Lesson Notes By Weeks and Term v5 - Grade 7
Fractions, decimals and percentages (Grade 7) – Week 9 focus
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Fractions, decimals and percentages (Grade 7) – Week 9 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: 9
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 absolutely crucial, not just for acing your maths exams, but also for navigating everyday life in South Africa. Imagine splitting a Gatsby with your friends, calculating discounts at Shoprite, or understanding the interest rates on your parents' loans – all of these involve fractions, decimals, and percentages! They are the building blocks for more advanced mathematical concepts you'll encounter in high school and beyond, and they are essential for financial literacy and problem-solving in general. A solid foundation now will benefit you immensely in the future.
Let's break down the core concepts: Fractions: A fraction represents a part of a whole. It's written as a/b, where 'a' is the numerator (the number of parts we have) and 'b' is the denominator (the total number of equal parts the whole is divided into). For example, 1/2 means one out of two equal parts. We also have proper fractions (numerator = denominator), and mixed numbers (whole number + a proper fraction).
Decimals: A decimal is another way to represent a part of a whole. It uses a base-10 system, where each digit to the right of the decimal point represents a fraction with a denominator that is a power of 10 (tenths, hundredths, thousandths, etc.). For example, 0.75 means 75 hundredths (75/100).
Percentages: Percent means "out of one hundred." A percentage is a way of expressing a number as a fraction of
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0. The symbol "%" is used to denote percentage. For example, 60% means 60 out of 100 (60/100). Converting between Fractions, Decimals, and Percentages: Fraction to Decimal: Divide the numerator by the denominator.
Example: 3/4 = 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 if possible.
Example: 0.6 = 6/10 = 3/5
Example: 0.25 = 25/100 = 1/4 Decimal to Percentage: Multiply the decimal by 100 and add the "%" sign.
Example: 0.8 = 0.8 x 100 = 80% Percentage to Decimal: Divide the percentage by
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0. Example: 45% = 45 ÷ 100 = 0.45 Fraction to Percentage: Convert the fraction to a decimal (by dividing numerator by denominator) and then convert the decimal to a percentage (by multiplying by 100).
Example: 1/5 = 1 ÷ 5 = 0.2 = 0.2 x 100 = 20% Finding a Percentage of a Quantity: To find x% of a quantity, multiply the quantity by x/
1
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0. Example: Find 20% of R50. 20% of R50 = (20/100) x R50 = 0.2 x R50 = R10 Increasing or Decreasing a Quantity by a Percentage: Increase: To increase a quantity by x%, multiply the quantity by (1 + x/100).
Example: Increase R200 by 15%. New amount = R200 x (1 + 15/100) = R200 x (1 + 0.15) = R200 x 1.15 = R230 Decrease: To decrease a quantity by x%, multiply the quantity by (1 - x/100).
Example: Decrease R200 by 15%. New amount = R200 x (1 - 15/100) = R200 x (1 - 0.15) = R200 x 0.85 = R170