Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Convert between fractions, decimals, and percentages.
• Compare and order these different forms.
• Solve word problems using fractions and decimals.
• Visually represent fractions and decimals.
• Simplify fractions to their lowest terms.

Lesson summary

This week, we'll be solidifying our understanding of how whole numbers, common fractions, and decimals relate to each other. Building a strong foundation in these areas is crucial for many reasons. Think about going to the local shop in your community (spaza shop) to buy sweets. You need to understand fractions to share sweets fairly with your friends, decimals to work with money accurately when paying for your purchases, and whole numbers to count how many sweets you have in total. These mathematical concepts are essential for everyday tasks, not just in the classroom.

Lesson notes

2.1 Fractions, Decimals, and Percentages: A Family Affair Fractions, decimals, and percentages are simply different ways of representing the same portion of a whole.

Fractions: Represent a part of a whole. They are written as a ratio of two numbers: a numerator (top number) and a denominator (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.

Decimals: Represent a part of a whole using a base-10 system. The decimal point separates the whole number part from the fractional part. Each digit to the right of the decimal point represents a fraction with a denominator of 10, 100, 1000, and so on.

Percentages: Represent a part of a whole as a fraction out of

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0. The word "percent" means "out of one hundred," so 50% means 50 out of 100 (or 50/100). 2.2 Converting Between Fractions, Decimals, and Percentages Fraction to Decimal: Divide the numerator by the denominator.

Example: Convert 3/4 to a decimal. 3 ÷ 4 = 0.75 Therefore, 3/4 = 0.75 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: Convert 0.6 to a fraction. 0.6 = 6/10 Simplify by dividing both numerator and denominator by their greatest common factor (2): 6/10 = 3/5 Therefore, 0.6 = 3/5 Fraction to Percentage: Convert the fraction to a decimal first. Then, multiply the decimal by 100 and add the percent sign (%).

Example: Convert 1/2 to a percentage. 1 ÷ 2 = 0.5 0.5 x 100 = 50 Therefore, 1/2 = 50% Percentage to Fraction: Write the percentage as a fraction with a denominator of

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0. Then, simplify the fraction.

Example: Convert 25% to a fraction. 25% = 25/100 Simplify by dividing both numerator and denominator by their greatest common factor (25): 25/100 = 1/4 Therefore, 25% = 1/4 Decimal to Percentage: Multiply the decimal by 100 and add the percent sign (%).

Example: Convert 0.35 to a percentage. 0.35 x 100 = 35 Therefore, 0.35 = 35% 2.3 Comparing and Ordering Fractions, Decimals, and Percentages To compare and order fractions, decimals, and percentages, it's easiest to convert them all to the same form – usually decimals. Once they are all in decimal form, you can easily compare their values.

Example: Order the following from smallest to largest: 1/4, 0.3, 20%, 1/

5. Convert all to decimals: 1/4 = 0.25 0.3 = 0.3 20% = 0.20 1/5 = 0.2 Now, order the decimals: 0.2, 0.20, 0.25, 0.3 Therefore, the original numbers ordered from smallest to largest are: 1/5, 20%, 1/4, 0.3 2.4 Working with Mixed Numbers and Improper Fractions Mixed Number: A whole number and a fraction combined (e.g., 2 1/2).

Improper Fraction: A fraction where the numerator is greater than or equal to the denominator (e.g., 5/2). Converting a Mixed Number to an Improper Fraction: Multiply the whole number by the denominator of the fraction, add the numerator, and keep the same denominator.

Example: Convert 2 1/2 to an improper fraction. (2 x 2) + 1 = 5 Keep the same denominator: 5/2 Therefore, 2 1/2 = 5/2 Converting an Improper Fraction to a Mixed Number: Divide the numerator by the denominator. The quotient is the whole number part, the remainder is the numerator of the fractional part, and the denominator stays the same.

Example: Convert 7/3 to a mixed number. 7 ÷ 3 = 2 with a remainder of

1. Therefore, 7/3 = 2 1/3 2.5 Simplifying Fractions To simplify a fraction, divide both the numerator and the denominator by their greatest common factor (GCF). This results in an equivalent fraction in its simplest form.

Example: Simplify 8/

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2. The greatest common factor of 8 and 12 is

4. Divide both numerator and denominator by 4: 8/4 = 2 and 12/4 = 3 Therefore, 8/12 simplifies to 2/

3. Guided Practice (With Solutions)

Question 1: Convert 0.85 to a fraction in its simplest form.

Solution: Write 0.85 as a fraction: 85/100 Find the greatest common factor (GCF) of 85 and

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0. The GCF is

5. Divide both the numerator and the denominator by 5: 85/5 = 17 and 100/5 = 20 Therefore, 0.85 = 17/20 Question 2: Arrange the following from smallest to largest: 3/5, 65%, 0.

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2. Solution: Convert all values to decimals: 3/5 = 0.6 65% = 0.65 0.62 = 0.62 Compare the decimals: 0.6, 0.62, 0.65 Therefore, the order from smallest to largest is: 3/5, 0.62, 65% Question 3: Sarah has 1/2 of a pizza, and Thabo has 0.3 of the same pizza. Who has more pizza?

Solution: Convert both to decimals: 1/2 = 0.5 Compare: Sarah has 0.5 of the pizza, and Thabo has 0.3 of the pizza. Since 0.5 > 0.3, Sarah has more pizza than Thabo.

Question 4: Convert 2 3/4 to an improper fraction.

Solution: Multiply the whole number (2) by the denominator (4): 2 x 4 = 8 Add the numerator (3): 8 + 3 = 11 Keep the same denominator (4).

Therefore, 2 3/4 = 11/4 Independent Practice (Questions Only) Convert 7/8 to a decimal and a percentage. Convert 0.125 to a fraction in its simplest form. What is 45% of 200? Simplify the fraction 15/25.