Chapter 1
Numbers and Operations
Course: Elementary Education Multiple Subjects 7001
Subject: Elementary Education Mathematics Subtest 7003
Chapter: Algebraic Thinking
1. Differentiates between algebraic expressions and equations
An algebraic expression is a mathematical phrase that includes variables (letters that represent numbers), constants (fixed numbers), and operations (such as addition, subtraction, multiplication, or division). Expressions do not include an equals sign, and therefore, they cannot be solved—only simplified or evaluated.
Examples of expressions:
- 4x+7
- 3a2−2b+9
An equation, on the other hand, shows that two expressions are equal and does include an equals sign. Equations are solved by finding the value of the variable that makes the statement true.
Examples of equations:
- 4x+7=23
- 3a=9
Key distinction:
- Expressions can only be simplified or evaluated.
- Equations can be solved to find unknown values.
Real-life application:
- Expression: “The cost of bananas is $2 per pound.” If x represents the number of pounds, the cost is modeled by the expression 2x.
- Equation: If someone spends $10 on bananas, the relationship becomes 2x=10. Solving gives x=5 pounds.