A set is closed under a particular operation (like division, addition, subtraction, etc) if whenever two elements of the set are combined by the operation, the answer is always an element of the original set. Examples: I) The positive integers are closed under addition, because adding any two positive integers gives another positive integer. II) The integers are notclosed under division, because it is not true that an integer divided by an integer is an integer (as in the case of 1 divided by 5, for example). In this case, the answer depends on the definition of "whole numbers". If this term is taken to mean positive whole numbers (1, 2, 3, ...), then the answer is no, they are not closed under subtraction, because it is possible to subtract two positive whole numbers and get an answer that is not a positive whole number (as in the case of 1 - 10 = -9, which is not a positive whole number)
Negative. Sorry. No you do not. Adding a negative to a negative gives you a number that is even more negative. Picture a number line. A negative number is to the left of zero, and adding a negative number moves further left. ■
Look at it the other way - by reverting the operation. The reason it is not a whole number is because if it where, then the subtraction of two integers would be a fraction! If a + b = c (a is a non-integer fraction, b and c are integers), then c - b = a. You would have a fraction as a result of subtracting two integers. However, adding or subtracting two integers always gives you an integer.
Take any negative integers, say -5 and -10, their sum is -15 which is smaller than both of them. We could have used 0 as well, so I should have said any non-positive integers. To see that is does not work with positive integers, take 5 and 10 whose sum is 15 which is BIGGER than either one.
There can be no such integers: a smaller integer cannot be 5 times the larger number.
Adding all integers from 33 to 112 inclusive gives you 5800.
900 This explains it. A positive integer is a palindrome if it reads the same forward and backwards such as 1287821 and 4554. Determine the number of 5-digit positive integers which are NOT palindromes. We start by counting the total number of 5 digit positive integers. The first digit is between 1 and 9, so we have 9 choices. Each of the other 4 digits can be anything at all (10 choices for each). This gives us 9(10)4 = 90000 five-digit positive integers. Now we need to count the number of 5 digit palindromes. Again, we have 9 choices for the first digit and 10 choices for each of the next two. The tens and units digits however are fixed by our choices so far. Therefore, there are only 900 five-digit palindromes. Therefore, the total number of five-digit positive integers which are not palindromes is 90000-900 = 89100.
Every integer from 800 to 899 begins with 8. Every tenth integer from 708 to 898 end in 8, however all of these from 808 to 898 will already be counted by the first statement. There are ten tens between 708 and 798 and 100 integers between 800 and 899 inclusive. This gives a total of 110.
The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5.
Let x = 1st integer, since consecutive even integer differs by 2 then the 2nd integer = x + 2. So we have, x + 4(x + 2) = 48 x + 4x + 8 = 48 5x = 40 x = 8 (1st integer) Thus, the integers are 8 and 10. Check.
Adding two negative numbers always gives a negative number.
3(n + 2) = n - 10 3n + 6 = n - 10 2n + 6 = -10 2n = -16 n = -8 -8 and -6
These are really simple to solve. Just divide by 3 and that gives you your middle integer. In this case 348/3 = 116 so the trio are 115, 116 and 117.
Just multiply the two numbers. Remember that multiplying two negative numbers gives a positive result.
The four possible combinations are:A = (+, +)B = (+, -)C = (-, +) andD = (-, -)In A and D, the two numbers have the same signs and the multiplication gives a positive answer.In B and C, the two numbers have different signs and the multiplication gives a negative answer.
if you have the expression a + b*sqrt(c), the radical conjugate is a - b*sqrt(c). this is important because multiplying those two expressions together gives you an integer if a, b, and c are integers.
The average is 2 - Adding all the numbers together gives a total of 42. There are 21 numbers in the range - therefore the average is 2.
There are no such integers.
A negative, since subtracting a positive is equivalent to moving left done the number line. Since we start left of 0 on the number line, it is only possible to end left of it after subtraction, resulting in a negative. Since the subtraction is the opposite of addition, to subtract a positive really means that you are adding a negative. So you are adding two negatives which gives you a negative sum.
Because of the definition of addition and subtraction. When looking at a real number line: when you add you move to the left or up, when you add the opposite of a number you move in the opposite direction.
The lowest common multiple of 2 3 4 and 5 is 60 and that gives an answer of just one
Try it! Find the square of some integers, until you either (a) find one that gives exactly 360 when squared, or (b) find two consecutive integers, one of which is smaller, the other larger, than 360. You can also take your calculator and find the square root of 360. If it is an integer (no decimals), that means it is a square number.
Adding another quadrillion to 999 quadrillion gives 1 quintillion.
A rational number can be stated in the form a/b where and b are integers. Adding or multiplying such numbers always gives another number that can be expressed in this form also. So it is also rational.