100% I 12:38 PM4G[Template] MODUL..."expression' in mathbooksdifferent entities. They don't overlap. If something is an expression,then it's not a sentence. If something is a sentence, then it's not anexpression. Be careful about this.There are many types of expressions in mathematics, becausethere are many types of mathematical objects to be discussed.Some types of expressions are listed below. Don't worry aboutwords you don't recognize: in this book, we'll primarily concernourselves only with numbers and sets.NUMBERSWhat types ofexpressions are there?SETSMATRICESFUNCTIONSVECTORSORDERED PAIRSAs mentioned earlier, a key idea in mathematics is thatexpressions have lots of different names. Even more importantly,the name we use depends on what we are doing with theexpression. For example, the number 1 goes by all thefollowing names:expressions have lotsof different names;the name we use2 – 1depends on whatwe are doingwith the expression3The name +- is appropriate, for example, if we have to divide acandy bar evenly between two people.The name+ is appropriate if we need to measure one cupof our, but only have a one-third cup measure.EXERCISE 2.1.Give a name for the number `3' that would be appropriate in eachsituation:a) three candy bars must be equally divided among three peopleb) three candy bars must be equally divided among six peoplec) you need three cups of our, but only have a one-quarter cupScan me!measured) you need three cups of our, but only have a one-half cup measureThe most common problem type involving an expression is:common type ofproblem involvingexpressionsSIMPLIFY: (Some expression)To simplify an expression means to get a different name for theexpression, that in some way is simpler.GE 4: MATHEMATICS IN THE MODERN WORLD | s. 2020Page 10 of 13The notion of 'simpler', however, can have di_erent meanings:FEWER SYMBOLS: Often, `simpler' means using fewersymbols. For example, 3 + 1 + 5' and `9' are both names forthe same number, but ` 9'uses fewer symbols.FEWER OPERATIONS: Sometimes, `simpler' means usingfewer operations (an `operation' is something like addition ormultiplication). For example, 3+3+3+3+3' and ` 5•3 are bothnames for the same number, but the latter uses feweroperations. (Recall that the centered dot denotesmultiplication.) There are four additions used in*3 + 3 + 3 + 3 + 3', but only one multiplication used in'5•3'.BETTER SUITED FOR CURRENT USE: In some cases,`simpler' means better suited for the current use. ForWhat does 'simpler'mean?1footexample, we'll see in a future section that the nameis a great name for the number `1' if we need to convert units12inchesof inches to units of feet.• PREFERRED STYLE/FORMAT: Finally, `simpler' oftenmeans in a preferred style or format. For example, (two-

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100% I 12:38 PM4G[Template] MODUL...&#34;expression' in mathbooksdifferent entities. They don't overlap. If something is an expression,then it's not a sentence. If something is a sentence, then it's not anexpression. Be careful about this.There are many types of expressions in mathematics, becausethere are many types of mathematical objects to be discussed.Some types of expressions are listed below. Don't worry aboutwords you don't recognize: in this book, we'll primarily concernourselves only with numbers and sets.NUMBERSWhat types ofexpressions are there?SETSMATRICESFUNCTIONSVECTORSORDERED PAIRSAs mentioned earlier, a key idea in mathematics is thatexpressions have lots of different names. Even more importantly,the name we use depends on what we are doing with theexpression. For example, the number 1 goes by all thefollowing names:expressions have lotsof different names;the name we use2 – 1depends on whatwe are doingwith the expression3The name +- is appropriate, for example, if we have to divide acandy bar evenly between two people.The name+ is appropriate if we need to measure one cupof our, but only have a one-third cup measure.EXERCISE 2.1.Give a name for the number `3' that would be appropriate in eachsituation:a) three candy bars must be equally divided among three peopleb) three candy bars must be equally divided among six peoplec) you need three cups of our, but only have a one-quarter cupScan me!measured) you need three cups of our, but only have a one-half cup measureThe most common problem type involving an expression is:common type ofproblem involvingexpressionsSIMPLIFY: (Some expression)To simplify an expression means to get a different name for theexpression, that in some way is simpler.GE 4: MATHEMATICS IN THE MODERN WORLD | s. 2020Page 10 of 13The notion of 'simpler', however, can have di_erent meanings:FEWER SYMBOLS: Often, `simpler' means using fewersymbols. For example, 3 + 1 + 5' and `9' are both names forthe same number, but ` 9'uses fewer symbols.FEWER OPERATIONS: Sometimes, `simpler' means usingfewer operations (an `operation' is something like addition ormultiplication). For example, 3+3+3+3+3' and ` 5•3 are bothnames for the same number, but the latter uses feweroperations. (Recall that the centered dot denotesmultiplication.) There are four additions used in*3 + 3 + 3 + 3 + 3', but only one multiplication used in'5•3'.BETTER SUITED FOR CURRENT USE: In some cases,`simpler' means better suited for the current use. ForWhat does 'simpler'mean?1footexample, we'll see in a future section that the nameis a great name for the number `1' if we need to convert units12inchesof inches to units of feet.• PREFERRED STYLE/FORMAT: Finally, `simpler' oftenmeans in a preferred style or format. For example, (two-

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EXERCISE 2.1. Give a name for the number `3' that would be appropriate in each situation: a) three candy bars must be equally divided among three people b) three candy bars must be equally divided among six people c) you need three cups of our, but only have a one-quarter cup measure