www.numberpower.org Integers What are integers? Integers are either positive or negative, but they are not decimals and are not fractions. Before you can understand integers you need to understand operation signs. An operation sign tells you what to do in a problem. It tells you to add, subtract, multiply or divide. The problem (4 + 3) has an addition operation sign, which means that you are adding the two numbers 4 and 3. The problem (9 x 5) has the multiplication operation sign, which means that you multiply to solve the problem. What is a positive integer? A positive integer has a (+) or addition sign in front of the number and looks like ( 9 or (+ 9). Did you notice a positive integer doesn't need a sign? Think of (+4) as your have 4 cents. What is a negative integer? A negative integer has a (-) or negative sign in front of the number and looks like (- 12) when written on a computer. You can think of a negative integer as owing someone something. Think of it as (-7) means owing someone 7 cents. Zero in neither positive or negative and is always larger than a negative integer. Positive integers are always larger than zero and any negative number. The larger a positive integer is the bigger it is. Therefore a +7 is greater than a +5, written another way +7 > +5. The larger a negative integer is the smaller in value it is - think of (- 6) and (- 7), which is it better to do - Owe someone 6 cents or 5 cents - why 5 cents of course. Therefore (-6) < (-5). When written on a number line integers would look like this: _____________________________________________________ (-6) (-5) (-4) (-3) (-2) (-1) O (+1) (+2) (+3) (+4) (+5) (+6) and so on Integer multiplication operation sign and division operation sign follow the same rules: 1) Like signs are positive (+5) x (+6) = (+30) or 30 and (- 55) ÷ ( - 5) = (+11) or 11 2) Unlike signs are negative (+12) ÷ (- 4) = (- 3) and (+7) x (- 4) = (- 28) Integer addition operation sign rules: 1) Like signs you add 2) Unlike signs you subtract 3) Take the sign of the highest number ( yes Number). Like signs add and take sign of highest number (+5) + (+6 ) = (+11) and (- 55) + (- 5) = (- 60) Unlike signs subtract and take sign of the highest number (+12) + (- 4) = (+ 8) and (- 7) + (+ 4) = (- 3) Integer subtraction operation sign rules: 1) Change the subtraction operation sign to it's reciprocal - addition operation sign 2) Change the operation sign of the integer that follows to its reciprocal 3) Use the addition operation sign rules. Change the subtraction operation sign to it's reciprocal - addition operation sign (- 8) - (+ 7) = becomes (- 8) - (+ 7) = Change the operation sign of the integer that follows to its reciprocal (- 8) - (+ 7) = becomes (- 8) + (- 7) = Use the addition operation sign rules. (- 8) + (- 7) = (-15) 