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 delve deeper into the fascinating relationship between fractions and decimals. Understanding fractions and decimals is crucial in everyday life, from sharing a pizza fairly with your friends after a soccer game to calculating discounts at your local spaza shop or understanding the nutritional information on the packaging of your favourite Simba chips. In South Africa, where resource sharing and budgeting are essential aspects of daily living, a solid grasp of fractions and decimals becomes even more important. This week's focus is on converting fractions to decimals and vice-versa, and comparing and ordering decimals.
Fractions and Decimals: A Close Relationship Fractions and decimals are simply different ways of representing parts of a whole. Think of a loaf of bread cut into equal slices. Each slice represents a fraction of the whole loaf. Decimals, similarly, represent parts of a whole using a base-10 system. This means each place value to the right of the decimal point represents a power of ten (tenths, hundredths, thousandths, and so on). Converting Fractions to Decimals (Denominators of 10, 100, 1000) The easiest fractions to convert to decimals are those with denominators of 10, 100, and
1
0
0
0. This is because the place values in decimals are based on powers of
1
0. Fractions with a denominator of 10: The numerator becomes the digit in the tenths place.
Example: 3/10 = 0.3 (Read as "zero point three" or "three tenths").
Think: You are dividing the whole into 10 equal parts, and you have 3 of those parts.
Fractions with a denominator of 100: The numerator becomes the digits in the tenths and hundredths places. If the numerator is a single digit, place a 0 in the tenths place.
Example: 27/100 = 0.27 (Read as "zero point two seven" or "twenty-seven hundredths").
Example: 5/100 = 0.05 (Read as "zero point zero five" or "five hundredths").
Think: You are dividing the whole into 100 equal parts, and you have 27 or 5 of those parts.
Fractions with a denominator of 1000: The numerator becomes the digits in the tenths, hundredths, and thousandths places. If the numerator has fewer than three digits, place 0s in the necessary place values.
Example: 123/1000 = 0.123 (Read as "zero point one two three" or "one hundred and twenty-three thousandths").
Example: 9/1000 = 0.009 (Read as "zero point zero zero nine" or "nine thousandths").
Example: 50/1000 = 0.050 (Read as "zero point zero five zero" or "fifty thousandths"). Note that 0.050 is the same as 0.05 Think: You are dividing the whole into 1000 equal parts, and you have 123, 9, or 50 of those parts. Converting Decimals to Fractions (Tenths, Hundredths, Thousandths) Converting decimals back to fractions involves identifying the place value of the last digit.
Decimals to Tenths: The digit in the tenths place becomes the numerator, and the denominator is
1
0. Example: 0.7 = 7/10 Think: "Zero point seven" means seven tenths, so write 7 over
1
0. Decimals to Hundredths: The digits in the tenths and hundredths places together become the numerator, and the denominator is
1
0
0. Example: 0.45 = 45/100 Think: "Zero point four five" means forty-five hundredths, so write 45 over
1
0
0. Decimals to Thousandths: The digits in the tenths, hundredths, and thousandths places together become the numerator, and the denominator is
1
0
0
0. Example: 0.678 = 678/1000 Think: "Zero point six seven eight" means six hundred and seventy-eight thousandths, so write 678 over
1
0
0
0. Comparing and Ordering Decimals Comparing and ordering decimals is like comparing and ordering whole numbers, but you need to pay close attention to the place value of each digit. Start by comparing the whole number part. If the whole number parts are different, the decimal with the larger whole number part is greater.
Example: 3.5 is greater than 2.9 because 3 is greater than
2. If the whole number parts are the same, compare the tenths place. The decimal with the larger digit in the tenths place is greater.
Example: 0.6 is greater than 0.4 because 6 is greater than
4. If the tenths places are the same, compare the hundredths place. The decimal with the larger digit in the hundredths place is greater.
Example: 0.37 is greater than 0.32 because 7 is greater than
2. If the hundredths places are the same, compare the thousandths place. The decimal with the larger digit in the thousandths place is greater.
Example: 0.125 is greater than 0.121 because 5 is greater than
1. Important Tip: If a decimal has fewer digits than another, you can add zeros to the end without changing its value to make the comparison easier. For example, to compare 0.5 and 0.56, you can think of 0.5 as 0.
5
0. Now it is easy to see that 0.56 is greater than 0.
5
0. Representing Fractions and Decimals on a Number Line A number line provides a visual representation of fractions and decimals. When representing them, divide the space between whole numbers into equal parts based on the denominator of the fraction or the place value of the decimal.
Example: To represent 0.4 on a number line, divide the space between 0 and 1 into ten equal parts. 0.4 will be at the fourth mark.
Example: To represent 3/10 on a number line, divide the space between 0 and 1 into ten equal parts. 3/10 will be at the third mark. Notice that both 0.4 and 3/10 are at the same point! Guided Practice (With Solutions)
Question 1: Convert the fraction 7/10 to a decimal.
Solution: The denominator is 10, so the numerator (7) goes in the tenths place. The decimal is 0.
7. Question 2: Convert the decimal 0.63 to a fraction.
Solution: The decimal extends to the hundredths place.