Lesson Notes By Weeks and Term v5 - Grade 7
Fractions, decimals and percentages (Grade 7) – Week 6 focus
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Fractions, decimals and percentages (Grade 7) – Week 6 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 7
Term: 1st Term
Week: 6
Theme: General lesson support
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This week, we delve deeper into the interconnected world of fractions, decimals, and percentages. Understanding these concepts is crucial not just for Mathematics, but also for navigating everyday life in South Africa. From calculating discounts at your local supermarket to understanding interest rates on a savings account or figuring out cricket averages, these skills are essential. Fractions, decimals, and percentages are different ways of representing parts of a whole, and this week, we will focus on converting between them, comparing them, and applying them to solve real-world problems. This understanding will build a solid foundation for more advanced mathematical concepts later on.
What are Fractions, Decimals, and Percentages?
Fractions: A fraction represents a part of a whole. It is written as a/b, where 'a' is the numerator (the number of parts we have) and 'b' is the denominator (the total number of parts). For example, 1/2 means one out of two equal parts.
Decimals: A decimal is another way to represent a part of a whole. It uses a decimal point to separate the whole number part from the fractional part. For example, 0.5 represents five-tenths or half.
Percentages: A percentage is a way of expressing a number as a fraction of
1
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0. The word "percent" means "per hundred" or "out of 100." It is represented by the symbol %. For example, 50% means 50 out of 100, or half. Converting Between Fractions, Decimals, and Percentages: Fraction to Decimal: Divide the numerator by the denominator.
Example: Convert 3/4 to a decimal. 3 ÷ 4 = 0.75 Decimal to Fraction: Write the decimal as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places. Simplify the fraction to its lowest terms.
Example: Convert 0.25 to a fraction. 0.25 = 25/100 = 1/4 Fraction to Percentage: Convert the fraction to a decimal (by dividing), then multiply by 100%.
Example: Convert 1/5 to a percentage. 1 ÷ 5 = 0.2. 0.2 x 100% = 20% Percentage to Fraction: Write the percentage as a fraction with a denominator of 100 and simplify.
Example: Convert 75% to a fraction. 75/100 = 3/4 Decimal to Percentage: Multiply the decimal by 100%.
Example: Convert 0.8 to a percentage. 0.8 x 100% = 80% Percentage to Decimal: Divide the percentage by
1
0
0. Example: Convert 15% to a decimal. 15 ÷ 100 = 0.15 Comparing Fractions, Decimals, and Percentages: To compare them, convert them all to the same form (either all fractions, all decimals, or all percentages). Then compare the numbers.
Example: Which is larger: 1/2, 0.6, or 45%?
Convert 1/2 to a decimal: 1 ÷ 2 = 0.5 Convert 45% to a decimal: 45 ÷ 100 = 0.45 Now we can compare: 0.5, 0.6, and 0.45. 0.6 is the largest.
Therefore, 0.6 is the largest.
Percentage Increase and Decrease: Percentage Increase: To find the percentage increase, calculate the amount of increase, divide by the original amount, and multiply by 100%.
Formula: ((New Value - Original Value) / Original Value) x 100% Percentage Decrease: To find the percentage decrease, calculate the amount of decrease, divide by the original amount, and multiply by 100%.
Formula: ((Original Value - New Value) / Original Value) x 100% Expressing one quantity as a percentage of another: Divide the quantity you are expressing as a percentage by the total quantity, and then multiply by 100%.
Formula: (Quantity / Total Quantity) x 100%