Math Word Problems - Translating Expressions - Quick Guides

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Study GuideMath Word Problems–Translating Expressions1. Keywords for Change in OrderWhen you translate English phrases into algebraic expressions,the order of the numberssometimes changes.Words that signal this change are calledturnaround words.Turnaround words tell you that the order in the English sentence isnotthe same order you shoulduse in the math expression.1.1Why Turnaround Words MatterThink about a cooking example:“Three eggs addedtothe mix”Which goes into the bowl first?Themixgoes in first, then the eggs.So mathematically, this means:•mix + eggs•noteggs + mix1.2Basic Turnaround WordsAll turnaround expressions include at least one of these words:•TO•FROM•THANWhenever you see one of these,pause and check the order.

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Study Guide1.3Addition Turnaround WordsAddition phrases that cause a turnaround:•ADD _____ TO _____•_____ ADDED TO _____•_____ MORE THAN _____Example 1:Steps:1.Box the turnaround wordTO2.Replace words with numbers3.Reverse the orderTranslation:−4 + 12Example 2:Steps:1.ADDis aleading keyword→ it tells you the operation2.Underline what comes before and afterTO3.BoxTO(turnaround word)4.Reverse the orderTranslation:5 + (-3)

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Study GuideEven though addition is commutative (−3 + 5 = 5 − 3),writing it correctly builds good habitsfor subtraction and division, which arenot commutative.1.4Subtraction Turnaround WordsSubtraction phrases that cause a turnaround:•SUBTRACT _____ FROM _____•_____ SUBTRACTED FROM _____•_____ LESS THAN _____Example 3:Steps:1.Box the turnaround wordTHAN2.Reverse the orderTranslation:7-xExample 4:Steps:1.SUBTRACTis a leading keyword2.Underline what comes before and afterFROM3.BoxFROM4.Reverse the orderTranslation:54-17

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Study Guide1.5Multiplication and OrderImportant Note:Multiplication does NOT use turnaround words.All multiplication phrases can be translateddirectly.Example:•the product of a number and 8→ ( n\times 8 )Most often, mathematicians write this as:•( 8n )This is calledimplied multiplication:•No × sign is shown•The multiplication is understood1.6Division Turnaround WordsDivision phrases that cause a turnaround:•DIVIDE _____ INTO _____•_____ DIVIDED INTO _____Notice:•INTOcontains the wordTO•That means the order must be reversedExample 5:divide five into 125

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Study GuideSteps:1.DIVIDEis the leading keyword2.Underline values aroundINTO3.BoxINTO4.Reverse the orderTranslation:125 ÷ 5Example 6:Steps:1.BoxINTO2.Reverse the orderTranslation:100 ÷ 251.7Why Learn Correct Order Every Time?Even when the answer is the same (like addition),correct translation mattersbecause:1.Subtraction and divisiondepend on order2.It builds strong algebra habits3.It shows you understand what the words mean, not just the result

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Math Word Problems - Translating Expressions - Page 1

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