 # The Basic of Algebra BY Nathaniel Jefferson. The Number Line  ---------------|---------------  0 Always start at zero.

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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.  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.

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?

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

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.

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 ) =

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.

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

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) =

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.

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

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.

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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