POSITIVE AND NEGATIVE INTEGERS
POSITIVE AND NEGATIVE INTEGERSINSTRUCTION SHEETA. Rules for Adding Positive and Negative NumbersTo add two positive numbers, add and keep the positive signExample: (+6) + (+7) = +13To add two negative numbers, add and keep the negative signExample: (-13) + (-24) = -37To add numbers with different signs, find the difference between the two numbers (subtract) and give the answer the sign of the larger numberExample #1: (+17) + (-6) = +11Example #2: (-32) + (+18) = -14B. Rules for Subtracting Positive and Negative NumbersTo subtract signed numbers (either positive or negative), change the subtraction sign to addition and change the sign of the number that follows, then revert back to the addition rulesExample #1: (+8) - (+5) = (+8) + (-5) = +3Example #2: (+7) - (-4) = (+7) + (+4) = +11Example #3: (-12) - (+6) = (-12) + (-6) = -18Example #4: (-23) - (-16) = (-23) + (+16) = -7C. Rules for Multiplying and Dividing Positive and Negative NumbersWith both multiplication and division, when the signs are the same, the answer will be positiveExample #1: (+5) × (+7) = +35Example #2: (-5) × (-7) = +35Example #3: (+10) ÷ (+2) = +5Example #4: (-10) ÷ (-2) = +5When the signs are different in a multiplication or division problem, the answer will be negativeExample #1: (+8) × (-7) = -56Example #2: (-12) × (+4) = -48Example #3: (+9) ÷ (-3) = -3Example #4: (-14) ÷ (+2) = -7D. Order of Operations and Positive and Negative NumbersWhen a number of mathematical operations are to be performed in a problem, you must follow a specific order for solving the problemStep 1 – Do anything that is inside parenthesesStep 2 - Solve anything that contains an exponent (a power – 52 – the 2 is the exponent and it means the base number is to be multiplied by itself that number of times, so52 = 5 ×5 = 25)Step 3 – Solve any multiplication or division within the problem, moving from left to rightStep 4 – Solve any addition or subtraction within the problem, moving from left to rightExample #1: -2(12 – 8) + -33 + 4 ? -6-2(4) + -33 + 4 ? -6-2(4) + -27 + 4 ? -6-8 + -27 + -24-35 + -24-59Example #2: -3 + 4(2 - 6)2 ÷ -2-3 + 4(-4)2 ÷ -2-3 + 4(16) ÷ -2-3 + 64 ÷ -2-3 + -32-35If the operations to be performed are in fractional form, solve the numerator first, then the denominator, then reduce.Example: 7(-4) - (-2) = (-28) - (-2) = -26 = -2 8 - (-5) 13 13POSITIVE AND NEGATIVE INTEGERSPRACTICE SHEETA. Solve the following problems.1) -2 + (+3) = 11) -3(-4) =21) 45 - (-27) =2) -5 + (+4) = 12) 24 ÷ (-6) = 22) 19(-4) =3) 5 - (-3) =13) 5(-18) =23) -42 ÷ (-6) =4) -7 - (-3) =14) -8 ÷ (-4) =24) -21 + -19 =5) -14 - 6 =15) 17(-4) = 25) 32 ÷ (-4) =6) 6 + (-8) = 16) 81 ÷ (-9) = 26) 14 - (-7) + (-2) =7) 12 + (+7) =17) -21 ÷ (-7) = 27) -8 ? -4 ÷ -2 = 8) -8 + (-1) =18) -7(9) = 28) -24 ÷ 4 + -17 =9) -9 - (+6) =19) 8(7) = 29) 7 - (-3) + (-2) - 4 =10) 11 + (-2) =20) 56 ÷ (-14) = 30) 12 + (-7) - (-28) =B. Use order of operations to solve the following problems.1) 18 - (-12 - 3) =7) -19 + (7 + 4)3 =2) 18 + (-7) ? (32 – 6) =8) -19 - (-3) + -2(8 + -4) =3) 20 + -4(32 - 6) =9) -3 + 2(-6 ÷ 3)2 =4) 3 ? (-4) + (52 + -4 ? 2) =10) 23 + (-16) ÷ 42 ? 5 - (-3) =5) -6(12 - 15) + 23 =11) 4(-6) + 8 - (-2) =15 – 7 + 26) -50 ÷ (-10) + (5 - 3)4 =12) 1.4(4.7 – 4.9) - 12.8 ÷ (-0.2)= ................
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