1. Numerical and Algebraic Expressions Jean MacIntosh
From English to Math
Numerical and Algebraic Expressions
Jean MacIntosh
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2. Writing Math Expressions
A variable is a symbol used to represent a number in an expression or an equation. The value of this number can change. An algebraic expression is a mathematical expression that consists of variables, numbers and operations. The value of this expression can change.

3. Math Words Translation Guide
Math symbol
Sum
More than
Product
Times
Divided
Decreased
Twice
Less than
Increased
Per

4. Example Expression the sum of nine and eight
Write each phrase as a mathematical expression.
Phrase
Expression
the sum of nine and eight
the sum of nine and a number x

5. Example : Expression the sum of nine and eight 9+8
Write each phrase as a mathematical expression.
Phrase
Expression
the sum of nine and eight
9+8
the sum of nine and a number x
9+x

6. Example 2:  
Write each phrase as an algebraic expression using the variable n.
Phrase
Expression
five more than twice a number
the product of a number and 6
seven divided by twice a number   
three times a number decreased by 11

7. Example 3: Write each phrase as an algebraic expression. Phrase
Phrase
Expression
nine increased by a number x
9+x
fourteen decreased by a number p
14-p
seven less than a number t
7-n
the product of 9 and a number n
9xn
thirty-two divided by a number y
   32 ÷ y   or   32/y

8. Example 3: Write each phrase as an algebraic expression. Phrase
Phrase
Expression
nine increased by a number x
9 + x
fourteen decreased by a number p
14 - p
seven less than a number t
t - 7
the product of 9 and a number n
9 · n   or   9n
thirty-two divided by a number y
32 ÷ y    

9. Example 4: An electrician charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression to represent his earnings for one day.

10. Solution: Let x represent the number of hours the electrician works in one day. The electrician's earnings can be represented by the following algebraic expression: Solution: 45x - 20

11. Independent Practice 1. Fifteen less than twice a number
1. 
Fifteen less than twice a number
A x B 2x + 15 C 2x - 15 D None of the above.

12. 2. Three times a number, increased by seventeen
A 3(a + 17) B 3a + 17 C (17 + 3)a D None of the above