Algebra I – Signed Numbers Fractions and Percents - Quick Guides | Mathematics

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Study GuideAlgebra I–Signed Numbers FracƟons and Percents1.Signed Numbers (PosiƟve Numbers and NegaƟve Numbers)What Are Signed Numbers?Signed numbers are numbers that have either apositive (+)sign or anegative (−)sign.•Apositive numberis greater than zero.•Anegative numberis less than zero.If a number doesnot show a sign, it is automatically consideredpositive.Example+5→positive number−3→negative number7→positive (because no sign is written)Understanding Number LinesAnumber linehelps us see how numbers are ordered.•Numbersto the right of 0arepositive.•Numbersto the left of 0arenegative.This makes it easy to compare numbers.Figure 1.A number line using integers.

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Study GuideImportant IdeaOn a number line:•The numberfarther to the right is always larger.•The numberfarther to the left is smaller.Example•+2 is greater than +1•−1 is greater than−3 (because−1 is to the right of−3)Fractions on a Number LineFractions can also be placed on a number line.For example:These fractions appearbetween whole numbersdepending on their values.Figure 2.A number line using fractions.Addition of Signed NumbersNow let's learn how toadd positive and negative numbers.

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Study GuideThere aretwo situationsto remember.1. Adding Numbers with the Same SignIf both numbers have thesame sign(both positive or both negative):Step 1Add theirabsolute values.Theabsolute valuemeans the numberwithout its sign.Step 2Keep thesame sign.Example 1+5 + (+7)Step 1:Add the absolute values5 + 7 = 12Step 2:Keep the positive signAnswer: +12Example 2−8 + (−3)

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Study GuideStep 1:Add the absolute values8 + 3 = 11Step 2:Keep the negative signAnswer:−112. Adding Numbers with Different SignsIf one number ispositiveand the other isnegative:Step 1Subtract thesmaller absolute valuefrom thelarger absolute value.Step 2Keep thesign of the number with the larger absolute value.Example+7 + (−4)Step 1:Subtract absolute values7−4 = 3Step 2:The larger absolute value is 7 (positive)Answer: +3How Addition Problems Can Be WrittenAddition of signed numbers can appear in two forms:Vertical FormNumbers are writtenone under the other.Example:

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Study GuideHorizontal FormNumbers are writtenside by side.Example:+5 + (+7) = +12Both forms give thesame answer.Example 2Add the following numbers.We are adding apositive numberand anegative number. When the signs are different, followthese steps.Step 1:Compare the absolute valuesAbsolute value means the numberwithout its sign.

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Study Guide5 and 7Step 2:Subtract the smaller value from the larger value7−5 = 2Step 3:Keep the sign of the number with the larger absolute valueSince7 is largerand it isnegative (−7), the answer will be negative.Final Answer+5 + (−7) =−2Another Example−59 + (+72)Step 1:Compare the absolute values59 and 72Step 2:Subtract the smaller value from the larger value72−59 = 13Step 3:Keep the sign of the number with the larger absolute value72 is positive, so the result is positive.Final Answer−59 + (+72) =+13Example 3Add the following numbers.

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Study GuideSolve each problem using the rules for adding signed numbers.1.+9 + (+6)2.Both numbers are positive.3.Add the values.9 + 6 =152.−12 + 93.The signs are different.4.Subtract the absolute values.12−9 = 3The larger absolute value is12, which is negative.Answer:−33.−(−5)4.A double negative becomes positive.Answer:+5

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Study Guide4.23 + (−18)5.Different signs.23−18 = 5The larger absolute value is23, which is positive.Answer:+55.15Answer:156.3Answer:37.3Answer:38.5Answer:5Subtraction of Signed NumbersSubtracting signed numbers is actually very simple.Key RuleTo subtract a number,change its sign and then add.

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Study GuideThis means subtraction can be turned into anaddition problem.Example7−(−3)Step 1:Change the sign of−3 to +37 + 3Step 2:Add the numbers7 + 3 =10Another Example8−(+5)Step 1:Change the sign of +5 to−58 + (−5)Step 2:Add the numbers8−5 =3Subtracting and Working with Signed NumbersWhen you subtract numbers that havepositive (+)ornegative (−)signs, it helps to remember oneimportant rule:Subtracting a number is the same as adding its opposite.So:This simple idea makes signed number problems much easier.

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Study GuideExample 4:Subtract the FollowingProblemStep 1:Change subtraction to additionSubtracting(+4)is the same as adding(−4).Step 2:Add the numbersSo,Another ExampleStart with:Change subtraction to addition:Now add:

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