0
What else can I help you with?
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
Why is it true for any two nonzero integers the product and quotient have the same sign?
For any two nonzero integers, the product and quotient will have the same sign because both operations depend on the signs of the integers involved. If both integers are positive or both are negative, their product is positive and their quotient is also positive. Conversely, if one integer is positive and the other is negative, their product is negative and their quotient is also negative. Thus, in both cases, the product and quotient share the same sign.
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.
If the quotient of two numbers is an integer then both number must be integers?
No, it is not necessary for both numbers to be integers for their quotient to be an integer. For example, if you divide a rational number by another rational number that shares a common factor, the result can still be an integer. For instance, ( \frac{4.0}{2.0} = 2 ), where both numbers are not integers but the quotient is an integer. However, if both numbers are integers, their quotient will also be an integer if the numerator is divisible by the denominator.
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.
What statements is true p is and integer and q is a nonzero integer?
If ( p ) is an integer and ( q ) is a nonzero integer, then the expression ( \frac{p}{q} ) will always yield a rational number. Additionally, since ( q ) is nonzero, ( p ) cannot be divided by zero, ensuring the division is valid. Furthermore, ( p + q ) will also be an integer, as the sum of two integers is always an integer.
How many integers have reciprocally that are also integers?
The only integers that have reciprocals that are also integers are 1 and -1. This is because the reciprocal of an integer ( n ) is ( \frac{1}{n} ), which is only an integer when ( n ) is either 1 or -1. Therefore, there are exactly two integers whose reciprocals are also integers.
Are all negative rational numbers integers?
No, they are not because fractions can be negative also. fractions aren't integers
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.
What property do all nonzero numbers have that integers do not?
Of not being equal to zero. Also, of being closed under division.
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
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.
