7th Grade Integers: Help with 7th Grade Math

Help with Integers

Integers include all of the whole numbers (0, 1, 2 and so on) and their inverses (-1, -2 and so on). A good rule of thumb is that any number typically listed on a number line is an integer.

Integer Operations

Addition and Subtraction

When you're adding and subtracting integers, keep in mind that their order is critical. The answer to 5 - 3 is not the same as the answer to 3 - 5. It's also helpful to remember when you add a negative number, it's the same as subtracting it. For instance, 3 + (-7) = 3 - 7. Here are some basic instructions to follow when you're adding or subtracting integers:

1. Find the first number in the expression on the number line. For the problem 3 - 6, you would begin at three.
2. The sign in the middle of the problem tells you which direction to move from that number. A positive sign tells you to move to the right, and a negative sign tells you to move to the left. The negative sign in 3 - 6 tells you to move left from three.
3. The second number in the problem tells you how many spaces to move. In 3 - 6, the six tells you to move six spaces to the left of three.
4. The number that you land on is your answer. For instance, if you count six spaces to the left of three, you'll arrive at negative three (-3), which is your answer (3 - 6 = -3).

Multiplying and Dividing Integers

You multiply and divide integers the same way that you multiply and divide whole numbers. The only difference is that you must follow these rules to make sure your answer has the correct sign:

1. When you're multiplying or dividing two numbers with the same sign (two positive numbers or two negative numbers), the answer will be positive. For example, 2 x 2 = 4 and -2 x -2 = 4.
2. If you multiply or divide two numbers that have opposite signs, the answer will be negative. For instance, -1 x 5 = -5 and 3 x -3 = -9.
3. When you're multiplying more than two integers, count the total number of negative integers that you want to multiply. If that number is even, then your answer will be positive (-2 x -2 x 2 = 8). If it's odd, then your answer will be negative (-2 x 2 x 2 = -8).

Properties of Integers

Additive Inverses

The additive inverse of a number is its positive or negative counterpart. For instance, the additive inverse of negative six (-6) is positive six (6), and the additive inverse of positive two (2) is negative two (-2). A number plus its additive inverse always equals zero. For instance, -6 + 6 = 0 and 2 + (-2) = 0.

Absolute Values

Every integer has an absolute value that's equal to its distance from zero stated as a positive number. The absolute value of a positive integer is the integer itself (|2| = 2). However, the absolute value of a negative integer is that integer's additive inverse (|-2| = 2).