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1.8 Chapter summary

  • Natural numbers are those numbers that we use for counting. The set of whole numbers includes all the natural numbers along with zero.
  • A number that cannot be expressed as a product of two whole numbers, except as the product of \(1\) and the number itself, is called a prime number.
  • Composite numbers are natural numbers with more than two different factors.
  • \(1\) is neither prime nor composite.
  • If a whole number is not divisible by \(2\), then it is odd.
  • Addition and multiplication are commutative. The numbers can be swopped around and their order does not change the answer.
  • If three or more numbers must be multiplied, it does not matter which two of the numbers are multiplied first. In the same way, if three or more numbers must be added, it does not matter which two of the numbers are added first. This is called the associative property of addition and multiplication.
  • Addition and multiplication are distributive:
    • \[a(b + c) = a \times b + a \times c\]
    • \[a(b - c) = a \times b - a \times c\]
  • Addition and subtraction as inverse operations.
  • Multiplication and division as inverse operations.
  • The additive property of \(0\): when we add zero to any number, the answer is that number.
  • Any number divided by \(0\) is undefined.
  • Any number multiplied by \(0\) is \(0\).
  • When dividing by \(1\), the answer remains the same.
  • To estimate is to try to get close to an answer without actually doing the required calculations with the given numbers. An estimate may also be called an approximation
  • The sum is what you get after you do addition. We can add in any order.
  • The difference is what is left after you do subtraction. We must subtract in the given order.
  • The product is what you get after you do multiplication. We can multiply in any order.
  • The quotient is what is left after you do division.
  • If \(n\) is a natural number, then \(2n\) represents the multiples of \(2\).
  • A multiple of any natural number is a value that is equal to the original number multiplied by another natural number.
  • The factor of a natural number can divide into that number perfectly without leaving a remainder.
  • The ladder method is a way of finding the prime factors of a number. You divide the number by prime numbers, until you get \(1\).
  • An LCM is the lowest common multiple of two or more numbers.
  • An HCF is the highest common factor of two or more numbers
  • A rate compares two quantities of different kinds. Speed is one example that describes the rate of movement compared with time.
  • We use ratios to show how many times more, or less, one quantity is than another. A ratio is a comparison of two (or more) quantities.
  • The amount for which a dealer buys an article from a producer or manufacturer is called the cost price. The price marked on the article is called the marked price and the price of the article after discount is the selling price.
  • The discount on an article is a percentage (or fraction) of the marked price of the article, so it is always less.
  • A percentage is a number of hundredths.
  • A budget is a plan about how you will spend, and save, your money.
  • The profit is the amount by which the selling price exceeds the costs: profit = selling price – cost price.
  • The loss is the amount by which the costs exceed the selling price: loss = cost price – selling price.
  • When a person borrows money from a bank or some other institution, they normally have to pay for the use of the money. This is called interest.
  • Value added tax (VAT) is an amount added to the price of goods. The current VAT percentage in South Africa is \(15\%\).
  • A hire purchase agreement is a credit agreement between a buyer and a financial institution. The agreement is about hiring instead of purchasing an item. The buyer pays an agreed amount in monthly payments. The item does not belong to the buyer until the final payment is made.
  • An exchange rate is the amount of money in one currency that we pay to get another currency.