Grade 6 Mathematics Numbers – WholeNumbers Notes

What are whole numbers?

Whole numbers are the numbers we use for counting and for saying "none". They are: 0, 1, 2, 3, 4, 5, 6, ... (That means every number with no fractions or decimals and no negatives.)

In simple words: whole numbers = 0 + all the natural counting numbers.

Examples

• 0 (zero) — e.g. no pencils left.
• 7 — e.g. 7 students in a team.
• 120 — e.g. KSh 120 for a cloth.

Number line (simple)

Use the number line to compare numbers, add small numbers, or show counting.

Place value (how digits give the value)

Example number: 5 4 2 3 (written as 5,423)

Expanded form: 5,423 = 5,000 + 400 + 20 + 3

Comparing and ordering

To compare two whole numbers: look at the number with more digits — it is larger. If same digits, compare from the leftmost digit.

Example: Which is greater — 3,512 or 3,421? Start at thousands (3 = 3), then hundreds (5 > 4) so 3,512 > 3,421.

Addition and subtraction (whole numbers)

Rules: add or subtract digit by digit, carry (add) or borrow (subtract) when needed.

Multiplication and division (whole numbers)

Multiplication gives groups of whole numbers. Division shares or groups into equal parts. Whole numbers are closed under these operations only when the result is also a whole number (division can give a remainder).

Example: 24 × 6 = 144. 144 ÷ 12 = 12 (no remainder). 25 ÷ 4 = 6 remainder 1.

Important properties (simple)

• Closure: Adding or multiplying two whole numbers gives a whole number.
• Commutative: a + b = b + a and a × b = b × a (e.g., 4 + 6 = 6 + 4).
• Associative: (a + b) + c = a + (b + c).
• Identity: a + 0 = a; a × 1 = a.
• Not all operations stay whole: subtraction can give negative numbers; division can give fractions or remainders.

Rounding whole numbers

Rounding makes numbers easier to work with. To round to the nearest ten: look at the ones digit.

Example: Round 237 to nearest ten: ones digit = 7, so round up to 240. Round 232 → 230.

To nearest hundred: look at the tens digit. 567 → 600 (because tens digit 6 means round up).

Kenyan context examples (word problems)

1. A teacher has 120 exercise books. She gives 8 books to each student. How many students get books? (Do division; answer is a whole number if no remainder.)
2. A matatu (minibus) charges KSh 50 per passenger. If 9 passengers pay, how much money is collected? (Use multiplication.)
3. A farmer harvested 2,450 kg of maize and sold 1,375 kg. How much maize remains? (Use subtraction.)

Practice questions

1. Write the following in expanded form: 6,307.
2. Which is greater: 8,091 or 8,109? Explain.
3. Compute: 246 + 587.
4. Compute and show remainder: 101 ÷ 9.
5. Round 3,784 to the nearest hundred.
6. (Word problem) A shop has 432 apples. They pack them in boxes of 12. How many full boxes can they make? How many apples are left?

Answers (check your work)

1. 6,307 = 6,000 + 300 + 0 + 7.
2. 8,109 is greater. Compare digits from left: 8=8, 0=0, tens: 1 < 9? Actually compare hundreds/tens correctly: 8,091 vs 8,109 — look at hundreds place: 0 = 1? Better to compare: digits: (8,0,9,1) vs (8,1,0,9) → at the hundreds place 0 < 1 so 8,109 > 8,091.
3. 246 + 587 = 833.
4. 101 ÷ 9 = 11 remainder 2 (because 9×11=99, left 2).
5. 3,784 to nearest hundred → 3,800 (tens digit 8 → round up).
6. 432 ÷ 12 = 36 full boxes, remainder 0 (since 12×36 = 432). No apples left.