The set of integers consists of the whole numbers, their opposites and zero. Numbers greater than zero are positive integers, and numbers less than zero are negative. Use a (+) sign (or no sign) to indicate a positive number and a (–) sign to indicate a negative number. Zero is neutral. You must learn to add, subtract, multiply and divide integers in order to realize success in algebra. Learning one operation, such as addition, might seem simple, but it’s easy to get confused when the operations are mixed. Study the rules for each operation and get plenty of practice.
Use a number line of positive and negative numbers and zero. Put a dot above the first addend. Think of the number’s sign as a direction on the number line: go right for positive numbers and left for negative numbers. If you are adding -8 and -6, place a dot above -8 on the number line. Since -6 is negative, move six spaces to the left. End at -14.
Draw an “X” for each positive integer and an “O” for each negative number that you add. If you add (-9) + (7), draw seven X’s and nine O’s. Cross out pairs of positive and negative numbers until there are no more pairs. The numbers that remain – in this case, two negatives – indicate the sum, -2.
Memorize the rules for adding integers. When adding positive numbers, add absolute values and label the answer positive. When adding negative numbers, add absolute values and label the answer negative. When the signs are different, find the difference; label the sum with the sign of the number with the greater absolute value.
Transform the subtraction problem into an addition problem. Remember to “add the opposite.” Leave the first number alone, change the subtraction sign to an addition sign and change the second number to its opposite. When subtracting (-10) – (+7), write the transformed problem: (-10) + (-7).
Follow the rules for adding integers after you have changed the subtraction problem into an addition problem. (-10) + (-7) = -17.
Remember the chant, “Change the sign…Change the sign.” Think of this chant to help you recall that you must change the subtraction sign to an addition sign and the second number’s sign to its opposite.
Multiplication and Division
If you don't understand how to work with integers, you will encounter much difficulty in higher level math.
Multiply or divide the numbers “normally,” as if there were no signs. In other words, multiply or divide their absolute values. In the problem (-8) x (+9), multiply eight times nine and get 72.
Label the answers correctly. When multiplying or dividing two numbers with the same signs, label the answer positive. When multiplying or dividing two numbers with different signs, label the answer negative.
Visit the Khan Academy website. Go to the pre-algebra video section and watch the related integer videos for detailed explanations and a review of the concepts.
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