Addition is the process of combining two or more numbers to find their total sum. For example:

- 3 + 4 = 7
- 8 + 5 + 2 = 15

Subtraction involves taking away one number from another to find the difference. For example:

- 10 - 5 = 5
- 15 - 8 = 7

Multiplication is the process of repeated addition or combining equal groups. For example:

- 4 * 3 = 12 (4 groups of 3)
- 7 * 2 = 14 (7 groups of 2)

Division involves splitting a number into equal parts or finding the number of equal groups. For example:

- 12 / 3 = 4 (12 divided into 3 equal parts)
- 15 / 5 = 3 (15 divided into 5 equal parts)

When working with operations in math, it's important to understand the properties and rules that govern these operations. Here are some key points to remember:

- Commutative Property: The order of the numbers does not change the result of addition or multiplication. For example, a + b = b + a and a * b = b * a.
- Associative Property: The grouping of numbers does not change the result of addition or multiplication. For example, (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c).
- Distributive Property: Multiplication distributes over addition. For example, a * (b + c) = a * b + a * c.
- Order of Operations: When performing multiple operations in an expression, follow the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right) to determine the correct result.

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.