 15% = 0.15 0.15 x 150 = 22.5 Therefore, 15% of 150 is 22.5 Guided Practice (With Solutions)

Question 1: Convert 3/20 to a percentage.

Solution: Convert the fraction to a decimal: 3 ÷ 20 = 0.15 Multiply the decimal by 100: 0.15 x 100 = 15% Therefore, 3/20 = 15%. The key here is remembering that percentages are "out of 100," so converting to a decimal allows us to easily scale the fraction.

Question 2: What is 35% of 200?

Solution: Convert the percentage to a decimal: 35 ÷ 100 = 0.35 Multiply the decimal by the whole number: 0.35 x 200 = 70 Therefore, 35% of 200 is

7

0. This is a common calculation when dealing with discounts or increases.

Question 3: Convert 0.85 to a fraction in its simplest form.

Solution: Write the decimal as a fraction with a denominator of 100: 0.85 = 85/100 Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 5: 85 ÷ 5 = 17 and 100 ÷ 5 = 20 Therefore, 0.85 = 17/

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0. Simplifying is important to express the fraction in its most concise form.

Question 4: A shop is offering a 25% discount on a pair of shoes that originally cost R

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0. What is the discounted price?

Solution: Calculate the discount amount: 25% of R400 = 0.25 x R400 = R100 Subtract the discount amount from the original price: R400 - R100 = R300 Therefore, the discounted price is R

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0. This demonstrates a practical application of percentages in financial contexts. Independent Practice (Questions Only) Convert 7/25 to a percentage. Convert 65% to a fraction in its simplest form. What is 45% of 300? Convert 0.375 to a fraction. A shirt costs R

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0. If there is a 10% discount, what will the shirt cost? Express 11/20 as a decimal. Convert 0.08 to a percentage. What percentage of 50 is 15? Calculate 12.5% of 48.