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Algebra Cheat SheetsAlgebra Cheat Sheets provide you with a tool for teaching your studentsnote-taking, problem-solving, and organizational skills in the context ofalgebra lessons. These sheets teach the concepts as they are presented inthe Algebra Class Software.ConceptCheat SheetAdding IntegersSubtracting IntegersMultiplying IntegersDividing IntegersAbsolute ValueCombining Like TermsDistributive Property IAdding ExpressionsSubtracting ExpressionsWriting ExpressionsEvaluating ExpressionsSolving EquationsSolving InequalitiesWriting EquationsWriting InequalitiesSolving Literal EquationsPoints on the Coordinate PlaneGraphing – Using Slope and InterceptGraphing – Using Function TablesFind the Slope of a Line from Two PointsEquation of a LineGraphing InequalitiesCopyright 2004 Senari ProgramsAlgCS ri.com

Algebra Cheat SheetsConceptCheat SheetForms of Linear EquationsSolving Equations IIMultiplying MonomialsDividing MonomialsRaising Monomials to a PowerNegative Powers of MonomialsDividing by a MonomialGreatest Common Factor (GCF)Combining Like Terms IIAdding PolynomialsSubtracting PolynomialsMissing FactorsDegree of a PolynomialMultiplying Polynomials by –1Multiplying a Polynomial by a VariableMultiplying a Polynomial by an IntegerMultiplying a Polynomial by a MonomialMultiplying Two BinomialsCopyright 2004 Senari ProgramsAlgCS ari.com

Algebra CheatSheet 1Adding Integers Adding means combining1. If the signs are the same, thenadd and use the same sign.8 4 12– 8 – 4 – 122. If the signs are different, thensubtract and use the sign of thelarger number.–8 4 –48 –4 4Adding Integers – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 2SubtractingIntegersSubtracting is the opposite of adding.Change the sign of the second term and add.8 – ( 4) 8 – 4 4– 8 – ( 4) – 8 – 4 –128 – (– 4) 8 4 12– 8 – (– 4) – 8 4 – 4Subtracting Integers – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 3MultiplyingIntegersMultiply integers as you would whole numbers,then apply the sign rules to the answer.1. If the signs are the same, theproduct is positive.(8) (4) 32(– 8) (– 4) 322. If the signs are different, theproduct is negative.(– 8) (4) – 32(8) (– 4) – 32Multiplying Integers – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 4Dividing IntegersDivide integers as you would whole numbers, thenapply the sign rules to the answer.1. If the signs are the same, thequotient is positive.32 8 4– 32 – 8 42. If the signs are different, thequotient is negative.32 – 8 – 4– 32 8 – 4Dividing Integers – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 5Absolute ValueThe absolute value of a number is the distance anumber is from ‘0’ on the number line.The absolute values of ‘7’ and ‘-7’ are 7 since bothnumbers have a distance of 7 units from ‘0.’Absolute Value – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 6Combining LikeTermsTo combine terms, the variables must be identical.1. Put the terms in alphabetical order.2. Combine each set of like terms.3. Put the answers together.Combining Like Terms – Examples3a 4b 2c 5a – 6c – 2b1. Put the terms in alphabetical order:3a 5a 4b – 2b 2c – 6c2. Combine each set of like terms: 3a 5a 8a 4b – 2b 2b 2c – 6c – 4c3. Put the answer together:8a 2b – 4cCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 6Combining LikeTermsTo combine terms, the variables must be identical.1. Put the terms in alphabetical order.2. Combine each set of like terms.3. Put the answers together.Combining Like Terms – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 7DistributiveProperty IMultiply each term inside the parenthesis by theterm on the outside of the parenthesis. c(a b) ca cb c(a - b) ca - cbDistributive Property – Examples3b (a 4) 3b (a) 3b (4) 3ab 12bCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

DistributiveProperty IAlgebra CheatSheet 7Multiply each term inside the parenthesis by theterm on the outside of the parenthesis. c(a b) ca cb c(a - b) ca - cbDistributive Property – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

AddingExpressionsAlgebra CheatSheet 81. Set the problem up vertically.2. Combine the terms.Adding Expressions – ExamplesWrite the problem vertically:8c 2d - 4g-7c 4d - 8g1. Combine the c’s:8c - 7c c2. Combine the d’s:2d 4d 6d3. Combine the g’s:-4g - 8g -12g4. The answer is:c 6d - 12gCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

AddingExpressionsAlgebra CheatSheet 81. Set the problem up vertically.2. Combine the terms.Adding Expressions – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

SubtractingExpressionsAlgebra CheatSheet 93. Set the problem up vertically.4. Change the signs of each term on the bottom line.5. Combine the terms.Subtracting Expressions – ExamplesChange the bottom signs:Combine the terms:8c 2d - 4g8c 2d - 4g7c - 4d 8g-7c 4d - 8g-1. Combine the c’s:8c - 7c c2. Combine the d’s:2d 4d 6d3. Combine the g’s:-4g - 8g -12g4. The answer is:c 6d - 12gCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

SubtractingExpressionsAlgebra CheatSheet 91. Set the problem up vertically.2. Change the signs of each term on the bottom line.3. Combine the terms.Subtracting Expressions – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

WritingExpressionsAlgebra CheatSheet 10Look for ‘clue’ words:1. For the clue words, ‘the product of’ place theconstant before the variable. Do not use a sign.2. The clue words ‘more than’ and ‘less than’indicate inverted order.3. If there are no clue words, write the expression inthe order that the words appear.Writing Expressions – Examples1. The product of 4 and xThe product of y and 52. x more than three3 xy – 13thirteen less than y3. the sum of ten and xthe difference betweeny and 4Copyright 2004 Senari Programs4x5yAlgCS.doc10 xy–4www.senari.com

WritingExpressionsAlgebra CheatSheet 10Look for ‘clue’ words:1. For the clue words, ‘the product of’ place theconstant before the variable. Do not use a sign.2. The clue words ‘more than’ and ‘less than’indicate inverted order.3. If there are no clue words, write the expressionin the order that the words appear.Writing Expressions – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

EvaluatingExpressionsAlgebra CheatSheet 11Step 1. Replace the variable with parentheses.Step 2. Place the value of the variable inside theparentheses.Step 3. Calculate the answer.Evaluating Expressions – ExamplesEvaluate 10x 7, when x 5.Step 1.10 (Step 2.10 (5) 7Step 3.50 7 57Copyright 2004 Senari Programs) 7AlgCS.docwww.senari.com

EvaluatingExpressionsAlgebra CheatSheet 11Step 1. Replace the variable with parentheses.Step 2. Place the value of the variable inside theparentheses.Step 3. Calculate the answer.Evaluating Expressions – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 12Solving EquationsStep 1. Get all the variables on the left and all thenumbers on the right of the equal sign by addingopposites.Step 2. Divide by the coefficient of the variable todetermine its value.Solving Equations – Examples2d 3 –7– 3 –31.2d –10d –52.Copyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 12Solving EquationsStep 1. Get all the variables on the left and all thenumbers on the right of the equal sign by addingopposites.Step 2. Divide by the coefficient of the variable todetermine its value.Solving Equations – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

SolvingInequalitiesAlgebra CheatSheet 13Step 3. Get all the variables on the left and all thenumbers on the right of the sign by addingopposites.Step 4. Divide by the positive value of the variable’scoefficient.Step 5. If the variable is negative, divide by –1 andreverse the sign.Solving Inequalities – Examples–2d 3 –7–3 –31.–2d –10Copyright 2004 Senari Programs2.–d –53.d 5AlgCS.docwww.senari.com

SolvingInequalitiesAlgebra CheatSheet 13Step 1. Get all the variables on the left and all thenumbers on the right of the sign by addingopposites.Step 2. Divide by the positive value of the variable’scoefficient.Step 3. If the variable is negative, divide by –1 andreverse the sign.Solving Inequalities – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

WritingEquationsAlgebra CheatSheet 14Look for ‘clue’ words:1. For the clue words, ‘the product of’ place theconstant before the variable. Do not use a sign.2. The clue words ‘more than’ and ‘less than’indicate inverted order.3. If there are no clue words, write the equation inthe order that the words appear.4. The equal sign is used in place of the word ‘is.’Writing Equations – Examples1. The product of 4 and x is 12.The product of y and 5 is 10.2. x more than three is 12.4x 125y 10Thirteen less than y is – 3.3 x 12y – 13 33. The sum of ten and x is 12.10 x 12The difference between yand 4 is – 2.y–4 –2Copyright 2004 Senari ProgramsAlgCS.docwww.senari.com

WritingEquationsAlgebra CheatSheet 14Look for ‘clue’ words:1. For the clue words, ‘the product of’ place theconstant before the variable. Do not use a sign.2. The clue words ‘more than’ and ‘less than’indicate inverted order.3. If there are no clue words, write the equation inthe order that the words appear.4. The equal sign is used in place of the word ‘is.’Writing Equations – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

WritingInequalitiesAlgebra CheatSheet 15Look for ‘clue’ words:1. For the clue words, ‘the product of’ place theconstant before the variable. Do not use a sign.2. The clue words ‘more than’ and ‘less than’indicate inverted order.3. If there are no clue words, write the equation inthe order that the words appear.4. The is used in place of ‘is less than.’5. The is used in place of ‘is greater than.’Writing Inequalities – Examples1. The product of 4 and x isgreater than 12.2. x more than three is lessthan 12.3. The difference between yand 4 is greater than – 2.Copyright 2004 Senari ProgramsAlgCS.doc4x 123 x 12y–4 –2www.senari.com

WritingInequalitiesAlgebra CheatSheet 15Look for ‘clue’ words:1. For the clue words, ‘the product of’ place theconstant before the variable. Do not use a sign.2. The clue words ‘more than’ and ‘less than’indicate inverted order.3. If there are no clue words, write the equation inthe order that the words appear.4. The is used in place of ‘is less than.’5. The is used in place of ‘is greater than.’Writing Inequalities – ExamplesCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Solving LiteralEquationsAlgebra CheatSheet 16Step 1. Get the desired variable on the left and all theothers on the right of the equal sign by addingopposites.Step 2. Divide both sides by the positive value of anyother variable on the left.Solving Literal Equations – ExampleSolve for l (length)A lwlw A1.Divide by w2.Copyright 2004 Senari ProgramsAl wAlgCS.docwww.senari.com

Solving LiteralEquationsAlgebra CheatSheet 16Step 1. Get the desired variable on the left and all theothers on the right of the equal sign by addingopposites.Step 2. Divide both sides by the positive value of anyother variable on the left.Solving Literal Equations – ExampleCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Points on theCoordinate PlaneAlgebra CheatSheet 17Locating Points:Step 1. Find the locationon the x-axis. It is–3.Step 2. Find the locationon the y-axis. It is4.Step 3. Write the locationin this form (x, y).The point is (–3, 4).Plotting points:Plot the point (5, –3) on the coordinate plane.Step 1. Begin at point (0, 0). Move 5 to the right (on thex-axis) since 5 is positive.Step 2. Move 3 down since –3 is negative.Step 3. Plot the point.Notes – Points on the Coordinate Plane Use graph paper. Begin by marking the x-axis and y-axis as shownin the diagram above.Copyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 18Graphing – UsingSlope and Intercept The y-intercept is the constant in the equation. It isthe value of y when x 0. A line with a positive slope goes up and to the right. A line with a negative slope goes down and to the right.To graph the equation: y 5x – 3Step 1. The y-intercept is –3. Plot the point (0, –3).Step 2. The slope is 5. Move 1 to the right and 5 upfrom the first point. Plot the second point at(1, 2).Step 3. Draw the line connecting the two points.Graphing - Using the Slope and y-intercepty 5x – 3Copyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Algebra CheatSheet 18Graphing – UsingSlope and Intercept The y-intercept is the constant in the equation. It isthe value of y when x 0. A line with a positive slope goes up and to the right. A line with a negative slope goes down and to the right.To graph the equation: y 5x – 3Step 1. The y-intercept is –3. Plot the point (0, –3).Step 2. The slope is 5. Move 1 to the right and 5 upfrom the first point. Plot the second point at(1, 2).Step 3. Draw the line connecting the two points.Graphing - Using the Slope and y-interceptCopyright 2004 Senari ProgramsAlgCS.docwww.senari.com

Graphing – UsingFunction TablesAlgebra CheatSheet 19Step 1. Substitute ‘0’ for x, and calculate the value of y.Enter both on the first line of the function table.Step 2. Substitute ‘1’ for x, then calculate the value of y.Enter both numbers on the second line of thefunction table.Step 3. Plot the two points, and draw a line betweenthem.Graphing - Using Function Tablesy 5x – 3Step 1. Substitu