Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Add and subtract common fractions with related denominators.
• Multiply common fractions by whole numbers.
• Add and subtract decimal fractions (to two decimal places).
• Multiply decimal fractions by whole numbers.
• Solve word problems using all these skills.

Lesson summary

This week, we delve deeper into the fascinating world of numbers, specifically focusing on whole numbers, common fractions, and decimals. Understanding these number types is absolutely crucial, not only for success in mathematics but also for navigating everyday life in South Africa. Imagine going to the local spaza shop – you need to calculate change, compare prices (often expressed as fractions or decimals), and understand quantities. Think about measuring ingredients for a family recipe – fractions are essential! Even calculating distances or time involves these number concepts.

Lesson notes

Whole Numbers: Whole numbers are the counting numbers starting from zero: 0, 1, 2, 3, and so on. They are fundamental and form the basis for understanding all other number types. Remember, whole numbers do not include fractions or decimals.

Common Fractions: A common fraction represents a part of a whole.

It consists of two parts: the numerator (the number above the line) and the denominator (the number below the line). 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. Examples include 1/2, 3/4, 5/8, and 2/

3. Equivalent Fractions: These are fractions that represent the same value, even though they have different numerators and denominators. For example, 1/2, 2/4, and 4/8 are all equivalent fractions. You can find equivalent fractions by multiplying (or dividing) both the numerator and denominator by the same number.

Mixed Numbers: A mixed number consists of a whole number and a proper fraction (where the numerator is smaller than the denominator). For example, 2 1/4 (two and one-quarter) is a mixed number. To convert a mixed number to an improper fraction (where the numerator is larger than or equal to the denominator), multiply the whole number by the denominator and add the numerator. Keep the same denominator. So, 2 1/4 = (2 4 + 1) / 4 = 9/

4. Adding and Subtracting Fractions with Related Denominators: The key is to make sure the denominators are the same before you add or subtract. Find the Lowest Common Multiple (LCM) of the denominators. The LCM becomes the common denominator. Then, adjust the numerators accordingly.

Example 1 (Adding Fractions): A farmer has 1/4 of his land planted with maize and 3/8 of his land planted with sunflowers. What fraction of his land is planted with crops?

Step 1: Identify the fractions: 1/4 and 3/

8. Step 2: Find the LCM of 4 and

8. The LCM is

8. Step 3: Convert 1/4 to an equivalent fraction with a denominator of 8: 1/4 = (1 2) / (4 * 2) = 2/

8. Step 4: Add the fractions: 2/8 + 3/8 = (2 + 3) / 8 = 5/

8. Answer: The farmer has 5/8 of his land planted with crops.

Example 2 (Subtracting Fractions): Maria buys 5/6 of a loaf of bread. She eats 1/3 of the loaf. What fraction of the loaf is left?

Step 1: Identify the fractions: 5/6 and 1/

3. Step 2: Find the LCM of 6 and

3. The LCM is

6. Step 3: Convert 1/3 to an equivalent fraction with a denominator of 6: 1/3 = (1 2) / (3 * 2) = 2/

6. Step 4: Subtract the fractions: 5/6 - 2/6 = (5 - 2) / 6 = 3/

6. Step 5: Simplify the fraction (optional, but good practice): 3/6 = 1/

2. Answer: Maria has 1/2 of the loaf left. Example 3 (Multiplying a fraction by a whole number): A recipe for rusks calls for 1/2 cup of sugar per batch. You want to make 3 batches. How much sugar do you need?

Step 1: Identify the fraction and the whole number: 1/2 and

3. Step 2: Multiply the fraction by the whole number: (1/2) 3 = 3/2 Step 3: Convert the improper fraction to a mixed number: 3/2 = 1 1/

2. Answer: You need 1 1/2 cups of sugar.

Decimal Fractions: Decimal fractions are another way of representing parts of a whole. They are based on powers of 10 and use a decimal point to separate the whole number part from the fractional part. Examples include 0.5, 1.75, and 3.

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4. Each digit after the decimal point represents a fraction with a denominator of 10, 100, 1000, and so on.

Adding and Subtracting Decimals: Line up the decimal points vertically to ensure that you are adding or subtracting digits with the same place value. Add zeros as placeholders if necessary.

Multiplying Decimals by Whole Numbers: Multiply as you would with whole numbers. Then, count the number of decimal places in the decimal fraction. The answer will have the same number of decimal places.

Example 4 (Adding Decimals): Thando buys a loaf of bread for R12.50 and a packet of butter for R25.

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5. How much does she spend in total?

Step 1: Write the numbers vertically, lining up the decimal points: ``` 12.50 + 25.75 ------- ``` Step 2: Add the numbers as you would with whole numbers: ``` 12.50 + 25.75 ------- 38.25 ``` Answer: Thando spends R38.25 in total.

Example 5 (Subtracting Decimals): Sipho has R50.

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0. He buys a cold drink for R15.

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5. How much money does he have left?

Step 1: Write the numbers vertically, lining up the decimal points: ``` 50.00 15.25 ------- ``` Step 2: Subtract the numbers, borrowing as needed: ``` 50.00 15.25 ------- 34.75 ``` Answer: Sipho has R34.75 left. Example 6 (Multiplying a Decimal by a Whole Number): A pencil costs R3.

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0. How much will 4 pencils cost?

Step 1: Multiply the decimal by the whole number: 3.50 4 = 14.00 Step 2: Count the decimal places in the decimal number (2 places)

Step 3: Put two decimal places into the product.

Answer: 4 pencils will cost R14.

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0. Guided Practice (With Solutions)

Question 1: Sarah walks 1/3 of a kilometre to school and then 2/6 of a kilometre to her friend's house. How far does she walk in total?

Solution: Step 1: Identify the fractions: 1/3 and 2/6.