3, . . .■ RATIONAL NUMBERS—RATIONAL NUMBERS ARE ALL■ A DOT BETWEEN...

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2, 3, . . .■ Rational numbers—Rational numbers are all■ A dot between factors indicates multiplication:numbers that can be written as fractions (23), ter-5 • 6 = 30minating decimals (.75), and repeating decimals■ Parentheses around any part of the one or more.666. . .factors indicates multiplication:■ Irrational numbers—Irrational numbers are(5)6 = 30, 5(6) = 30, and (5)(6) = 30numbers that cannot be expressed as terminating■ Multiplication is also indicated when a number isor repeating decimals:πor 2.placed next to a variable:5a= 30 In this equation, 5 is being Comparison Symbolsmultiplied by a.The following table will illustrate the different com-parison symbols on the SAT.Like TermsA variableis a letter that represents an unknown num-= is equal to 5 = 5ber. Variables are frequently used in equations, formu-≠ is not equal to 4 ≠3las, and mathematical rules to help you understand> is greater than 5 > 3how numbers behave.≥ is greater than or equal to x≥5When a number is placed next to a variable, indi-(xcan be 5 cating multiplication, the number is said to be theor any number > 5)coefficientof the variable.< is less than 4 < 6≤ is less than or equal to x≤3Example:(xcan be 3 8c 8 is the coefficient to the variable c.or any number < 3)6ab 6 is the coefficient to both variables,aand b.If two or more terms have exactly the same vari-able(s), they are said to be like terms.■ Distributive Property.When a value is being7x+ 3x= 10x The process of grouping likemultiplied by a quantity in parentheses, you canterms together performingmultiply that value by each variable or numberwithin the parenthesis and then take the sum.mathematical operations iscalled combining like terms.5(a+ b) = 5a+ 5b This can be provenIt is important to combine like terms carefully,making sure that the variables are exactly the same. Thisby doing the math:5(1 + 2) = (5 ×1) + (5 ×2)is especially important when working with exponents.5(3) = 5 + 1015 = 157x3y+ 8xy3These are not like terms because x3yOrder of Operationsis not the same as xy3. In the firstThere is an order for doing every mathematical oper-term, the xis cubed, and in the sec-ation. That order is illustrated by the followingond term, it is the ythat is cubed.acronym:Please Excuse My Dear Aunt Sally. Here isBecause the two terms differ inwhat it means mathematically:more than just their coefficients,they cannot be combined as likeP:Parentheses. Perform all operations withinterms. This expression remains inparentheses first.its simplest form as it is written.E:Exponents. Evaluate exponents.M/D:Multiply/Divide. Work from left to rightLaws of Arithmeticin your division.Listed below are several “math laws,” or properties.Just think of them as basic rules that you can use asA/S:Add/Subtract. Work from left to right inyour subtraction.tools when solving problems on the SAT exam.■ Commutative Property. This law enables you tochange the order of numbers being either multi-2020 5 + [ ] = 5 + [ ](1)2(3 – 2)2plied or added.= 5 + 210= 5 + 20Examples:= 255 ×2 = 2 ×5 5a= a5Powers and Roots■ Associative Property.This law states that paren-theses can be moved to group numbers differentlyExponentswhen adding or multiplying.An exponent tells you how many times the number,called the base, is a factor in the product.2 ×(3 ×4) = (2 ×3) ×4 2(ab) = (2a)b25-exponent= 2 ×2 ×2 ×2 ×2 = 32⇑baseSometimes, you will see an exponent with a vari-root is 25and it is called the radical. The numberable:bn. The “b” represents a number that will be a fac-inside of the radical is called the radicand.tor to itself “n” times.52= 25; therefore,25= 5bnwhere b= 5 and n= 3 Don’t let the variablesfool you. MostSince 25 is the square of 5, we also know that 5 isexpressions are verythe square root of 25.easy once you substi-tute in numbers.Perfect Squaresbn= 53= 5 ×5 ×5 = 125The square root of a number might not be a whole number. For example, the square root of 7 isLaws of Exponents

Answer

2, 3, . . .■ Rational numbers—Rational numbers are all■ A dot between factors indicates multiplication:numbers that can be written as fractions (23), ter-5 • 6 = 30minating decimals (.75), and repeating decimals■ Parentheses around any part of the one or more.666. . .factors indicates multiplication:■ Irrational numbers—Irrational numbers are(5)6 = 30, 5(6) = 30, and (5)(6) = 30numbers that cannot be expressed as terminating■ Multiplication is also indicated when a number isor repeating decimals:πor 2.placed next to a variable:5a= 30 In this equation, 5 is being Comparison Symbolsmultiplied by a.The following table will illustrate the different com-parison symbols on the SAT.Like TermsA variableis a letter that represents an unknown num-= is equal to 5 = 5ber. Variables are frequently used in equations, formu-≠ is not equal to 4 ≠3las, and mathematical rules to help you understand> is greater than 5 > 3how numbers behave.≥ is greater than or equal to x≥5When a number is placed next to a variable, indi-(xcan be 5 cating multiplication, the number is said to be theor any number > 5)coefficientof the variable.< is less than 4 < 6≤ is less than or equal to x≤3Example:(xcan be 3 8c 8 is the coefficient to the variable c.or any number < 3)6ab 6 is the coefficient to both variables,aand b.If two or more terms have exactly the same vari-able(s), they are said to be like terms.■ Distributive Property.When a value is being7x+ 3x= 10x The process of grouping likemultiplied by a quantity in parentheses, you canterms together performingmultiply that value by each variable or numberwithin the parenthesis and then take the sum.mathematical operations iscalled combining like terms.5(a+ b) = 5a+ 5b This can be provenIt is important to combine like terms carefully,making sure that the variables are exactly the same. Thisby doing the math:5(1 + 2) = (5 ×1) + (5 ×2)is especially important when working with exponents.5(3) = 5 + 1015 = 157x3y+ 8xy3These are not like terms because x3yOrder of Operationsis not the same as xy3. In the firstThere is an order for doing every mathematical oper-term, the xis cubed, and in the sec-ation. That order is illustrated by the followingond term, it is the ythat is cubed.acronym:Please Excuse My Dear Aunt Sally. Here isBecause the two terms differ inwhat it means mathematically:more than just their coefficients,they cannot be combined as likeP:Parentheses. Perform all operations withinterms. This expression remains inparentheses first.its simplest form as it is written.E:Exponents. Evaluate exponents.M/D:Multiply/Divide. Work from left to rightLaws of Arithmeticin your division.Listed below are several “math laws,” or properties.Just think of them as basic rules that you can use asA/S:Add/Subtract. Work from left to right inyour subtraction.tools when solving problems on the SAT exam.■ Commutative Property. This law enables you tochange the order of numbers being either multi-2020 5 + [ ] = 5 + [ ](1)2(3 – 2)2plied or added.= 5 + 210= 5 + 20Examples:= 255 ×2 = 2 ×5 5a= a5Powers and Roots■ Associative Property.This law states that paren-theses can be moved to group numbers differentlyExponentswhen adding or multiplying.An exponent tells you how many times the number,called the base, is a factor in the product.2 ×(3 ×4) = (2 ×3) ×4 2(ab) = (2a)b25-exponent= 2 ×2 ×2 ×2 ×2 = 32⇑baseSometimes, you will see an exponent with a vari-root is 25and it is called the radical. The numberable:bn. The “b” represents a number that will be a fac-inside of the radical is called the radicand.tor to itself “n” times.52= 25; therefore,25= 5bnwhere b= 5 and n= 3 Don’t let the variablesfool you. MostSince 25 is the square of 5, we also know that 5 isexpressions are verythe square root of 25.easy once you substi-tute in numbers.Perfect Squaresbn= 53= 5 ×5 ×5 = 125The square root of a number might not be a whole number. For example, the square root of 7 isLaws of Exponents

3, . . .■ RATIONAL NUMBERS—RATIONAL NUMBERS ARE ALL■ A DOT BETWEEN...

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