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What is a quotient of integers?
A quotient of integers is the result of dividing one integer by another. When dividing two integers, the result may be a whole number if the division is exact, or a decimal/fraction if there is a remainder. For example, when dividing 10 by 2, the quotient is 5, which is also an integer.
All rational numbers are also integers?
No; 3/4 is rational but not an integer.
The quotient of two integers is always a rational number?
Yes. All numbers are rational numbers except repeating decimals like 1.3(repeating). * * * * * Repeating decimals are also rationals. However, the quotient is not defined if the second number is the integer zero!
Is the square root of 7 an integer?
No. Integers are counting numbers, or whole numbers.Only squares of integers (e.g. 4, 9, 16, 25) can have integer roots.Square roots of numbers that are not squares of integers are also not rational numbers, because they have repeating or non-repeating decimal extensions.
Are percents integers?
Any number which is a whole number (0, 8, 87, 453 ...and so) is an integer. Technically, integers also include negative whole numbers but it is unlikely that this is of concern in relation to this question. In a percentage expression such as 23%, 76% then 23 and 76 are integers. With expressions such as 14.6%, 51.9% then the numbers are not integers. The result of a percentage calculation may result in an integer solution, 14.5% of 5800 = 841 even though one of the terms is a non-integer number. Equally, a calculation can result in a non-integer solution even when the opening terms are all integers such as 17% of 53 = 9.01
How Every nonzero integer has a multiplicative inverse as an integer?
A nonzero integer does not have a multiplicative inverse that is also an integer. The multiplicative inverse of an integer ( n ) is ( \frac{1}{n} ), which is only an integer if ( n ) is ( 1 ) or ( -1 ). For all other nonzero integers, the result is a rational number, not an integer. Therefore, only ( 1 ) and ( -1 ) have multiplicative inverses that are integers.
What is a quotient of integers?
A quotient of integers is the result of dividing one integer by another. When dividing two integers, the result may be a whole number if the division is exact, or a decimal/fraction if there is a remainder. For example, when dividing 10 by 2, the quotient is 5, which is also an integer.
Are all negative rational numbers integers?
No, they are not because fractions can be negative also. fractions aren't integers
What property do all nonzero numbers have that integers do not?
Of not being equal to zero. Also, of being closed under division.
Why are fractions rational numbers but not every rational number is a fraction?
'Rational' in a mathematic sense means 'can be written as a finite fraction'. Since you can obviously write a fraction as a fraction - by a triviality - it is rational. Rational numbers also include the integers; however these can also be written as fractions in the form a/1, so technically every rational number is a fraction.Note to the author of the above quote: - I don't believe that is correct. Here's why:A fraction is a number that expresses part of a whole as a quotient of integers (where the denominator is not zero).A rational number is a number that can be expressed as a quotient of integers (where the denominator is not zero), or as a repeating or terminating decimal. Every fraction fits the first part of that definition. Therefore, every fraction is a rational number.But even though every fraction is a rational number, not every rational number is a fraction.Why? Consider this:Every integer (all the whole numbers, including zero, and their negatives....-3,-2,-1,0,1,2,3...) is a rational number, because it can be expressed as a quotient of integers, as in the case of 4 = 8/2 or 1 = 3/3 or -3 = 3/-1 and so on. So integers such as 4 or 1 can be expressed as the quotient of integers.But an integer is not a fraction. 4 is an integer, but it is not a fraction. 4 is not expressed as the quotient of integers. The difference here is in the wording.A fraction is a number that expresses part of a whole. An integer does not express a part. It only expresses a whole number.A rational number is a number that can be expressed as a quotient of integers, or as part of a whole, but fraction is a number that is (must be) expressed as a quotient of integers, or as part of a whole - there is a difference. The difference is subtle, but it is real.In a nutshell, the fractions are a subset of the rational numbers. The rational numbers contain the integers, and fractions don't.
How can you use a number to explain what an integer and rational number are?
An integer is any whole number, positive or negative, including zero, such as -3, 0, or 5. A rational number, on the other hand, can be expressed as the quotient of two integers, where the denominator is not zero, like 1/2 or -4 (since -4 can be written as -4/1). For example, the integer 3 is also a rational number because it can be represented as 3/1. Thus, all integers are rational numbers, but not all rational numbers are integers.
Is nonnegative integers a positive integer?
Yes but a double negative integer is also positive as for example --2 = +2
All rational numbers are also integers?
No; 3/4 is rational but not an integer.
Are all integers negative?
noNo. There are positive and negative integers. Zero is also an integer.-----------------------An integer simply means a whole number/value. It shouldn't matter whether it is positive or negative.
What are the integers of 6?
The integers of 6 refer to the integers that can be generated by multiplying 6 by any integer. This includes the multiples of 6, which are ..., -12, -6, 0, 6, 12, ... and so on. In a more general sense, the integers of 6 can also refer to the number itself as an integer.
What is the definition of add integers?
An integer is a whole number. Some examples are 0, 1, 2, 3, etc. Negative whole numbers are also integers, e.g. -5. Add integers means take two or more integers and add them together. For example, 1+2=3 is an example of adding two integers (1 and 2) to get 3. Notice that 3 is also an integer. Adding integers together will always result in another integer. More than one integer can be added together. For example: 1+2+3=6.
The quotient of two integers is always a rational number?
Yes. All numbers are rational numbers except repeating decimals like 1.3(repeating). * * * * * Repeating decimals are also rationals. However, the quotient is not defined if the second number is the integer zero!
