Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Convert fractions (denominators 10, 100, 1000) to decimals and back.
• Compare and order decimals up to two decimal places.
• Add and subtract decimals, especially with money.
• Recognize equivalent fractions and decimals.

Lesson summary

This week, we're diving deeper into the fascinating world of fractions and decimals! Understanding fractions and decimals is crucial, not just in school, but in everyday life here in South Africa. From splitting a pizza with your friends, understanding the price of a discounted pair of takkies (shoes) at a shop, to measuring ingredients when baking malva pudding, fractions and decimals are everywhere. They help us understand parts of a whole and represent quantities accurately. Imagine trying to share a slab of chocolate equally without knowing about fractions! This week will build upon what you've already learned about fractions and introduce the connection to decimals.

Lesson notes

What are Fractions? A fraction represents a part of a whole.

It has two parts: the numerator (the top number) and the denominator (the bottom number). 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. For example, in the fraction 3/4, the denominator (4) tells us the whole is divided into 4 equal parts, and the numerator (3) tells us we have 3 of those parts. What are Decimals? Decimals are another way of representing parts of a whole. They use a decimal point to separate the whole number part from the fractional part. The digits after the decimal point represent tenths, hundredths, thousandths, and so on.

Tenths: The first digit after the decimal point represents tenths (1/10). For example, 0.1 is one tenth.

Hundredths: The second digit after the decimal point represents hundredths (1/100). For example, 0.01 is one hundredth.

Thousandths: The third digit after the decimal point represents thousandths (1/1000). For example, 0.001 is one thousandth. Converting Fractions to Decimals (and vice versa): The easiest way to convert fractions to decimals is when the denominator is 10, 100, or

1

0

0

0. Example 1: Converting a fraction to a decimal: Convert 7/10 to a decimal. Since the denominator is 10, we know the decimal will have one digit after the decimal point. The numerator (7) becomes the digit after the decimal point.

Therefore, 7/10 = 0.7 Example 2: Converting a fraction to a decimal: Convert 45/100 to a decimal. Since the denominator is 100, we know the decimal will have two digits after the decimal point. The numerator (45) becomes the two digits after the decimal point.

Therefore, 45/100 = 0.45 Example 3: Converting a fraction to a decimal: Convert 123/1000 to a decimal. Since the denominator is 1000, we know the decimal will have three digits after the decimal point. The numerator (123) becomes the three digits after the decimal point.

Therefore, 123/1000 = 0.123 Example 4: Converting a decimal to a fraction: Convert 0.3 to a fraction. The decimal has one digit after the decimal point, so the denominator will be

1

0. The digit after the decimal point (3) becomes the numerator.

Therefore, 0.3 = 3/10 Example 5: Converting a decimal to a fraction: Convert 0.65 to a fraction. The decimal has two digits after the decimal point, so the denominator will be

1

0

0. The digits after the decimal point (65) become the numerator.

Therefore, 0.65 = 65/100 Comparing and Ordering Decimals: To compare decimals, we first look at the whole number part. If the whole number parts are the same, we compare the digits after the decimal point, starting with the tenths place, then the hundredths place, and so on.

Example 1: Compare 0.6 and 0.

5

8. The whole number part is 0 in both cases. The tenths digit of 0.6 is

6. The tenths digit of 0.58 is

5. Since 6 is greater than 5, 0.6 is greater than 0.58. (0.6 > 0.58) We can also think of 0.6 as 0.60, so it's easier to compare to 0.

5

8. Example 2: Order the following decimals from smallest to largest: 0.25, 0.3, 0.19, 0.32 19 (smallest, as the tenths digit '1' is the smallest) 25 3 (which is the same as 0.30) 32 (largest)

Adding and Subtracting Decimals (Money): When adding or subtracting decimals, it is crucial to line up the decimal points. This ensures that you are adding or subtracting the correct place values (tenths with tenths, hundredths with hundredths, etc.). This is particularly important when working with money. Remember that in South Africa, we use Rands and cents. 1 Rand is equal to 100 cents.

Example 1: Adding decimals (Money): Aisha buys a packet of chips for R4.50 and a Coke for R6.

2

5. How much does she spend in total? Write the numbers vertically, lining up the decimal points: ``` R 4.50 + R 6.25 --------- ``` Add each column, starting from the right: 0 + 5 = 5, 5 + 2 = 7, 4 + 6 =

1

0. Bring down the decimal point. The answer is R10.

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5. Example 2: Subtracting decimals (Money): Sipho has R

2

0. He buys a Simba chips for R7.

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0. How much change does he receive? Write the numbers vertically, lining up the decimal points: ``` R 20.00 R 7.80 --------- ``` Subtract each column, starting from the right. We need to borrow from the Rands column to subtract the cents. 0 - 0 = 0 0 - 8 (borrow one from the 20, so 10-8 = 2, leaving 19 at the top). 9 - 7 = 2 1 – 0 = 1 Bring down the decimal point. The answer is R12.

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0. Equivalent Fractions and Decimals: Equivalent fractions and decimals represent the same value, even though they look different.

Example: 1/2 is equivalent to 0.5 (one half is the same as five tenths) and also to 50/100 (fifty hundredths).

Example: If you have half a loaf of bread (1/2) and someone else has 50 hundredths of a loaf (50/100 or 0.50), you both have the same amount of bread. Guided Practice (With Solutions)

Question 1: Convert the following fraction to a decimal: 8/10 Solution: The denominator is 10, so the decimal will have one digit after the decimal point.