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Rational Numbers

Number: Rational Numbers & Indices. By the end of this lesson you will be able to explain and calculate the following: A Rational Number An Irrational Number Order of Operations. Rational Numbers. Real Numbers. We use numbers such as integers, fractions and decimals every day.

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Rational Numbers

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  1. Number:Rational Numbers & Indices By the end of this lesson you will be able to explain and calculate the following: A Rational Number An Irrational Number Order of Operations Rational Numbers

  2. Real Numbers • We use numbers such as integers, fractions and decimals every day. • They form part of what is called the Real Number System. • Real numbers can be divided into two categories • rational numbers and • irrational numbers

  3. The set of real numbers, R • The set of real numbers is a collection that contains natural, integer, rational and irrational numbers. • Let us first define each of these sets and see their relationship to each other.

  4. Order of operations using integers • Anton has calculated the answer to 5 + 6 × 4 as 44 • Marco insists that the answer is 29. • Who is correct? • The order of operations requires that: • all expressions in brackets are evaluated first, beginning with the innermost pair of brackets • then, all multiplication and division are evaluated, working from left to right • and finally, any addition and subtraction, working from left to right. B.O.D.M.A.S

  5. Worked Example

  6. Worked Example

  7. A number line can help us with negative numbers -3 + 4 = 1 This is our start number This is the number of places we need to move This is the direction of move - +

  8. A number line can help us with negative numbers -3 - 4 = -7 This is our start number This is the number of places we need to move This is the direction of move - +

  9. What calculation do you think this number line represents? -3 + 4 = 1 -4 – 6 = -10

  10. Now.…there is one more thing we need to know. Remembering AIS and SID can help us with this next stage. A I S and S I D

  11. AIS = Add IfSame Look at the signs in the middle, if they are the same, then replace them with +. + 8 - - 6 = 14

  12. AIS = Add If Same + -2 - - 5 = 3

  13. SID = Subtract If Different Look at the signs in the middle, if they are different, then replace them with -. - 8 + - 6 = 2

  14. SID = Subtract If Different - -4 + - 6 = -10

  15. Can you use all your knowledge of negative numbers so far to find the answer to these calculations? Remember: This is your start number and the new sign in the middle is the direction But what about this one? - -6 + -2 = -6 - -8 = -8 2 +

  16. Multiplying / Dividing • When multiplying integers, the following rules are obeyed. • Positive × Positive = Positive 5 × 8 = 40 • Positive × Negative = Negative 5 × −8 = −40 • Negative × Positive = Negative −5 × 8 = −40 • Negative × Negative = Positive −5 × −8 = 40 • When dividing integers, use the same rules • Positive ÷ Positive = Positive 16 ÷ 2 = 8 • Positive ÷ Negative = Negative 16 ÷ −2 = −8 • Negative ÷ Positive = Negative −16 ÷ 2 = −8 • Negative ÷ Negative = Positive −16 ÷ −2 = 8

  17. Multiplying / Dividing • When multiplying and dividing integers: • like signs give positive answers, • unlike signs give negative answers.

  18. Homework Answers

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