Lesson Notes By Weeks and Term v5 - Grade 5
Fractions and decimals (Grade 5) – Week 7 focus
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Fractions and decimals (Grade 5) – Week 7 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 5
Term: 1st Term
Week: 7
Theme: General lesson support
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This week, we will be diving deeper into the relationship between fractions and decimals. Understanding this relationship is crucial because fractions and decimals are everywhere around us! Whether you're sharing a chocolate bar with your friends, measuring ingredients for a delicious koeksister recipe, or figuring out how much money you've saved from your pocket money, knowing how fractions and decimals work together will make your life much easier and help you solve problems every day. In South Africa, where sharing and resourcefulness are important values, understanding fractions and decimals helps us share fairly and manage our resources wisely.
Understanding the Connection Fractions and decimals are different ways of representing parts of a whole. A fraction shows how many parts we have out of a total number of parts, while a decimal uses a base-ten system to represent these parts.
Think of it this way: a fraction is like saying "I have a piece of the pie," while a decimal tells you exactly how much of the pie you have, in a more precise way. Fractions to Decimals The easiest way to convert a fraction to a decimal is when the denominator (the bottom number) is a power of 10 (10, 100, 1000, etc.).
Denominator of 10: The digit in the numerator (the top number) represents the tenths place in the decimal.
Denominator of 100: The digits in the numerator represent the tenths and hundredths places in the decimal.
Denominator of 1000: The digits in the numerator represent the tenths, hundredths, and thousandths places in the decimal.
Example 1: Convert 3/10 to a decimal.
Explanation: We have 3 parts out of
1
0. This means we have 3 tenths.
Decimal Form: 0.3 Example 2: Convert 47/100 to a decimal.
Explanation: We have 47 parts out of
1
0
0. This means we have 47 hundredths.
Decimal Form: 0.47 Example 3: Convert 123/1000 to a decimal.
Explanation: We have 123 parts out of
1
0
0
0. This means we have 123 thousandths.
Decimal Form: 0.123 Important
Note: If the numerator has fewer digits than the number of zeros in the denominator, you need to add zeros as placeholders before the digits of the numerator.
Example 4: Convert 7/100 to a decimal.
Explanation: We have 7 parts out of
1
0
0. We need two decimal places (tenths and hundredths), but 7 only has one digit. So, we add a zero before the
7. Decimal Form: 0.07 Decimals to Fractions Converting decimals to fractions is the reverse process. The place value of the last digit in the decimal tells you what the denominator should be.
One decimal place (tenths): The denominator is
1
0. Two decimal places (hundredths): The denominator is
1
0
0. Example 5: Convert 0.6 to a fraction.
Explanation: The last digit, 6, is in the tenths place. So, the denominator is
1
0. The numerator is the number without the decimal point (6).
Fraction Form: 6/10 Example 6: Convert 0.85 to a fraction.
Explanation: The last digit, 5, is in the hundredths place. So, the denominator is
1
0
0. The numerator is the number without the decimal point (85).
Fraction Form: 85/100 Number Line Representation Both fractions and decimals can be represented on a number line. To accurately place them, divide the space between whole numbers into the correct number of equal parts based on the denominator (for fractions) or the place value (for decimals).
Example 7: Represent 0.4 and 3/10 on a number line.
Explanation: Both 0.4 and 3/10 represent four tenths and three tenths respectively. Divide the space between 0 and 1 into 10 equal parts. 0.4 will be at the fourth mark, and 3/10 at the third mark. Comparing Decimals To compare decimals, start by comparing the whole number part. If the whole number parts are the same, compare the tenths place, then the hundredths place, and so on.
Example 8: Compare 0.6 and 0.54 Explanation: Both numbers have 0 as the whole number part. Comparing the tenths place, 0.6 has 6 tenths, while 0.54 has 5 tenths. Since 6 is greater than 5, 0.6 is greater than 0.
5
4. Comparison: 0.6 > 0.54 Guided Practice (With Solutions)
Question 1: Convert 9/10 to a decimal.
Solution: Step 1: The denominator is 10, so we have tenths.
Step 2: The numerator is 9, so we have 9 tenths.
Answer: 0.9 Question 2: Convert 0.23 to a fraction.
Solution: Step 1: The last digit (3) is in the hundredths place, so the denominator is
1
0
0. Step 2: The number without the decimal is 23, so the numerator is
2
3. Answer: 23/100 Question 3: Represent 0.7 on a number line between 0 and
1. Solution: Step 1: Draw a number line between 0 and
1. Step 2: Divide the number line into 10 equal parts.
Step 3: Place a dot at the 7th mark. This represents 0.
7. Answer: [Visual representation on a number line with 0.7 marked] Question 4: Compare 0.8 and 0.75 using , or =.
Solution: Step 1: Both numbers have 0 as the whole number part.
Step 2: Compare the tenths place: 0.8 has 8 tenths, and 0.75 has 7 tenths.
Step 3: Since 8 is greater than 7, 0.8 is greater than 0.
7
5. Answer: 0.8 > 0.75 Independent Practice (Questions Only) Convert 6/100 to a decimal. Convert 0.4 to a fraction. Convert 35/100 to a decimal. Convert 0.09 to a fraction. Convert 11/10 to a decimal. Represent 0.3 and 0.6 on a number line between 0 and
1. Compare 0.2 and 0.20 using , or =. Compare 0.9 and 0.89 using , or =. Arrange the following numbers in ascending order: 0.5, 1/10, 0.25, 7/
1
0. What decimal is halfway between 0.1 and 0.3?