closure property of multiplication number example

Therefore closure property is not true for subtraction of whole numbers.Įxample: 2 – 4 = –2. ( 3 + 4 ) × 5 = ( 3 × 5 ) + ( 4 × 5 ) = 35įor any two whole numbers a, b (a – b) may not be a whole number. This is called zero property in multiplication of whole numbers.įor any two whole numbers a, b if a b = 0, then either a = 0 or b = 0 or a = b = 0.ĭistributive Property of Multiplication over Additionįor any three whole numbers a, b, c a × ( b + c ) = ( a × b ) + ( a × c ) or ( b + c ) × aa = ( b × a ) + c × aĢ × ( 3 + 4 ) = ( 2 × 3 ) + ( 2 × 4 ) = 14 The whole number when multiplied by zero, the product is always zero, i.e., for any whole number a Ī × 0 = 0 × a = 0. Here 1 is called the multiplicative identity in the set of all whole numbers. 6 is also a whole number.įor any two whole numbers a, b a ×b = b ×aįor any three whole numbers a, b, c a × ( b × c ) = ( a × b ) × cįor any whole number a a × 1 = 1 × a = a. This is called closure property of multiplication.Įxample: 2 × 3 = 6. 0 is called the additive identity.įor any two whole numbers a and b their product a b is also a whole number. This is called associative property of addition.įor every whole number a a + 0 = 0 + a = a. This is called commutative property of addition.įor any three whole numbers a, b, c a + (b + c) = (a + b) + c. This is called closure property of addition.įor any two whole numbers a and b when added in any order gives the same sum i.e., a + b = b + a. Since the final position obtained on the number line is 15, the value of the expression 5 × 3 is 15.įor any two whole numbers a and b their sum (a + b) is also a whole number.

Since the number to be multiplied is 3, we will start from zero and make 3 jumps of 5 units each. Since the final position obtained on the number line is 7, the value of the expression (16 – 9) is 7. From this point, jump nine units to its left. We have to find the value of the expression 16 – 9 on the number line. Subtract 9 from 16 using the number line. Since the final position obtained on the number line is 13, we obtain 13 by adding 6 and 7. Since the number to be added is 7, we move seven units to the right of number 6 on the number line.

Since the first number is 6, we mark the position of number 6 on the number line. Therefore, it is 29.Īddition, Subtraction and Multiplication on a Number Lineĭo you know that basic mathematical operations such as addition, subtraction, and multiplication canīe carried out on a number line? It requires a good understanding of the number line. The second unknown point is 5 units away from 24. The first unknown point is 2 units away from 21. Locate the unknown points on the following number line. The distance between 11 and 14 is 3 units. Since the number 14 is on the right of 11, therefore, Now, we locate these two points on the number line as follows. Mark the successor of 10 and the predecessor of 15 on the number line and compare them. We can use this number line to determine whether a number is greater or lesser than another given number. These numbers can be represented on a line, which is called the number line. Remember: All natural numbers are whole numbers but all whole numbers are not natural numbers. Therefore, the natural number 1 has a predecessor 0 which is a whole number. Whole numbers are a set of numbers starting from 0, that is 0, 1, 2 … “If zero is added to the collection of natural numbers, we obtain the collection of whole numbers, or in other words, we can say that all natural numbers along with zero are called whole numbers.”

This is because 1 – 1 = 0 and 0 is not a natural number. Every number except 1 has a predecessor in case of natural numbers. Successor and predecessor are reverse of each other.įor example, 20 is the successor of 19 and 19 is the predecessor of 20.ģ. Every natural number has a successor because there is no largest natural number.Ģ. Predecessor “If 1 is subtracted from any natural number, then we obtain the predecessor of that number.”įor example, the predecessor of 11 will be 11 – 1 = 10.ġ. “If 1 is added to any natural number, then we obtain the successor of that number.”įor example, the successor of 11 will be 11 + 1 = 12.

Closure property of multiplication number example