Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Add and subtract common fractions with different denominators.
• Convert between common fractions and decimal fractions.
• Solve word problems involving decimals.
• Compare and order common fractions and decimals.
• Express fractions in their simplest form.

Lesson summary

This week, we'll be diving deeper into whole numbers, common fractions, and decimals, building on what we learned last week. Understanding these concepts is crucial because they are used constantly in everyday life. From calculating the cost of groceries at Shoprite to understanding measurements for baking a cake, these skills are essential for financial literacy, problem-solving, and overall success. Imagine you're helping your family budget for the month - you'll need to use fractions and decimals to track expenses accurately! Or, think about sharing a pizza fairly with your friends – fractions are key!

Lesson notes

2.1 Adding and Subtracting Fractions with Different Denominators: Before we can add or subtract fractions, they need to have the same denominator. This common denominator is a multiple of both original denominators. The lowest common denominator (LCD) is the smallest multiple that both denominators share.

Example: 1/3 + 1/4 Step 1: Find the LCD. The multiples of 3 are 3, 6, 9, 12, 15... The multiples of 4 are 4, 8, 12, 16... The LCD is

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2. Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator. To change 1/3 to a fraction with a denominator of 12, we need to multiply both the numerator and the denominator by 4: (1 x 4) / (3 x 4) = 4/12 To change 1/4 to a fraction with a denominator of 12, we need to multiply both the numerator and the denominator by 3: (1 x 3) / (4 x 3) = 3/12 Step 3: Add the numerators. 4/12 + 3/12 = 7/12 Example with Mixed Numbers: 2 1/2 - 1 1/4 Step 1: Convert mixed numbers to improper fractions. 2 1/2 = (2 x 2 + 1) / 2 = 5/2 1 1/4 = (1 x 4 + 1) / 4 = 5/4 Step 2: Find the LC

D. The multiples of 2 are 2, 4, 6... The multiples of 4 are 4, 8, 12... The LCD is

4. Step 3: Convert the fractions to equivalent fractions with the LCD as the denominator. To change 5/2 to a fraction with a denominator of 4, we need to multiply both the numerator and the denominator by 2: (5 x 2) / (2 x 2) = 10/4 5/4 already has the correct denominator.

Step 4: Subtract the numerators. 10/4 - 5/4 = 5/4 Step 5: Convert the improper fraction back to a mixed number. 5/4 = 1 1/4 2.2 Converting Fractions to Decimals and Vice Versa: Fraction to Decimal: Divide the numerator by the denominator.

Example: Convert 3/4 to a decimal.

Divide 3 by 4: 3 ÷ 4 = 0.75 Decimal to Fraction: Write the decimal as a fraction with a denominator that is a power of 10 (10, 100, 1000, etc.). Simplify if possible.

Example: Convert 0.6 to a fraction. 0.6 is the same as 6/

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0. Simplify 6/10 by dividing both the numerator and denominator by their greatest common factor, which is 2: (6 ÷ 2) / (10 ÷ 2) = 3/5 2.3 Word Problems Involving Decimals: Carefully read the word problem, identify the key information, and choose the correct operation (addition, subtraction, multiplication, or division).

Example: Thando buys a loaf of bread for R12.50 and a bottle of juice for R8.

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5. How much does she spend in total? This is an addition problem. We need to add the cost of the bread and the juice. R12.50 + R8.75 = R21.25 Thando spends R21.25 in total. 2.4 Comparing and Ordering Fractions and Decimals: To compare fractions, convert them to equivalent fractions with the same denominator. Then, compare the numerators. To compare decimals, line up the decimal points and compare the digits from left to right. To compare a fraction and a decimal, convert one to match the other (either both fractions or both decimals).

Example: Which is bigger: 1/2 or 0.6?

Convert 1/2 to a decimal: 1 ÷ 2 = 0.5 Compare 0.5 and 0.6. 0.6 is bigger than 0.

5. Therefore, 0.6 is bigger than 1/2. 2.5 Simplifying Fractions: Simplifying a fraction means reducing it to its lowest terms. This is done by dividing both the numerator and the denominator by their greatest common factor (GCF).

Example: Simplify 8/12 The factors of 8 are 1, 2, 4, and

8. The factors of 12 are 1, 2, 3, 4, 6, and

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2. The GCF of 8 and 12 is

4. Divide both the numerator and denominator by 4: (8 ÷ 4) / (12 ÷ 4) = 2/3 Therefore, 8/12 simplified is 2/

3. Guided Practice (With Solutions)

Question 1: Calculate: 2/5 + 1/10 Solution: The LCD of 5 and 10 is

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0. Convert 2/5 to an equivalent fraction with a denominator of 10: (2 x 2) / (5 x 2) = 4/10 4/10 + 1/10 = 5/10 Simplify 5/10 by dividing by their GCF of 5: (5 ÷ 5) / (10 ÷ 5) = 1/2 Answer: 1/2 Question 2: Convert 0.85 to a fraction in its simplest form.

Solution: 0.85 = 85/100 The GCF of 85 and 100 is 5. (85 ÷ 5) / (100 ÷ 5) = 17/20 Answer: 17/20 Question 3: Sarah buys a packet of chips for R6.75 and a chocolate bar for R4.

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0. How much change does she get from R20?

Solution: First, find the total cost: R6.75 + R4.50 = R11.25 Then, subtract the total cost from R20: R20 - R11.25 = R8.75 Answer: R8.75 Question 4: Which is smaller: 3/8 or 0.4?

Solution: Convert 3/8 to a decimal: 3 ÷ 8 = 0.375 Compare 0.375 and 0.4. 0.375 is smaller than 0.4 Answer: 3/8 Question 5: Calculate 3 1/3 + 1 1/6 Solution: Convert mixed numbers to improper fractions: 3 1/3 = (3 x 3 + 1) / 3 = 10/3 1 1/6 = (1 x 6 + 1) / 6 = 7/6 Find LCD of 3 and 6, which is

6. Convert 10/3 to a fraction with a denominator of 6: (10 x 2) / (3 x 2) = 20/6 20/6 + 7/6 = 27/6 Convert the improper fraction back to a mixed number: 27/6 = 4 3/6 Simplify 3/6: 3/6 = 1/2 Answer: 4 1/2 Independent Practice (Questions Only)

Calculate: 1/4 + 2/5 Calculate: 5/6 - 1/3 Convert 0.25 to a fraction in its simplest form. Convert 7/20 to a decimal. John buys a pen for R3.50, a ruler for R2.75, and an eraser for R1.

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5. How much does he spend in total? Mary has R

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0. She spends R22.75 at the market.