In mathematics, the term "equivalent" refers to two or more expressions, equations, or values that have the same meaning, or represent the same quantity. When two or more mathematical expressions are equivalent, they are essentially equal to each other and can be interchanged without changing the meaning or value they represent.

Two algebraic expressions are equivalent if they have the same value for all the variables in the expressions. This means that the expressions may look different, but they represent the same quantity. For example, the expressions 2x + 3 and x + x + 3 are equivalent because they both represent the same quantity for any value of x.

Equations are considered equivalent if they have the same solution. That is, when you solve each equation, you get the same value for the variable(s) in the equation. For instance, the equations 2x = 10 and x = 5 are equivalent because they both have the same solution, x = 5.

Fractions are equivalent if they represent the same portion of a whole. For example, 1/2 and 2/4 are equivalent fractions because they both represent half of a whole. To determine if two fractions are equivalent, you can simplify or reduce them to their simplest form and check if they are equal.

Here are some key points to remember when working with equivalent expressions, equations, and fractions:

- Expressions are equivalent if they have the same value for all the variables in the expressions.
- Equations are equivalent if they have the same solution when solved.
- Fractions are equivalent if they represent the same portion of a whole, and can be determined by simplifying or reducing them to their simplest form.
- When working with equivalent expressions, equations, or fractions, you can use properties and operations such as distribution, combining like terms, and simplifying to show their equivalence.

Understanding the concept of equivalence in mathematics is crucial for solving problems involving simplification, solving equations, and comparing quantities. Practice identifying equivalent expressions, equations, and fractions to strengthen your understanding of this fundamental concept.

.Study GuideRational numbers and operations Worksheet/Answer key

Rational numbers and operations Worksheet/Answer key

Rational numbers and operations Worksheet/Answer key

Rational numbers and operations

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Work flexibly with fractions, decimals, and percents to solve problems.

Understand meanings of operations and how they relate to one another.

Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

Compute fluently and make reasonable estimates.

Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.