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**Understanding Algebra Word Problems**

*Represent a given situation using algebraic expressions or equations in one variable. *Simplify and evaluate algebraic expressions.

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The biggest challenge to solving word problems is figuring out whether to add, subtract, multiply or divide. Words Meaning Addition and increased more more than plus sum total Words Meaning Subtraction decreased difference less less than left lower than minus Words Meaning Multiplication double half (× ½) product times triple twice Words Meaning Division divide into half (÷ 2) divide by divide among quotient

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To solve a word problem, you must first interpret the action you need to perform and then choose the correct operation for that action. Action Operation Possible Question Clues Combine Add How many all together? Combine equal groups Multiply How many all together? Separate Subtract How many more? How many less? Separate into equal groups Divide How many equal groups?

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** + – Word Phrases Expression a number plus 5 add 5 to a number**

sum of a number and 5 5 more than a number a number increased by 5 a number minus 11 subtract 11 from a number difference of a number and 11 x 11 11 less than a number a number decreased by 11 3 times a number 3 multiplied by a number 3m product of 3 and a number a number divided by 7 or a 7 a 7 7 divided into a number quotient of a number and 7

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**TEST YOUR SKILL!! Match the phrase with the correct algebraic expression. **

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1) 2 more than y y - 2 2y y + 2 y/2

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2) 16 divided into m 16 - m 16m m + 16 m/16

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3) 2 less than s s - 2 2s s + 2 s/2

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4) Triple John’s age j 3 + j j - 3 3j j ÷ 3

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5) Twice the sum of y and 15 2y + 15 2 + y + 15 2 (y + 15) 2(15) + y

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6) n feet lower than than 10 10 - n n - 10 n + 10 10 + n

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**7) The quotient t and 4 4 goes into t t goes into 4 Multiply 4 by t**

Add 4 and t

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8) 18 divided by a number, g 18 - g 18 ÷ g g + 18 18 × g

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**ABC 2.4 Setting Up Algebra Word Problems**

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**To set up algebra word problems:**

To complete an algebra problem, an equal sign must be added. The words is or are as well as equals tell you that you should add an equal sign. Double Jake’s age, x, minus 4 is 22. 2x - 4 = 22

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**Translate the word problem into an equation**

Translate the word problem into an equation. DO NOT find the solution yet. Triple the original number, n, is 2,700. The product of a number, y, and 5 is equal to 15. Four times the difference of a number, x, and 2 is 20. The total, t, divided into 5 groups is 45. 3n = 2700 5y = 15 4(x – 2) = 20 t ÷ 5 = 45

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**Translate the word problem into an equation**

Translate the word problem into an equation. DO NOT find the solution yet. The number of pants in the store, p, minus 54 pants sold today is 320. One-half an amount, x, added to $50 is $262. One hundred plants, divided by 5 rows, equals n number of plants per row. A number, y, less than 50 is 82. p – 54 = 320 x/ = 262 100 ÷ 5 = n y - 50 = 82

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**Translate the word problem into an equation**

Translate the word problem into an equation. DO NOT find the solution yet. Seventeen more than half a number, h, is 35. The quotient of a number, w, and 4 is 32. Six less a number, d, is 12. Four times the sum of a number, y, and 10 is 48. h/ = 35 w ÷ 4 = 32 d – 6 = 12 4(y + 10) = 48

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