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True or False The set of whole numbers is closed under subtraction Why?
False. The set of whole numbers is not closed under subtraction. Closure under subtraction means that when you subtract two whole numbers, the result is also a whole number. However, this is not always the case with whole numbers. For example, subtracting 5 from 3 results in -2, which is not a whole number.
Twice the smallest of three consecutive odd integers is seven more than the largest find the integers?
Let's represent the three consecutive odd integers as ( 2n-1 ), ( 2n+1 ), and ( 2n+3 ), where ( n ) is an integer. According to the given information, twice the smallest integer ( 2(2n-1) ) is equal to seven more than the largest integer ( 2n+3 ). Setting up the equation, we have ( 4n-2 = 2n+3+7 ). Solving this equation gives us ( n = 6 ). Therefore, the three consecutive odd integers are 11, 13, and 15.
A negative times or divided by a positive equals a?
A Negative times or divided by a Positive equals a Negative A Negative times or divided by a Negative gives a Positive A Positive times or divided by a Negative gives a Negative A Positive times or Divided by a Positive gives a Positive Zero is neither Positive or Negative so anything times Zero is not Positive or Negative.
Subtract -10 from -15?
Alright, buckle up buttercup. When you subtract a negative, it's like adding a positive. So, -15 minus -10 is the same as -15 plus 10, which equals -5. There you have it, simple math for your beautiful brain.
What is the smallest set of numbers closed under subtraction?
Any one of the sets of the form: {kz : where k is any fixed integer and z belongs to the set of all integers} Thus, k = 1 gives the set of all integers, k = 2 is the set of all even integers, k = 3 is the set of all multiples of 3, and so on. You might think that as k gets larger the sets become smaller because the gaps between numbers in the set increases. However, it is easy to prove that the cardinality of each of these infinite sets is the same.
What are some examples on adding integers?
Adding integers involves combining whole numbers, whether positive or negative. For example, adding two positive integers like 3 and 5 gives you 8 (3 + 5 = 8). When adding a positive and a negative integer, such as 7 and -4, you subtract the negative from the positive, resulting in 3 (7 + (-4) = 3). If both integers are negative, like -2 and -6, you simply add their absolute values and keep the negative sign, yielding -8 (-2 + -6 = -8).
When you add a negative integer with a negative integer do you get a positive integer?
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. ■
Why is the sum of a fraction and a whole number not a whole number?
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.
A pair of integers whose sum gives an integer smaller than the both integers?
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.
Why the quotient of two integers is not always an integer?
The quotient of two integers is not always an integer because division may result in a non-integer value when the numerator is not evenly divisible by the denominator. For example, dividing 5 by 2 gives 2.5, which is not an integer. Only when the numerator is a multiple of the denominator will the quotient be an integer.
What gives an example of a set that is closed under addition?
An example of a set that is closed under addition is the set of all integers, denoted as (\mathbb{Z}). This means that if you take any two integers and add them together, the result will also be an integer. For instance, adding 3 and -5 results in -2, which is still an integer. Thus, (\mathbb{Z}) satisfies the property of closure under addition.
What two consecutive even integer such that the smaller number is 5 times the larger number gives a sum of 34?
There can be no such integers: a smaller integer cannot be 5 times the larger number.
How can you find the distance between two integers using the difference?
To find the distance between two integers using the difference, you simply subtract the smaller integer from the larger integer. The result will be the distance between the two integers on the number line. For example, if you have integers 7 and 3, you would subtract 3 from 7 to get a distance of 4. This method works because the difference between two integers gives you the number of units separating them on the number line.
When multiplying two integer what are the four possible combination of sign how can they be grouped into two integers?
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.
When a negative integer is multiplied by another negative integer which sign will the resulting product take?
When a negative integer is multiplied by another negative integer, the resulting product will be positive. This is because the multiplication of two numbers with the same sign always yields a positive result. For example, multiplying -3 by -2 gives +6.
What is the sum of the sequence 33 34 35 36 ... 112?
Adding all integers from 33 to 112 inclusive gives you 5800.
True or False The set of whole numbers is closed under subtraction Why?
False. The set of whole numbers is not closed under subtraction. Closure under subtraction means that when you subtract two whole numbers, the result is also a whole number. However, this is not always the case with whole numbers. For example, subtracting 5 from 3 results in -2, which is not a whole number.
