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Math Word Problems - Translating Expressions

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    Study Guide Math Word Problems – Translating Expressions 1. Keywords for Change in Order When you translate English phrases into algebraic expressions, the order of the numbers sometimes changes . Words that signal this change are called turnaround words . Turnaround words tell you that the order in the English sentence is not the same order you should use in the math expression. 1.1 Why Turnaround Words Matter Think about a cooking example: “Three eggs added to the mix” Which goes into the bowl first? The mix goes in first, then the eggs. So mathematically, this means: • mix + eggs • not eggs + mix 1.2 Basic Turnaround Words All turnaround expressions include at least one of these words: • TO • FROM • THAN Whenever you see one of these, pause and check the order .

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    Study Guide 1.3 Addition Turnaround Words Addition phrases that cause a turnaround: • ADD _____ TO _____ • _____ ADDED TO _____ • _____ MORE THAN _____ Example 1: Steps: 1. Box the turnaround word TO 2. Replace words with numbers 3. Reverse the order Translation: − 4 + 12 Example 2: Steps: 1. ADD is a leading keyword → it tells you the operation 2. Underline what comes before and after TO 3. Box TO (turnaround word) 4. Reverse the order Translation: 5 + ( - 3)

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    Study Guide Even though addition is commutative (−3 + 5 = 5 − 3), writing it correctly builds good habits for subtraction and division, which are not commutative . 1.4 Subtraction Turnaround Words Subtraction phrases that cause a turnaround: • SUBTRACT _____ FROM _____ • _____ SUBTRACTED FROM _____ • _____ LESS THAN _____ Example 3: Steps: 1. Box the turnaround word THAN 2. Reverse the order Translation: 7 - x Example 4: Steps: 1. SUBTRACT is a leading keyword 2. Underline what comes before and after FROM 3. Box FROM 4. Reverse the order Translation: 54 - 17

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    Study Guide 1.5 Multiplication and Order Important Note: Multiplication does NOT use turnaround words. All multiplication phrases can be translated directly . Example: • the product of a number and 8 → ( n \ times 8 ) Most often, mathematicians write this as: • ( 8n ) This is called implied multiplication : • No × sign is shown • The multiplication is understood 1.6 Division Turnaround Words Division phrases that cause a turnaround: • DIVIDE _____ INTO _____ • _____ DIVIDED INTO _____ Notice: • INTO contains the word TO • That means the order must be reversed Example 5: divide five into 125

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    Study Guide Steps: 1. DIVIDE is the leading keyword 2. Underline values around INTO 3. Box INTO 4. Reverse the order Translation: 125 ÷ 5 Example 6: Steps: 1. Box INTO 2. Reverse the order Translation: 100 ÷ 25 1.7 Why Learn Correct Order Every Time? Even when the answer is the same (like addition), correct translation matters because: 1. Subtraction and division depend on order 2. It builds strong algebra habits 3. It shows you understand what the words mean, not just the result

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