In mathematics, the sum is the result of adding two or more numbers or quantities together. The sum is a basic arithmetic operation and is denoted by the plus sign (+). For example, the sum of 3 and 5 is 8, which can be written as 3 + 5 = 8.

**Commutative Property:**The sum of two numbers remains the same regardless of the order in which they are added. In other words, a + b = b + a.**Associative Property:**When adding three or more numbers, the grouping of the numbers does not affect the sum. In other words, (a + b) + c = a + (b + c).**Identity Property:**The sum of any number and zero is the number itself. In other words, a + 0 = a.

1. Find the sum of 7 and 4.

Sum: 7 + 4 = 11

2. Find the sum of 12, 5, and 8.

Sum: 12 + 5 + 8 = 25

To effectively work with sums, it's important to understand the basic properties and practice adding different numbers. Here are some key points to remember when dealing with sums:

- Understand the meaning of the sum and how it relates to addition.
- Learn and apply the commutative, associative, and identity properties of addition.
- Practice adding single-digit, double-digit, and triple-digit numbers to build fluency in finding sums.
- Apply the concept of sums to real-life situations, such as adding prices of items or calculating total distances traveled.

By mastering the concept of sum and practicing its application, you'll develop a strong foundation in arithmetic and be better equipped to solve more complex mathematical problems in the future.

.Study GuideUsing Integers Worksheet/Answer key

Using Integers Worksheet/Answer key

Using Integers Worksheet/Answer key

Using Integers Worksheet/Answer keyUsing Integers

Number and Operations (NCTM)

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

Develop meaning for integers and represent and compare quantities with them.

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

Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

Compute fluently and make reasonable estimates.

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

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.