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Numbers & Operations

Numbers & Operations. CRCT review. Real Numbers. All rational and irrational numbers – all numbers that can be expressed as a decimal Rational Numbers Irrational Numbers * natural numbers *whole numbers *integers. Natural Numbers. aka counting numbers ex: 1, 2, 3, 4, ….

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Numbers & Operations

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  1. Numbers & Operations CRCT review

  2. Real Numbers • All rational and irrational numbers – all numbers that can be expressed as a decimal Rational NumbersIrrational Numbers *natural numbers *whole numbers *integers

  3. Natural Numbers • aka counting numbers • ex: 1, 2, 3, 4, …

  4. Whole Numbers • The natural numbers and zero • ex: 0, 1, 2, 3, 4, …

  5. Integers • The set of whole numbers and their opposites • ex: …-4, -3, -2, -1, 0, 1, 2, 3, 4…

  6. Rational Numbers • A number that can be written as a/b, where a and b are integers and b doesn’t equal 0. • includes fractions, repeating/terminating decimals • ex: -1/4, 6/5, .0324, -3.272727

  7. Irrational Numbers • non-terminating and non-repeating decimals • Can’t be written as a/b • ex: 2.34567…, • All numbers that are not rational are irrational

  8. Rational or Irrational? 1. -7.2 2. 1.004 3. 4. 5. rational rational rational rational irrational

  9. Absolute Value • The distance a number is from 0 = 8 = 0 = 4 = -10

  10. Comparing/Ordering Rational Numbers • Write all numbers in the same form (all decimals, all fractions, or all percents) EX. Order the numbers from greatest to least

  11. Adding Signed (+/-) numbers 1. When numbers being added have the same sign, add the numbers and write the sign with the answer EX. 15 + 7 = 22 (-15) + (-7) = -22 2. When numbers being added have different signs: -subtract the absolute values of the numbers -use the sign of the number with the higher absolute value. EX. -15 + 7 = -8 (-7) + 15 = 8

  12. Subtracting Signed numbers • Add the opposite Ex. -15 – 7 = -22

  13. Multiplying/Dividing signed numbers • If there are an even number of (-), then the answer is (+) EX. (-2)(3)(-4) • If there are an odd number of (-), then the answer is (-) EX. (-2)(-3)(-4) = 24 = -24

  14. Adding/Subtracting Fractions • Must have a common denominator 3 12 10 12

  15. Multiplying fractions • Must write as improper fraction • Multiply the numerators • Multiply the denominators

  16. Dividing Fractions • Write as improper fractions • “When you have 2 fractions and you want to divide, flip the second fraction and multiply.”

  17. Adding/Subtracting Decimals • Line up the decimals • Add/subtract as normal • Write the decimal point in the answer

  18. Multiplying Decimals • Multiply as normal (ignore the decimals) • Count how many spaces over you need to place the decimal point in the answer

  19. Dividing Decimals • If the divisor (outside the house) has a decimal point in it, then you have to move the decimal to the end. • Move the decimal point in the dividend (inside the house) the same number of places.

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