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The Basic of Algebra BY Nathaniel Jefferson

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The Number Line ---------------|--------------- 0 Always start at zero.

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-|--|--|--|--|--|--|--|--|- -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.

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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?

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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

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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.

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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 ) =

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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.

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

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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) =

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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.

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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

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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.

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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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