Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Add and subtract fractions with unlike denominators.
• Multiply a common fraction by a whole number.
• Divide a 3-digit number by a 2-digit number.
• Convert between decimals and common fractions.
• Solve word problems using these skills.

Lesson summary

This week, we delve deeper into the fascinating world of whole numbers, common fractions, and decimals. Understanding these concepts is crucial because they are fundamental to everyday life in South Africa. From budgeting your pocket money at the tuck shop to calculating the cost of groceries for your family, these mathematical skills are constantly used.

Furthermore, fractions and decimals are essential for understanding concepts in other subjects like Science (measuring ingredients for experiments) and Social Sciences (interpreting statistics). Mastering these concepts now will build a strong foundation for more advanced mathematics in the future.

Lesson notes

2.1 Adding and Subtracting Fractions with Unlike Denominators The most important thing to remember when adding or subtracting fractions is that they must have the same denominator. This is because you can only add or subtract things that are measured in the same units. Think of it like trying to add apples and oranges – you need to convert them to a common unit, like "fruit." How to find a common denominator: Identify the denominators: Look at the bottom number of each fraction.

Find the Least Common Multiple (LCM): The LCM is the smallest number that both denominators divide into evenly. This is your common denominator. You can find the LCM by listing multiples of each denominator until you find a number they have in common.

Convert the fractions: Multiply both the numerator (top number) and the denominator of each fraction by a number that will make the denominator equal to the LC

M. Remember, you MUST multiply both the top and bottom to keep the fraction equivalent.

Example 1: Adding Fractions Let's add 1/3 + 1/

6. Denominators: 3 and 6 LCM of 3 and 6: 6 (Multiples of 3: 3, 6, 9...; Multiples of 6: 6, 12...)

Convert 1/3: Multiply the numerator and denominator by 2: (1 x 2) / (3 x 2) = 2/6 Now we have: 2/6 + 1/6 Add the numerators: 2 + 1 = 3 Keep the denominator: 3/6 Simplify: 3/6 = 1/2 (Divide both numerator and denominator by 3) Therefore, 1/3 + 1/6 = 1/2 Example 2: Subtracting Fractions (with mixed numbers) Let's subtract 2 1/4 - 1 1/

8. Convert mixed numbers to improper fractions: 2 1/4 = (2 x 4 + 1)/4 = 9/4 1 1/8 = (1 x 8 + 1)/8 = 9/8 Denominators: 4 and 8 LCM of 4 and 8: 8 Convert 9/4: Multiply the numerator and denominator by 2: (9 x 2) / (4 x 2) = 18/8 Now we have: 18/8 - 9/8 Subtract the numerators: 18 - 9 = 9 Keep the denominator: 9/8 Convert back to a mixed number: 9/8 = 1 1/8 Therefore, 2 1/4 - 1 1/8 = 1 1/8 2.2 Multiplying a Fraction by a Whole Number To multiply a fraction by a whole number, you simply multiply the numerator of the fraction by the whole number, keeping the denominator the same. Then, simplify the fraction if possible. Think of it as repeated addition. For example, 3 x (1/4) is the same as (1/4) + (1/4) + (1/4).

Example 3: Multiplying Let's multiply 5 x 2/

3. Multiply the numerator: 5 x 2 = 10 Keep the denominator: 10/3 Convert to a mixed number: 10/3 = 3 1/3 Therefore, 5 x 2/3 = 3 1/3 2.3 Dividing a 3-Digit Whole Number by a 2-Digit Whole Number Long division with 2-digit divisors requires a good understanding of multiplication facts and place value. We will be finding both quotients and remainders.

Example 4: Dividing Let's divide 145 ÷

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2. Set up the long division: ``` ______ 12 | 145 ``` How many times does 12 go into 14? Once (1 x 12 = 12) ``` 1____ 12 | 145 12 ``` Subtract 12 from 14: 14 - 12 = 2 ``` 1____ 12 | 145 12 -- 2 ``` Bring down the 5: ``` 1____ 12 | 145 12 -- 25 ``` How many times does 12 go into 25? Twice (2 x 12 = 24) ``` 12___ 12 | 145 12 -- 25 24 ``` Subtract 24 from 25: 25 - 24 = 1 ``` 12___ 12 | 145 12 -- 25 24 -- 1 ``` Therefore, 145 ÷ 12 = 12 remainder 1. 2.4 Converting Decimals to Common Fractions and Vice-Versa Decimals and fractions are two different ways of representing the same thing: parts of a whole.

Converting a Decimal to a Common Fraction: Write the decimal as a fraction with a denominator that is a power of 10 (10, 100, 1000, etc.). The power of 10 depends on the number of decimal places.

One decimal place: denominator of 10 Two decimal places: denominator of 100 Simplify the fraction to its simplest form.

Example 5: Converting Decimal to Fraction Let's convert 0.75 to a fraction. 0.75 has two decimal places, so the denominator is 100. 0.75 = 75/100 Simplify by dividing both numerator and denominator by their greatest common factor (25): 75/100 = 3/4 Therefore, 0.75 = 3/4 Converting a Common Fraction to a Decimal: Divide the numerator by the denominator.

Example 6: Converting Fraction to Decimal Let's convert 1/5 to a decimal.

Divide 1 by 5: 1 ÷ 5 = 0.2 Therefore, 1/5 = 0.2 Guided Practice (With Solutions)

Question 1: A baker uses 1/4 kg of flour for one loaf of bread and 2/5 kg of flour for another type of bread. How much flour does the baker use in total?

Solution: Add the fractions: 1/4 + 2/5 Find the LCM of 4 and 5: LCM = 20 Convert fractions: 1/4 = (1 x 5) / (4 x 5) = 5/20 2/5 = (2 x 4) / (5 x 4) = 8/20 Add the fractions: 5/20 + 8/20 = 13/20 Answer: The baker uses 13/20 kg of flour.

Question 2: Sipho has a plank of wood that is 3 meters long. He cuts off 2/7 of the plank. How long is the piece that he cuts off?

Solution: Multiply the whole number by the fraction: 3 x 2/7 3 x 2/7 = 6/7 Answer: Sipho cuts off 6/7 meters of the plank.

Question 3: Divide 255 by

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5. Solution: Set up the division: 255 ÷ 15 15 goes into 25 once (1 x 15 = 15) 25 - 15 = 10 Bring down the 5, giving 105 15 goes into 105 seven times (7 x 15 = 105) 105 - 105 = 0 Answer: 255 ÷ 15 = 17 Question 4: Convert 0.6 to a common fraction in simplest form.