Whole Numbers

Topic: Numbers — Subject: Mathematics
Target: Age 10 (Kenyan primary level)

What are whole numbers?

Whole numbers are the numbers we use for counting and for “no parts” (no fractions or decimals). They include zero and all the positive integers:

0, 1, 2, 3, 4, 5, 6, ...

Important ideas

• Zero is a whole number. It shows “nothing” — e.g. 0 cows.
• No negatives: Whole numbers do not include −1, −2, etc.
• No fractions or decimals: 1/2 and 2.5 are not whole numbers.
• Used for counting and order: 1st, 2nd, 3rd etc. (ordinal use).

Number line (showing whole numbers)

Read left to right: 0 then 1 then 2 and so on. Every step to the right adds 1.

Place value with whole numbers

Each digit has a place value. For example: 3 4 7

So 347 = 3 × 100 + 4 × 10 + 7 × 1

Basic operations with whole numbers

• Addition: 23 + 15 = 38. (Add ones, then tens.)
• Subtraction: 30 − 12 = 18. (Borrow if needed.)
• Multiplication: 6 × 4 = 24. (Groups of a number.)
• Division: 20 ÷ 5 = 4. (Share into equal whole groups.)

Properties of whole numbers

• Closure: Adding or multiplying two whole numbers gives a whole number (e.g., 2 + 3 = 5).
• Commutative: a + b = b + a and a × b = b × a (order does not change result).
• Associative: (a + b) + c = a + (b + c); same for multiplication.
• Identity: 0 is the additive identity (a + 0 = a). 1 is the multiplicative identity (a × 1 = a).

Even and odd whole numbers

- Even numbers end in 0, 2, 4, 6, 8 (e.g., 4, 10, 28).
- Odd numbers end in 1, 3, 5, 7, 9 (e.g., 3, 11, 57).

Examples from daily life (Kenyan context)

• You buy 3 mangoes: number of mangoes is a whole number (3).
• If you have 0 coins in your pocket, that is also a whole number (0).
• Counting pupils in class (25 pupils) — whole number.

Simple practice (try these)

1. Write the next three whole numbers after 17.
2. What is 50 − 23?
3. Is 0 a whole number? Explain in one sentence.
4. Which is bigger: 99 or 100?
5. Class has 28 pupils. If the teacher brings 7 more, how many pupils now?

Answers

1. 18, 19, 20.
2. 27.
3. Yes. Zero shows none and is included among whole numbers.
4. 100 is bigger.
5. 28 + 7 = 35 pupils.

Tip: Practice counting forwards and backwards on a number line. Try adding and subtracting using place value columns (ones, tens, hundreds).