An integer is a whole number that can be positive, negative, or zero. In mathematics, integers are used to represent quantities that are counted or measured. Integers are used in various mathematical operations and have specific rules for addition, subtraction, multiplication, and division.

- Positive integers are greater than zero (+1, +2, +3, ...)
- Negative integers are less than zero (-1, -2, -3, ...)
- Zero is considered an integer (0)
- Adding integers with the same sign: Add the numbers and keep the sign.
- Adding integers with different signs: Subtract the smaller number from the larger number and keep the sign of the larger number.
- Subtracting integers: Add the opposite (additive inverse) of the integer being subtracted.
- Multiplying integers with the same sign: The product is positive.
- Multiplying integers with different signs: The product is negative.
- Dividing integers: The quotient has the same sign as the dividend and divisor.

Solve the following integer problems:

- What is the sum of -5 and 7?
- If you owe $15 and then earn $10, what is your new balance?
- Find the product of -4 and 6.
- If you divide 24 by -3, what is the quotient?

- The sum of -5 and 7 is 2.
- If you owe $15 and then earn $10, your new balance is -5.
- The product of -4 and 6 is -24.
- When you divide 24 by -3, the quotient is -8.

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.