Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Identify and create equivalent fractions.
• Simplify fractions to their lowest terms.
• Compare and order fractions.
• Convert between common fractions and decimals.
• Solve real-life problems with fractions and decimals.

Lesson summary

This week, we'll be diving deeper into whole numbers, common fractions, and decimals. These concepts are essential building blocks for understanding more complex mathematics and are used every day in real-life situations, especially in South Africa. Think about buying groceries at Shoprite, sharing a pizza with friends, or understanding the interest rates on a savings account – all these involve whole numbers, fractions, and decimals. Without a good understanding of these fundamentals, learners will struggle with later mathematical concepts and financial literacy.

This week's focus will be on: Equivalent Fractions: How fractions can look different but represent the same amount.

Lesson notes

2.1 Equivalent Fractions Equivalent fractions are fractions that have different numerators and denominators, but represent the same value. The key is that you multiply or divide both the numerator and the denominator by the same non-zero number. Why does this work? Think of multiplying by

1. Any number multiplied by 1 remains the same. A fraction like 2/2 is equal to

1. So, multiplying a fraction by 2/2 is the same as multiplying it by 1, which doesn't change its value, only its appearance.

Example 1: Find two equivalent fractions for 1/

3. Multiply the numerator and denominator by 2: (1 x 2) / (3 x 2) = 2/

6. So, 1/3 and 2/6 are equivalent. Multiply the numerator and denominator by 3: (1 x 3) / (3 x 3) = 3/

9. So, 1/3 and 3/9 are equivalent.

Example 2: Mrs. Dlamini is making vetkoek for a school fundraiser. The recipe calls for 1/4 cup of sugar. She needs to triple the recipe. How much sugar does she need? We are essentially looking for an equivalent fraction to 1/4 but multiplied by 3. (1x3)/(4x3) = 3/12 Therefore she needs 3/12 of sugar. 2.2 Simplifying Fractions (Reducing to Lowest Terms) Simplifying a fraction means finding an equivalent fraction where the numerator and denominator are the smallest possible whole numbers. This is also known as reducing the fraction to its lowest terms. To do this, we find the Greatest Common Factor (GCF) of the numerator and denominator and divide both by the GC

F. Greatest Common Factor (GCF): The largest number that divides evenly into both the numerator and the denominator.

Example 1: Simplify 6/

8. Find the factors of 6: 1, 2, 3, 6 Find the factors of 8: 1, 2, 4, 8 The GCF of 6 and 8 is

2. Divide both the numerator and denominator by 2: (6 ÷ 2) / (8 ÷ 2) = 3/

4. Therefore, 6/8 simplified is 3/

4. Example 2: Simplify 12/18 Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18 GCF of 12 and 18 is 6 (12 ÷ 6) / (18 ÷ 6) = 2/

3. Therefore 12/18 simplified is 2/3. 2.3 Comparing and Ordering Fractions To compare fractions, they must have the same denominator (a common denominator).

Steps: Find the Least Common Multiple (LCM) of the denominators. This will be the common denominator. Convert each fraction to an equivalent fraction with the common denominator. Compare the numerators. The fraction with the larger numerator is the larger fraction.

Least Common Multiple (LCM): The smallest number that is a multiple of both denominators.

Example 1: Compare 2/3 and 3/

4. Find the LCM of 3 and 4: Multiples of 3: 3, 6, 9, 12, 15… Multiples of 4: 4, 8, 12, 16… The LCM is

1

2. Convert 2/3 to an equivalent fraction with a denominator of 12: (2 x 4) / (3 x 4) = 8/12 Convert 3/4 to an equivalent fraction with a denominator of 12: (3 x 3) / (4 x 3) = 9/12 Compare: 8/12 2, 3/8 is larger than 2/8 (which is equivalent to 1/4).

Therefore, 3/8 is larger than 1/

4. Question 4: Convert 0.8 into a simplified common fraction.

Solution: 0.8 is eight tenths, so 0.8 = 8/

1

0. Now simplify the fraction. The GCF of 8 and 10 is 2. (8 ÷ 2) / (10 ÷ 2) = 4/

5. Therefore, 0.8 is equal to 4/

5. Independent Practice (Questions Only) Find three equivalent fractions for 3/

4. Simplify the fraction 15/

2

5. Order the following fractions from smallest to largest: 1/3, 2/6, 5/

1

2. Convert 0.45 to a simplified common fraction. Convert 7/10 to a decimal.

Which is bigger: 5/8 or 7/12? Simplify 24/

3

6. Write two fractions that are equivalent to 1/2 and have denominators less than

1

5. Sipho ate 2/5 of a pizza and Thandi ate 3/10 of the same pizza. Who ate more pizza? Convert 0.9 to a common fraction. Convert it also to a percentage