If a, b, c are any whole numbers, then (a × b) × c = a × (b × c) In other words, the multiplication of whole numbers is associative, that is, the product of three whole numbers does not change by changing their arrangements. We can multiply three or more numbers in any order. The number 1 is called the multiplication identity or the identity element for multiplication of whole numbers because it does not change the identity (value) of the numbers during the operation of multiplication.Īssociativity Property of Multiplication of Whole Numbers: We see that in each case a × 1 = a = 1 × a. Verification: In order to verify this property, we find the product of different whole numbers with 1 as shown below: For example: (i) 13 × 1 = 13 = 1 × 13 In other words, the product of any whole number and 1 is the number itself. If a is any whole number, then a × 1 = a = 1 × a. When a number is multiplied by 1, the product is the number IVMultiplicative Identity of Whole Numbers / Identity Property of Whole Numbers: We observe that the product of any whole number and zero is zero. Verification: In order to verify this property, we take some whole numbers and multiply them by zero as shown below For example: (i) 20 × 0 = 0 × 20 = 0 In other words, the product of any whole number and zero is always zero. If a is any whole number, then a × 0 = 0 × a = 0. When a number is multiplied by 0, the product is always 0. Multiplication By Zero/Zero Property of Multiplication of Whole Numbers: We find that in whatever order we multiply two whole numbers, the product remains the same. Verification: In order to verify this property, let us take a few pairs of whole numbers and multiply these numbers in different orders as shown below For Example: (i) 7 × 6 = 42 and 6 × 7 = 42 Therefore, 7 × 6 = 6 × 7 We can multiply numbers in any order, the product remains the The product does notĬhange when the order of numbers is changed.Īny two numbers, the product remains same regardless of the order of In other words, if a and b are any two whole numbers, then a × b = b × a. The multiplication of whole numbers is commutative. We find that the product is always a whole numbers.Ĭommutativity of Whole Numbers / Order Property of Whole Numbers: Verification: In order to verify this property, let us take a few pairs of whole numbers and multiply them For example: INT still returns the correct result for negative decimal numbers because the integer changes and the result of the comparison is always FALSE.In other words, if we multiply two whole numbers, we get a whole number. That said, it doesn't make a difference in this example. This matters for negative values, because they are rounded away from zero (i.e. In short, the TRUNC function actually removes the decimal portion of a number, while the INT function always rounds the number down to the next whole value. For example, if A1 contains -5.5: =A1=INT(A1) Both formulas work fine, but note they behave differently with negative decimal values. The formulas look like this: =A1=INT(A1)īoth of these formulas compare the original value in A1 to the same value after removing the decimal portion of the number (if any). If the values match, we know we have a whole number. In this approach, we run the value through one of these functions and compare the result to the original value. INT or TRUNCĪnother way to solve the problem is with the INT function or the TRUNC function. This is the approach taken in the worksheet as shown, where the formula in C5 is: =MOD(B5,1)=0Īt each row in the data, the formula returns TRUE for whole numbers only. Therefore, we can simply compare the result to zero with a logical expression that returns TRUE or FALSE: =MOD(5,1)=0 // returns TRUE Any whole number divided by 1 will result in a remainder of zero: =MOD(5,1)=0 // whole numbers return zeroĪny decimal number will have a remainder equal to the decimal portion of the number: =MOD(5.25,1)=0.25 One of the easiest ways is to use the MOD function with a divisor of 1. In this example, the goal is to test if a numeric value is a whole number.
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