# Algebraic Expressions

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Algebraic Expressions
Translate English to Math

Learning Goal 1 (HS.N-RN.B3 and HS.A-SSE.A.1):
The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions based on contextual situations. 4 3 2 1 In addition to level 3.0 and above and beyond what was taught in class,  the student may: ·         Make connection with other concepts in math ·         Make connection with other content areas. The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions on contextual situations. - justify the  sums and products of rational and irrational numbers -interpret expressions within the context of a problem The student will be able to use properties of rational and irrational numbers to write and simplify  expressions based on contextual situations. -identify parts of an expression  as related to the context and to each part With help from the teacher, the student has partial success with real number expressions. Even with help, the student has no success with real number expressions.

Parts of an Algebraic Expression
Algebraic expressions do not contain equal signs. Terms: Values that are added or subtracted. 3n + 5 has two terms. Factors: Values that are multiplied. The term 3n has two factors: 3 and n. terms 3n + 5 Coefficient: The number next a variable. Constant: The number without a variable.

Translate English to Math (translate between verbal statements and algebraic expressions)
In order to translate from the language of English to the language of Math, you need to understand the words that are commonly used to represent mathematical operations. Add Sum Increased by More than exceeds Total Plus In all Gain Deposit Subtract Difference Decreased by Fewer Less than Minus Take away Withdraw Reduced by Multiply Product Of Times Double Triple Twice Divide Quotient Per Divided equally Split into Fraction Ratio of

Tips: The phrase “less than” reverses the order of what you read.
For example: “5 less than n” translates to “n – 5” Watch for commas. They can help you decide how to group terms. For example: “8 times, a number increased by 12” translates to 8(n + 12) NOT 8n + 12

Practice: Translate the following into algebraic expressions.
Five increased by four times a number. Eight less than twice a number. Three times a number, increased by 9. The product of 4, and a number decreased by 7. The number of feet in x yards. A number repeated as a factor 3 times. 5 + 4n 2n – 8 3n + 9 4(n – 7) 3x n • n • n = n3

Complicated Expressions
Translate the following expression into English: 5x – (2 – 4y) “The difference between 5 times a number and the quantity 4 times another number less than 2” It’s much easier to just leave the expression in math symbols.  Look at the words “a number” and “another number.” These help you identify that there are multiple variables in the expression.

5x – (2 – 4y) How many terms are in this expression?
It is tempting to say 3. There are only 2 terms. -(2 – 4y) is one term. Because of the parenthesis, it groups it as one term. The “-” sign in front of the parenthesis, represents “-1” which could be multiplied by everything in the parenthesis.

P(1 + r)n How many variables are in the above expression?
3 How many terms are in the above expression? 1 How many factors are in the above expression? 2 One factor is “P” The other factor is “(1 + r)n”

Practice: How many terms are in each expression?
x2 + 4x + 3 ½ bh 2lw + 2lh + 2hw (9 – 2w) - 29 1 2 3

Practice: How many factors are in each expression?
x2 + 4x + 3 ½ bh 2lw + 2lh + 2hw 29 - (9 – 2w) 2 (9 & y) 2 (4 & n) 2 (3 & [6-4x]) 4 (x & x) & (4 & x) 3 (½ & b & h) 3 factors in each term for a total of 9 2 ([9-2w] & -1)

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