The negative numbers are the additive inverses of the corresponding positive numbers. The sign means ‘less than or equal to' and the sign means ‘greater than or equal to.An integer is the number zero ( 0), a positive natural number ( 1, 2, 3, etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.).
We could have said 3 n < 8 in which case, 3 would have been included in the answer, so n = 3, 4, 5, 6, 7. Read this: n such that n is greater than 3 and less than 8īecause 3 < n or 3 is less than n or n is greater than 3Īnd n < 8 or n is less than 8 or 8 is greater than n
Another way to express this would be the set of numbers that is greater than 3 but less than 8, which can be put into a mathematical sentence that looks like: What are the integers between 3 and 8? That would be 4, 5, 6, and 7. Each of these integers would be called a member or element of that set. The set of numbers that satisfies these conditions would be the set of all the positive integers. For example, the set of integers less than 0 would be expressed as n 0. Greater Than and Less Than and Sets of NumbersĪ set of numbers is a group of numbers that answers a given description. If it had been -6 x -2 x -3 x 5, the answer would have been -180 There are two negative signs (an even number), so the answer is positive. If it is an even number, the product will be positive, and if it is an odd number, the product will be negative.Ħ x 2 = 12, 12 x 3 = 36, and 36 x 5 = 180 To multiply multiple numbers, count the number of negative signs on the numbers to be multiplied. Rewrite the problem as the first term plus the opposite of the second term. When multiplying a positive number and a negative number (or a negative number and a positive number), multiply the absolute values, and give the answer a negative sign.Ĩ x -5 = |8| x |5| = 8 x 5 = 40, but give it the negative sign, making it -40 An integer is a positive or negative whole number. Multiplying Positive and Negative Numbers If you were to use a number line, you would go left for subtract and then reverse (to the right) for the negative number, so the final answer is to the right of the original number.Ī number's additive inverse is the number of the opposite sign such that when the two are added, the result is zero.Īs you can see this is the positive and negative numbers of the same absolute value. Interested in learning more? Why not take an online Basic Math course? Absolute value is denoted by writing the number between two vertical bars.
It is always expressed as positive but without a ‘plus' sign. The absolute value of a number is the number of units the number is from zero. We don't always have a number line with which to work, so we need to learn a few rules about working with negative numbers. Negative numbers also include various forms and various types of numbers that appear left of the zero. Positive numbers are not just the integers to the right of the zero, but all types of numbers like fractions, decimals, and radicals. If we start at -3 and move 7 spaces right, we will be at 4. Looking at the inverse operation, we can say that if 4 – 7 = -3, then -3 + 7 = 4. Because -3 is to the left of 0, it is less than zero. However, we can subtract a positive number from a positive number and suddenly, we don't get a positive number!įor example, if we subtract 7 from 4, we would start at 4 on the number line and move left 7 places. When we add two positive numbers or multiply two positive numbers, we get a positive number. This is generally the way a number line works. When we move to the right on the number line, we increase in numbers. Zero, the dividing point, is neither positive nor negative.įor the number line above, "1" corresponds or is related to the red point, "2" is related to the green point, "3" is related to the blue point, and so forth. The positive numbers are to the right of zero, so they are greater than zero. The negative numbers are to the left of zero, so they are less than zero. On the number line above, we can see three types of numbers, or integers: negative numbers, zero, and positive numbers.
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