Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Compare and order whole numbers, fractions, and decimals.
• Add and subtract common fractions with the same denominators.
• Add and subtract decimal fractions.
• Round off decimals to the nearest whole number.
• Find equivalent fractions and decimals.

Lesson summary

This week, we delve deeper into the interconnected world of whole numbers, common fractions, and decimals. Mastering these concepts is crucial because they are the building blocks for almost everything you'll do in mathematics and encounter in daily life. From managing your pocket money and sharing sweets with friends to understanding measurements for cooking and calculating distances, these skills are essential. Think about a spaza shop owner calculating profit margins, or a builder measuring the dimensions of a room – they all use these mathematical tools. This week, we'll focus on comparing, ordering, and performing basic operations with these numbers.

Lesson notes

2.1 Comparing and Ordering Whole Numbers, Common Fractions, and Decimal Fractions: Whole Numbers: Comparing whole numbers is relatively straightforward. Start by comparing the number of digits. The number with more digits is larger. If they have the same number of digits, compare the digits from left to right until you find a difference. For example, 1234 is greater than 987 because it has four digits while 987 has three. And 567 is greater than 562 because both have three digits, the first two digits are the same, but the third digit of 567 (7) is greater than the third digit of 562 (2).

Common Fractions: To compare common fractions, they must have the same denominator (the bottom number). If they do, the fraction with the larger numerator (the top number) is the larger fraction. If the denominators are different, you need to find a common denominator. The easiest way to do this is to find the Least Common Multiple (LCM) of the denominators and rewrite both fractions with this new denominator.

Example: Compare 2/5 and 3/

7. The LCM of 5 and 7 is

3

5. So, we rewrite 2/5 as (2/5) (7/7) = 14/35 and 3/7 as (3/7) * (5/5) = 15/

3

5. Now, we can compare 14/35 and 15/

3

5. Since 15 is greater than 14, 3/7 is greater than 2/

5. Decimal Fractions: To compare decimal fractions, line up the decimal points. Then, compare the digits from left to right, just like with whole numbers. You can add zeros to the end of a decimal without changing its value to make the comparison easier.

Example: Compare 0.65 and 0.

6. If we add a zero to the end of 0.6, we get 0.

6

0. Now we can compare 0.65 and 0.

6

0. Since 65 is greater than 60, 0.65 is greater than 0.

6. Mixing them all up: To compare whole numbers, fractions and decimals together, convert all numbers to either decimal form or fraction form.

Example: Order the following from smallest to largest: 2, 1/4, 0.6, 1.

5. Convert 1/4 to a decimal: 1/4 = 0.

2

5. Now compare: 0.25, 0.6, 1.5,

2. Order: 1/4, 0.6, 1.5, 2. 2.2 Adding and Subtracting Common Fractions with the Same Denominators: When adding or subtracting common fractions with the same denominator, simply add or subtract the numerators and keep the denominator the same.

Example: Imagine you have a pizza cut into 8 slices. You eat 3 slices (3/8) and your friend eats 2 slices (2/8). How many slices did you eat altogether? 3/8 + 2/8 = (3+2)/8 = 5/

8. You and your friend ate 5 slices out of the

8. Example: You have 7/10 of a loaf of bread. You use 2/10 of the loaf to make a sandwich. How much of the loaf is left? 7/10 - 2/10 = (7-2)/10 = 5/

1

0. You have 5/10 of the loaf left. 2.3 Adding and Subtracting Decimal Fractions: When adding or subtracting decimal fractions, the most important thing is to line up the decimal points. Then, add or subtract each column as you would with whole numbers, starting from the rightmost column. If necessary, you can add zeros to the end of a decimal fraction without changing its value to make the columns line up properly.

Example: A shop sells a loaf of bread for R12.50 and a bottle of juice for R8.

7

5. How much will it cost to buy both? ``` 12.50 + 08.75 ------- 21.25 ``` It will cost R21.25 in total.

Example: You have R50.00 and you buy sweets for R17.

2

5. How much money do you have left? ``` 50.00 17.25 ------- 32.75 ``` You have R32.75 left. 2.4 Rounding off Decimal Fractions to the Nearest Whole Number: To round a decimal fraction to the nearest whole number, look at the digit immediately to the right of the decimal point (the tenths place). If this digit is 5 or greater, round the whole number up. If this digit is less than 5, round the whole number down (keep it the same).

Example: Round 4.7 to the nearest whole number. The digit in the tenths place is 7, which is greater than 5, so we round up to

5. Example: Round 12.3 to the nearest whole number. The digit in the tenths place is 3, which is less than 5, so we round down to

1

2. Example: Round 9.5 to the nearest whole number. The digit in the tenths place is 5, so we round up to 10. 2.5 Identifying Equivalent Forms of Common Fractions and Decimal Fractions: Some fractions and decimals represent the same value. These are called equivalent forms.

The most common examples are: 1/2 = 0.5 1/4 = 0.25 3/4 = 0.75 1/10 = 0.1 1/5 = 0.2 2/5 = 0.4 To convert a common fraction to a decimal fraction, divide the numerator by the denominator. 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.

Example: Convert 0.75 to a fraction. 0.75 = 75/

1

0

0. Simplifying this fraction by dividing both numerator and denominator by 25, we get 3/

4. Guided Practice (With Solutions)

Question 1: Arrange the following numbers in ascending order (smallest to largest): 0.8, 3/4, 0.5, 1 Solution: First, convert all numbers to decimal form.