Number & Numeration
Whole Numbers and Operations
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- ✓By the end of this lesson students will be able to count and write whole numbers up to millions.
- ✓By the end of this lesson students will be able to identify the place value of digits in whole numbers.
- ✓By the end of this lesson students will be able to perform addition, subtraction, multiplication, and division of whole numbers.
- ✓By the end of this lesson students will be able to find factors and multiples of given whole numbers.
- ✓By the end of this lesson students will be able to solve simple word problems involving the four basic operations.
Key concepts
Counting is the process of finding the number of objects in a group. Whole numbers are the set of numbers 0, 1, 2, 3, 4, and so on, without any fractions or decimals. We use number names to say or write these numbers in words (e.g., 1 is 'one', 10 is 'ten', 100 is 'one hundred', 1,000 is 'one thousand', 1,000,000 is 'one million').
Place value tells us the value of each digit in a number based on its position. In Nigeria, we commonly use the place value chart: Unit, Ten, Hundred, Thousand, Ten Thousand, Hundred Thousand, Million, and so on. For example, in the number 345, the digit 5 is in the Units place, 4 is in the Tens place, and 3 is in the Hundreds place.
Addition is the process of combining two or more numbers to find their total sum. The symbol for addition is '+'. When adding large numbers, we usually arrange them in columns according to their place values and add from the Units column first, carrying over to the next column if the sum is 10 or more.
Subtraction is the process of taking one number away from another to find the difference. The symbol for subtraction is '-'. When subtracting large numbers, we arrange them in columns and subtract from the Units column first. If a digit is smaller than the one below it, we 'borrow' from the digit in the next higher place value.
Multiplication is a quick way of doing repeated addition. It is finding the product of two or more numbers. The symbol for multiplication is '×' or '*'. Knowing your multiplication tables (times tables) is very important for quick and accurate multiplication.
Division is the process of sharing a number into equal parts or groups. It tells us how many times one number is contained in another. The symbol for division is '÷' or '/'. The number being divided is the 'dividend', the number dividing is the 'divisor', and the result is the 'quotient'. Sometimes there is a 'remainder' if the division is not exact.
Factors of a number are whole numbers that divide the number exactly, without leaving any remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 exactly.
Multiples of a number are the results you get when you multiply that number by other whole numbers (1, 2, 3, 4, etc.). They are like the 'times table' for that number. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
Key facts to remember
- 1Whole numbers include 0, 1, 2, 3, ... (no fractions or decimals).
- 2Place value determines the value of a digit based on its position (Unit, Ten, Hundred, Thousand, etc.).
- 3Addition combines numbers to find a sum.
- 4Subtraction finds the difference between two numbers.
- 5Multiplication is repeated addition and finds a product.
- 6Division is sharing equally or finding how many times one number goes into another, resulting in a quotient and possibly a remainder.
- 7Factors divide a number exactly without a remainder.
- 8Multiples are the results of multiplying a number by other whole numbers (its 'times table').
Worked examples
Example 1
1. Write the number 'Seven hundred and forty-five thousand, two hundred and nine' in figures and state the place value of the digit '4'.
Answer
The number in figures is 745,209. The place value of the digit '4' is Ten Thousand.
Always remember to count place values from right to left, starting with the Unit place.
Example 2
2. A farmer harvested 1,560 yams on Monday and 2,345 yams on Tuesday. He sold 1,800 yams in total. How many yams does he have left?
Answer
The farmer has 2,105 yams left.
For word problems, break them down into smaller, manageable steps. Perform addition first, then subtraction.
Example 3
3. Find all the factors of 30 and the first five multiples of 6.
Answer
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The first five multiples of 6 are 6, 12, 18, 24, 30.
To find factors, test numbers from 1 upwards. To find multiples, just multiply the number by consecutive whole numbers.
Common mistakes
- ✗Misaligning digits when performing column addition or subtraction, leading to incorrect place value calculations.
- ✗Forgetting to carry over in addition or borrow in subtraction, especially with multiple digits.
- ✗Confusing factors with multiples (e.g., saying 6 is a factor of 3 instead of a multiple of 3).
- ✗Errors in basic multiplication tables, which affects multiplication and division accuracy.
- ✗Not reading word problems carefully and performing the wrong operation or missing a step.
Exam tips
- ★Always show all your working steps clearly, as marks are often awarded for method.
- ★Practise your multiplication tables (1 to 12) regularly to improve speed and accuracy in multiplication and division.
- ★When solving word problems, read the question carefully, identify what is being asked, and decide which operation(s) to use.
- ★Check your answers, especially for addition and subtraction, by performing the inverse operation (e.g., check addition with subtraction).
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