Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Convert fractions to decimals and percentages.
• Convert decimals to fractions and percentages.
• Convert percentages to fractions and decimals.
• Solve problems using these conversions.
• Compare and order fractions, decimals, and percentages.

Lesson summary

Fractions, decimals, and percentages are different ways of representing the same value - a part of a whole. Understanding the relationship between them is crucial not just in mathematics class but also in everyday life, from sharing a kota with friends to understanding discounts at your local spaza shop. This week, we will focus on confidently converting between fractions, decimals, and percentages, and using these conversions to solve problems. This skill is directly applicable to budgeting pocket money, calculating sale prices, understanding proportions in recipes, and interpreting statistics in the news.

Lesson notes

Understanding 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). For example, 1/2 represents one out of two equal parts. Understanding Decimals A decimal is another way to represent a part of a whole. It uses a base-10 system, where each digit to the right of the decimal point represents a fraction with a denominator that is a power of 10 (tenths, hundredths, thousandths, etc.). For example, 0.5 represents five tenths (5/10), which is the same as one half (1/2). Understanding Percentages A percentage means "out of one hundred" or "per hundred." The symbol for percent is %. So, 50% means 50 out of 100, or 50/100, which is the same as 1/2 or 0.

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

Example 1: Convert 3/4 to a decimal. 3 ÷ 4 = 0.75 Therefore, 3/4 = 0.75 Example 2: Convert 1/8 to a decimal. 1 ÷ 8 = 0.125 Therefore, 1/8 = 0.125 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. Simplify the fraction to its lowest terms.

Example 1: Convert 0.6 to a fraction. 0.6 = 6/10 Simplifying 6/10 by dividing both numerator and denominator by their greatest common factor (2), we get 3/

5. Therefore, 0.6 = 3/5 Example 2: Convert 0.125 to a fraction. 0.125 = 125/1000 Simplifying 125/1000 by dividing both numerator and denominator by their greatest common factor (125), we get 1/

8. Therefore, 0.125 = 1/8 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 % sign.

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

1

0

0. Simplify the fraction to its lowest terms.

Example 1: Convert 75% to a fraction. 75% = 75/100 Simplifying 75/100 by dividing both numerator and denominator by their greatest common factor (25), we get 3/

4. Therefore, 75% = 3/4 Example 2: Convert 20% to a fraction. 20% = 20/100 Simplifying 20/100 by dividing both numerator and denominator by their greatest common factor (20), we get 1/

5. Therefore, 20% = 1/5 Converting Percentages to Decimals To convert a percentage to a decimal: Divide the percentage by

1

0

0. Example 1: Convert 45% to a decimal. 45 ÷ 100 = 0.45 Therefore, 45% = 0.45 Example 2: Convert 120% to a decimal. 120 ÷ 100 = 1.2 Therefore, 120% = 1.2 Comparing and Ordering Fractions, Decimals and Percentages To compare and order fractions, decimals, and percentages, you must first convert them all to the same form (either all fractions, all decimals, or all percentages). Converting to decimals is often the easiest method. Once they are in the same form, you can easily compare their values. Guided Practice (With Solutions)

Question 1: Convert 2/5 to a decimal and a percentage.

Solution: To Decimal: 2 ÷ 5 = 0.4 To Percentage: 0.4 × 100 = 40% Therefore: 2/5 = 0.4 = 40%

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

Question 2: Convert 0.85 to a fraction (in simplest form) and a percentage.

Solution: To Fraction: 0.85 = 85/

1

0

0. Simplifying by dividing both numerator and denominator by 5 gives us 17/

2

0. To Percentage: 0.85 × 100 = 85% Therefore: 0.85 = 17/20 = 85%

Commentary: Converting to a fraction involved recognizing the place value (hundredths) and simplifying. The percentage conversion is straightforward multiplication.

Question 3: Convert 12.5% to a decimal and a fraction (in simplest form).

Solution: To Decimal: 12.5 ÷ 100 = 0.125 To Fraction: 12.5% = 12.5/100 = 125/

1

0

0

0. Simplifying by dividing both numerator and denominator by 125 gives us 1/

8. Therefore: 12.5% = 0.125 = 1/8

Commentary: Remember to divide by 100 to convert percentage to decimal. Then convert either the decimal or original percentage to a fraction.

Question 4: Which is larger: 3/8 or 35%?

Solution: Convert 3/8 to a decimal: 3 ÷ 8 = 0.375 Convert 35% to a decimal: 35 ÷ 100 = 0.35 Compare: 0.375 > 0.35 Therefore: 3/8 is larger than 35%

Commentary: By converting both to decimals, the comparison becomes much easier. Independent Practice (Questions Only) Convert 7/10 to a decimal and a percentage. Convert 0.2 to a fraction (in simplest form) and a percentage. Convert 65% to a decimal and a fraction (in simplest form). Order the following from smallest to largest: 1/4, 0.3, 20%. Sipho ate 3/5 of his vetkoek. What percentage of the vetkoek did he eat?