Equal To

Definition

The term 'equal to' refers to a mathematical relationship where two quantities or expressions have the same value. It signifies that the two sides of an equation or comparison are identical in magnitude or worth.

5 Must Know Facts For Your Next Test

1. The concept of 'equal to' is fundamental in algebra and is used to represent balanced or equivalent relationships between quantities.
2. Equations, where two expressions are connected by the equals sign (=), are the primary way to express the 'equal to' relationship in mathematics.
3. Solving equations involves finding the unknown value that makes the two sides of the equation equal to each other.
4. Verifying that two expressions are 'equal to' each other is a crucial step in problem-solving and simplifying mathematical expressions.
5. Understanding the 'equal to' relationship is essential for manipulating and rearranging equations to isolate variables and find solutions.

Review Questions

• Explain how the concept of 'equal to' is used in the context of a problem-solving strategy.
  • When using a problem-solving strategy, the 'equal to' relationship is crucial for setting up and solving equations. Identifying the quantities that are equal to each other allows you to write equations that represent the given information and constraints of the problem. Solving these equations, by isolating the unknown variable, then provides the solution that satisfies the 'equal to' condition. Verifying that the final answer makes the two sides of the equation equal is an important step in confirming the validity of the solution.
• Describe how the 'equal to' relationship is used to simplify and manipulate mathematical expressions.
  • When working with mathematical expressions, the 'equal to' relationship is used to perform algebraic operations that maintain the equivalence between the two sides. This includes combining like terms, applying the distributive property, factoring, and other algebraic techniques. By ensuring that the expressions on both sides of the equals sign remain equal, you can simplify the overall expression and isolate variables or unknown quantities. The ability to recognize and apply the 'equal to' relationship is essential for transforming complex expressions into simpler, more manageable forms.
• Evaluate how the understanding of 'equal to' can help in checking the validity of a solution to a problem.
  • Verifying that the final solution satisfies the 'equal to' condition is a crucial step in problem-solving. By substituting the proposed solution back into the original equation or problem statement, you can confirm that the two sides are indeed equal. This step ensures that the solution accurately represents the balanced relationship between the given quantities, as described by the 'equal to' concept. If the solution does not make the two sides equal, it indicates an error in the problem-solving process and prompts a re-evaluation of the steps taken to arrive at the final answer.

Related terms

Equation: A mathematical statement that shows two expressions are equal, typically using the equals sign (=).

Inequality: A mathematical statement that shows two expressions are not equal, using symbols like greater than (>), less than (<), or not equal to (≠).

Equivalence: The state of being equal or equivalent in value, worth, or meaning.