Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Convert fractions (denominators 10, 100, 1000) to decimals.
• Convert decimals (up to two places) to fractions.
• Compare and order decimals.
• Add and subtract decimals, especially with money.
• Solve word problems using decimals.

Lesson summary

Fractions and decimals are essential tools for understanding the world around us. In South Africa, we use them daily, from sharing a koeksister fairly amongst friends to calculating discounts at the shops. Understanding these concepts will help you make informed decisions, solve everyday problems, and build a strong foundation for future mathematics studies. This week, we'll be focusing on further developing your understanding of the relationship between fractions and decimals, with an emphasis on converting between them and using them in calculations.

Lesson notes

Understanding the Relationship Between Fractions and Decimals Fractions and decimals are simply different ways of representing parts of a whole. A fraction expresses a part of a whole as a ratio of two numbers (numerator and denominator), while a decimal expresses a part of a whole using a base-10 system. The connection becomes clearest when the fraction has a denominator of 10, 100, or

1

0

0

0. Denominator of 10: A fraction with a denominator of 10 represents tenths. For example, 3/10 means 3 out of 10 equal parts. As a decimal, this is written as 0.3 (zero point three). The '3' is in the tenths place.

Denominator of 100: A fraction with a denominator of 100 represents hundredths. For example, 45/100 means 45 out of 100 equal parts. As a decimal, this is written as 0.45 (zero point forty-five). The '4' is in the tenths place, and the '5' is in the hundredths place.

Denominator of 1000: A fraction with a denominator of 1000 represents thousandths. For example, 123/1000 means 123 out of 1000 equal parts. As a decimal, this is written as 0.123 (zero point one two three). The '1' is in the tenths place, the '2' is in the hundredths place, and the '3' is in the thousandths place. Converting Fractions to Decimals To convert a fraction with a denominator of 10, 100, or 1000 to a decimal, simply write the numerator after the decimal point, ensuring it occupies the correct place value.

Example 1: Convert 7/10 to a decimal. The denominator is 10, so we're dealing with tenths. The numerator is

7. Therefore, 7/10 = 0.7 Example 2: Convert 63/100 to a decimal. The denominator is 100, so we're dealing with hundredths. The numerator is

6

3. Therefore, 63/100 = 0.63 Example 3: Convert 5/100 to a decimal. The denominator is 100, so we're dealing with hundredths. The numerator is

5. Since we need two places after the decimal point to represent hundredths, we add a zero as a placeholder.

Therefore, 5/100 = 0.05 Converting Decimals to Fractions To convert a decimal to a fraction, identify the place value of the last digit. If it's in the tenths place, the denominator is

1

0. If it's in the hundredths place, the denominator is

1

0

0. The numerator is the number after the decimal point.

Example 1: Convert 0.4 to a fraction. The last digit (4) is in the tenths place.

Therefore, the denominator is

1

0. The numerator is

4. Therefore, 0.4 = 4/10 Example 2: Convert 0.75 to a fraction. The last digit (5) is in the hundredths place.

Therefore, the denominator is

1

0

0. The numerator is

7

5. Therefore, 0.75 = 75/100 Comparing and Ordering Decimals To compare decimals, start by comparing the whole number part. If the whole number parts are the same, compare the digits in the tenths place, then the hundredths place, and so on.

Example: Compare 0.6 and 0.

5

8. Both decimals have a whole number part of

0. Comparing the tenths place, 0.6 has 6 tenths, and 0.58 has 5 tenths. Since 6 is greater than 5, 0.6 > 0.58 (0.6 is greater than 0.58) Adding and Subtracting Decimals When adding or subtracting decimals, it's important to align the decimal points. This ensures that you are adding or subtracting digits with the same place value (tenths with tenths, hundredths with hundredths, etc.). You can add zeros as placeholders if needed.

Example 1: Add 0.35 and 0.2. ``` 0.35 + 0.20 (Added a zero as a placeholder) 0.55 ``` Example 2: Subtract 0.8 from 1.25 ``` 1.25 0.80 (Added a zero as a placeholder) 0.45 ``` Working with Money When dealing with money (Rands and cents), remember that 1 Rand is equal to 100 cents.

Therefore, amounts of money are naturally expressed as decimals. For example, R5.75 represents 5 Rands and 75 cents. Guided Practice (With Solutions)

Question 1: Convert 2/10 to a decimal.

Solution: The denominator is 10 (tenths). The numerator is

2. Therefore, 2/10 = 0.2

Commentary: This is a straightforward application of the conversion rule. We directly write the numerator after the decimal point since we are dealing with tenths.

Question 2: Convert 0.85 to a fraction.

Solution: The last digit (5) is in the hundredths place. The denominator is

1

0

0. The numerator is

8

5. Therefore, 0.85 = 85/100

Commentary: It is important to identify the place value of the last digit to choose the correct denominator (10 or 100).

Question 3: Which is bigger: 0.7 or 0.65?

Solution: Both have a whole number part of

0. Comparing the tenths place: 0.7 has 7 tenths and 0.65 has 6 tenths. Since 7 > 6, 0.7 > 0.65

Commentary: Remember to compare place values starting from the left. Comparing tenths before hundredths is crucial here.

Question 4: Sipho buys a loaf of bread for R12.50 and a packet of chips for R8.

2

5. How much does he spend in total?

Solution: ``` R12.50 + R 8.25 R20.75 ``` Sipho spends R20.75 in total.

Commentary: Aligning the decimal points is crucial in addition and subtraction of decimals. Ensuring all monetary values are in the same denomination (Rands and cents) also helps prevent errors.

Question 5: Thandi has R

5

0. She buys a juice for R15.75.