Natural numbers and Whole numbers Test - 1

Successor of a number can be obtained by adding 1 to the number whereas the predecessor of a number can be obtained by subtracting 1 from the number.

∴Successor of 2971 = 2971 + 1 = 2972

Successor of 926 = 926 + 1 = 927

Successor of 56021 = 56021 + 1 = 56022

Therefore, sum of the successors of the numbers 2971, 926, and 56021 = 2972 + 927 + 56022

= 59921

Predecessor of 22 = 22 − 1 = 21

Thus, required difference = 59921 − 21 = 59900

Smallest whole number = 0

Smallest natural number = 1

Difference between the smallest natural number and smallest whole number = 1 − 0 = 1

Whole numbers start from 0 and natural numbers start from 1.

Therefore, every natural number is a whole number.

8 × 3 = (4 × 2) × 3

= 4 × (2 × 3) [by associative property of multiplication]

= 4 × 6

The additive identity for whole numbers is 0. Therefore, the product of any whole number and 0 is 0 only.

Thus, only statement C is incorrect.

The given expression is 214 × 56 + 144 × 214.

214 × 56 + 144 × 214

= 214 × 56 + 214 × 144          [By commutative property of multiplication]

= 214 × (56 + 144)                 [By distributivity of multiplication over addition]

= 214 × 200

Whole numbers are not closed under subtraction, i.e., the difference of two whole numbers may or may not give a whole number. For example, take the whole numbers 2 and 5.

5 − 2 = 3 is a whole number

However, 2 − 5 does not give a whole number.

Thus, row D is incorrectly matched.

The given expression is

1627× ? = 1627 × 70 + 1627 × 8 + 1627 × 10

According to the distributive property of multiplication over addition of whole numbers, say, a, b and c,

a × (b + c) = a × b + a × c

∴ 1627 × 70 + 1627 × 8 + 1627 × 10 = 1627 × (70 + 8 + 10)

⇒ 1627 × 70 + 1627 × 8 + 1627 × 10 = 1627 × 88

Thus, the number 88 will complete the given expression.

It is known that the successor of a number can be obtained by adding 1 to the number and the predecessor of a number can be obtained by subtracting 1 from the number.

∴ Predecessor of 1320 = 1320 − 1 = 1319

Successor of 42906 = 42906 + 1 = 42907

Thus, required sum = 1319 + 42907 = 44226

Smallest whole number = 0

∴ a = 0

Smallest natural number = 1

∴ b = 1

Let us form the greatest and the smallest four-digit numbers using the digits 0, 8, 5 and 1 without repetition.

If we arrange the numbers in descending order, then we will obtain the greatest number. Therefore, the greatest number that can be formed by using the given digits is 8510.

If we arrange the numbers in ascending order, then we will obtain the smallest number. Therefore, the smallest number is 1058 (since we need to form a four-digit number and a number cannot begin with 0, so it cannot be placed at the thousands place).

∴ Required difference = 8510 − 1058 = 7452