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The Basic of Algebra

The Basic of Algebra. BY Nathaniel Jefferson. The Number Line. ---------------|--------------- 0 Always start at zero. -|--|--|--|--|--|--|--|--|- -4 -3 -2 -1 0 1 2 3 4. Numbers that are positive move to the right of zero. Numbers that are negative move to the left of zero.

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The Basic of Algebra

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  1. The Basic of Algebra BY Nathaniel Jefferson

  2. The Number Line ---------------|--------------- 0 Always start at zero.

  3. -|--|--|--|--|--|--|--|--|--4 -3 -2 -1 0 1 2 3 4 Numbers that are positive move to the right of zero. Numbers that are negative move to the left of zero. A number on the number line is greater than any number to its left. A number on the number line is less than any number to its right.

  4. Answer the Questions • Which is greater, -5 or +3? • Which is greater, 2 or –10? • Which is greater, -4 or +4? • Which is smaller, -5 or –7? • Which is smaller, -9 or +3? • Which is smaller, -6 or 6?

  5. Use Symbols • > greater than • < less than • = is equal to • -9 _____ -2; +3 _____ -5; -1 ____ +1 • 5 ______ +5; 12 ____ -3; -1 _____ -2 • +8 _____ -8; -7 ____ -10; 2 _____ -3

  6. Adding Signed Numbers • Rule: To add two signed numbers, follow these steps: • If the signs are the same, add and give the total sign of the number. • If the signs are different, subtract and use the sign of the greatest value.

  7. Example of Adding Signed Numbers • Find (-16) + (-8) = • Find (+3) + (2) = • Find - 4 + (-1) = • Find - 9 – 3 = • Find +7 + (- 15) = • Find 7 – 15 = • Find ( - 9 ) + ( -4 ) + ( +8) = • Find –12 + ( 10 ) + ( - 8 ) + ( -3 ) =

  8. Subtracting Signed Numbers • Rule: To subtract sign numbers, follow these steps: • Always change the sign of the number being subtracted and drop the subtraction sign. • Follow the rule for adding sign numbers.

  9. Examples of Subtracting Signed Numbers • Find ( -8 ) – ( +3) = • ( - 8) + ( - 3) = -11 • Find ( -10) – ( - 2) = • ( -10) + (+ 2) = - 8 • Find ( 16 ) – ( - 4) = • ( + 16) + ( 4) = 20

  10. Solve the Subtraction Signed Numbers • Solve. (+ 6) – (+4) = • Solve. ( - 8 ) – ( + 7) = • Solve. ( -10) – ( +12) = • Solve. ( +5) – ( - 1) = • Solve. ( - 15) – ( 20 ) = • Solve. ( - 60) – ( - 45) = • Solve. ( -9) – ( +4) – ( +10) =

  11. Multiplying Signed Numbers • Rule: To multiply two signed, follow these steps: • Multiply the two numbers. • If the signs of the two numbers are alike, make the product positive. • If the signs of the two numbers are different, make the product negative.

  12. Examples of Multiplying Signed Numbers • Find the product of ( -8 ) and ( -7) • ( -8) ( -7) = + 56 or 56 • Find the product of ( -2) and (+9) • ( - 2) ( +9) = - 18 • Find the product of – 7 * - 4 • ( -7) ( -4) = +28 or 28 • Find the product of ( +5) ( +4) ( - 2) = • [( +5) ( +4)] (- 2) = • ( +20) ( -2) = - 40

  13. Dividing Signed Numbers • Rule: To divide two signed numbers, follow these steps: • Divide or reduce the numbers. • If the signs are alike, make the quotient (answer) positive. • If the signs are different, make the quotient (answer) negative.

  14. Examples of Dividing Signed Numbers • Find (+30)/( -6) = • (+30)/( - 6) = - 5 • Find – 40/ - 20 = • ( - 40)/ ( - 20) = 2 or +2 • Find – 12 / + 6 = • Find 72 / - 9 = • Find 30 / - 36 =

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