Adding and Subtracting Real Numbers

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Adding and Subtracting Real Numbers
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Addition of Integers

• There are many ways to add integers
• You can add with a number line
• You can add using the plus and minus method
• You can add using the RULES of Addition

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Add two positive numbers

• You can use plus signs to represent the numbers
• 4 3 and 7
• 3 3
• 5 2
• 6 4
• 1 5
• When adding two positive numbers, you always get
  a positive answer!

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Add two negative numbers

• You can use minus signs to represent the
  numbers
• -4 (-3) ---- and --- -7
• -3 (-3)
• -5 (-2)
• -6 (-4)
• -1 (-5)
• When adding two negative numbers, you always get
  a negative answer!

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Adding one positive and one negative number

• A number and its opposite add to equal zero.
• That means that one positive sign and one
  negative sign cancel each other out.
• 4 (-3) and --- Rearrange so the opposite
  pairs are together - - - then pull out the
  cancelled pairs - - -
• and you are left with only ONE POSITIVE NUMBER
  so 4 (-3) 1

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Try these

• 5 (-3)
• -4 2
• -3 6
• 5 (-2)
• 7 (-3)
• -7 3
• Sometimes the answer is positive, sometimes the
  answer is negative. We have a rule so we dont
  get confused.

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RULES FOR ADDING INTEGERS

• If they have the SAME SIGN, SUM (add) the
  absolute values up and apply the common sign.
• If they have DIFFERENT SIGNS, take the DIFFERENCE
  (subtract) of the absolute values and apply the
  sign of the bigger absolute value.

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Subtraction of Integers

• You can show subtraction the same ways you do
  addition number line, blocks, chips, or the
  RULES of Algebra
• Heres how subtraction works.it means to TAKE
  AWAY something
• 5 2 or 5 take away 2
• to take away 2 ? you pull them out
  and you are left with or 3!

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Why ADD the Opposite?

• If I have the problem 2 5 it means have 2 on
  the table and take away 5. How can I take five
  away if there arent even 5 there yet? If you
  add on 5 zero pairs then you WILL have five to
  take away.
• You have 2 then ADD 5 zero pairs

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2 5 continued.

• Now take out the 5 you wanted to take away
• ?
• after rearranging and canceling zero pairs you
  get three RED or Negative pieces.
• So 2 5 -3

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2 5 AGAIN?! YES!

• Heres how Add the Opposite works
• What is the opposite of 5? Negative 5 or (-5)
• 2 5 becomes 2 (-5)
• Instead of subtracting 5, we ADDED the OPPOSITE
  of 5.
• 2 (-5) with Addition Rules that we already
  knowDifferent signs, take the difference use the
  sign of the bigger !
• 2 (-5) -3

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Try these.

• 4 (-2)
• 8 (-1)
• 3 4
• -5 2
• -4 (-3)
• -6 3
• 5 9

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One last thing

• Terms of an expression are the pieces or parts
  that are being added together. In order to
  determine the terms, you must ELIMINATE
  SUBTRACTION signs.
• x 3 2x 5 7x 10
• Change to addition
• x (-3) 2x (-5) (-7x) 10
• Identify all parts that are separated by a
• x, -3, 2x, -5, -7x, 10 are the TERMS of the
  expression