Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

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

Lesson summary

Fractions, decimals, and percentages are different ways of representing the same thing: parts of a whole. Mastering these concepts is absolutely crucial for success in mathematics and for navigating daily life in South Africa. From understanding discounts at your local Shoprite to calculating percentages for school marks, or even sharing a pizza fairly with your friends, these skills are fundamental. This week, we'll focus on fluently converting between fractions, decimals, and percentages, and applying these conversions to solve problems.

Lesson notes

2.1 Understanding Fractions A fraction represents a part of a whole.

It has two parts: the numerator (the top number) and the 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, in the fraction 3/4, the whole is divided into 4 equal parts, and we have 3 of those parts. 2.2 Understanding Decimals A decimal is another way of representing a part of a whole. Decimal places represent tenths, hundredths, thousandths, and so on. For example, 0.5 represents five-tenths, which is the same as one-half (1/2). 0.25 represents twenty-five hundredths, which is the same as one-quarter (1/4). The further to the right of the decimal point a digit is, the smaller its value. 2.3 Understanding Percentages A percentage means "out of one hundred." The symbol % means "divided by 100". So, 50% means 50 out of 100, which is the same as 50/100 or 1/2 or 0.5. 2.4 Converting Fractions to Decimals To convert a fraction to a decimal, divide the numerator by the denominator.

Example 1: Convert 3/8 to a decimal. 3 ÷ 8 = 0.375 Therefore, 3/8 = 0.375 Example 2: Convert 1/4 to a decimal. 1 ÷ 4 = 0.25 Therefore, 1/4 = 0.25 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 to its lowest terms.

Example 1: Convert 0.6 to a fraction. 6 = 6/10 = 3/5 (simplified by dividing both numerator and denominator by 2) Therefore, 0.6 = 3/5 Example 2: Convert 0.75 to a fraction. 75 = 75/100 = 3/4 (simplified by dividing both numerator and denominator by 25) 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 (as shown in 2.4), and then multiply the decimal by

1

0

0. Add the percentage sign (%).

Example 1: Convert 1/2 to a percentage. 1/2 = 0.5 5 x 100 = 50% Therefore, 1/2 = 50% Example 2: Convert 3/4 to a percentage. 3/4 = 0.75 75 x 100 = 75% Therefore, 3/4 = 75% 2.7 Converting Percentages to Fractions To convert a percentage to a fraction, write the percentage as a fraction with a denominator of

1

0

0. Then, simplify the fraction to its lowest terms.

Example 1: Convert 25% to a fraction. 25% = 25/100 = 1/4 (simplified by dividing both numerator and denominator by 25) Therefore, 25% = 1/4 Example 2: Convert 75% to a fraction. 75% = 75/100 = 3/4 (simplified by dividing both numerator and denominator by 25) Therefore, 75% = 3/4 2.8 Converting Decimals to Percentages To convert a decimal to a percentage, multiply the decimal by 100 and add the percentage sign (%).

Example 1: Convert 0.8 to a percentage. 8 x 100 = 80% Therefore, 0.8 = 80% Example 2: Convert 0.15 to a percentage. 15 x 100 = 15% Therefore, 0.15 = 15% Guided Practice (With Solutions)

Question 1: Express 0.45 as a simplified fraction and as a percentage.

Solution: Fraction: 0.45 = 45/100 = 9/20 (simplified by dividing both by 5).

Percentage: 0.45 x 100 = 45%.

Commentary: We first express the decimal as a fraction with a denominator of

1

0

0. Then, we look for a common factor (in this case, 5) to simplify the fraction to its lowest terms. To get the percentage, we multiply by

1

0

0. Question 2: Express 3/5 as a decimal and as a percentage.

Solution: Decimal: 3 ÷ 5 = 0.6 Percentage: 0.6 x 100 = 60%

Commentary: Here we divide the numerator by the denominator to get the decimal representation. Multiplying the decimal by 100 gives us the equivalent percentage.

Question 3: If a shop offers a 20% discount on a shirt that originally costs R150, what is the discount amount in Rands?

Solution: 20% = 20/100 = 0.20 Discount amount = 0.20 x R150 = R30

Commentary: We first convert the percentage into a decimal or fraction. Then, we multiply the original price by this value to find the discount.

Question 4: Arrange the following from smallest to largest: 1/2, 0.6, and 45%.

Solution: Convert all to decimals: 1/2 = 0.5, 0.6 is already a decimal, 45% = 0.45 Ordering from smallest to largest: 0.45, 0.5, 0.6 So, the original order is: 45%, 1/2, 0.6

Commentary: The easiest way to compare is to convert all values to the same format. Here, converting everything to decimals made the comparison straightforward. Independent Practice (Questions Only) Convert 7/20 to a decimal and a percentage. Convert 0.85 to a fraction in its simplest form and a percentage. Convert 64% to a fraction in its simplest form and a decimal. What is 35% of 200? A pair of shoes costs R

4

0

0. If there is a sale of 15%, what is the new price of the shoes? Express 0.375 as a simplified fraction. Arrange the following in ascending order (smallest to largest): 0.7, 3/8, 76%, 0.

0

9. John scored 40 out of 50 on a test. Express this as a percentage. Sarah spent 60% of her R250 airtime. How much airtime did she spend? What fraction of an hour is 20 minutes?