Natural Numbers and Whole Numbers (Including Patterns)

ICSE Class 6 · Mathematics · Chapter 5

What this chapter covers

Natural numbers are the counting numbers 1, 2, 3, 4, 5 and so on, without end.

Whole numbers are the natural numbers together with zero, so they are 0, 1, 2, 3, 4 and so on.

The commutative property of addition is the rule that two whole numbers can be added in either order and the sum stays the same.

The commutative property of multiplication is the rule that two whole numbers can be multiplied in either order and the product stays the same.

The associative property of addition is the rule that when three whole numbers are added, the grouping does not change the sum.

The associative property of multiplication is the rule that when three whole numbers are multiplied, the grouping does not change the product.

The distributive property is the rule that multiplying a number by a sum gives the same answer as multiplying it by each part and then adding.

The additive identity is the number which, when added to any whole number, leaves that number unchanged.

The multiplicative identity is the number which, when multiplied by any whole number, leaves that number unchanged.

Even numbers are whole numbers that can be split into two equal groups, such as 0, 2, 4, 6 and 8.

Odd numbers are whole numbers that leave 1 over when split into two equal groups, such as 1, 3, 5, 7 and 9.

Natural numbers are the counting numbers 1, 2, 3 and so on; the smallest is 1 and there is no largest.
Whole numbers are 0, 1, 2, 3 and so on; they are the natural numbers with zero added.
The successor of a number is 1 more than it; the predecessor is 1 less than it.
Addition and multiplication of whole numbers are commutative and associative; subtraction and division are not.
Multiplication distributes over addition and subtraction, which makes mental sums easier.
Zero is the additive identity and one is the multiplicative identity.
Any number multiplied by 0 gives 0, and division by 0 is not defined.
Patterns, such as sums of odd numbers giving square numbers, can be turned into rules and checked.

What is the smallest natural number, and what is the smallest whole number?

The smallest natural number is 1. The smallest whole number is 0.

Write the successor of 3,999 and the predecessor of 7,000.

The successor of 3,999 is 4,000. The predecessor of 7,000 is 6,999.

Which whole number is not a natural number?

Zero (0).

Name the property shown in (18 × 4) × 25 = 18 × (4 × 25).

The associative property of multiplication.

Use the distributive property to find 8 × 105.

8 × 100 + 8 × 5 = 800 + 40 = 840.

Which number is the additive identity, and which is the multiplicative identity?

Zero is the additive identity and one is the multiplicative identity.

What is 0 ÷ 15, and what is 15 ÷ 0?

0 ÷ 15 = 0, but 15 ÷ 0 is not defined.

Using the odd-number pattern, find 1 + 3 + 5 + 7 + 9 + 11 without adding.

These are the first 6 odd numbers, so the sum is 6 × 6 = 36.