Answer:
Problem: Ms. Jensen likes to divide her class into groups of 2. Use mathematical symbols to represent all the students in her class.
Solution: Let g represent the number of groups in Ms. Jensen's class.
Then 2 · g, or 2g can represent "g groups of 2 students".
In the problem above, the variable g represents the number of groups in Ms. Jensen's class. A variable is a symbol used to represent a number in an expression or an equation. The value of this number can vary (change). Let's look at an example in which we use a variable.
Example 1: 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
The expression 9 + 8 represents a single number (17). This expression is a numerical expression, (also called an arithmetic expression). The expression 9 + x represents a value that can change. If x is 2, then the expression 9 + x has a value of 11. If x is 6, then the expression has a value of 15. So 9 + x is an algebraic expression. In the next few examples, we will be working solely with algebraic expressions.
Example 2: Write each phrase as an algebraic expression.
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 or
In Example 2, each algebraic expression consisted of one number, one operation and one variable. Let's look at an example in which the expression consists of more than one number and/or operation.
Example 3: Write each phrase as an algebraic expression using the variable n.
Phrase Expression
five more than twice a number 2n + 5
the product of a number and 6 6n
seven divided by twice a number 7 ÷ 2n or
three times a number decreased by 11 3n - 11
Step-by-step explanation:
= 225
