Natural Numbers
Numbers · Natural Numbers
Syllabus tag: KCSE | Mathematics | Form 1 | Topic 1 Natural Numbers
Lesson objectives
By the end of this topic, you should be able to:
- Identify, read and write natural numbers in symbols and words.
- Round off numbers to the nearest ten, hundred, thousand and million.
- Perform the four basic operations on whole numbers.
- Identify even, odd and prime numbers.
- Apply operations on natural numbers to solve word problems.
Natural Numbers
Natural numbers are the counting numbers: 1, 2, 3, 4 and so on. Together with zero they form the whole numbers.
a) Place value and total value
The place value is what a position is worth. The total value is the digit multiplied by its place value.
Write large numbers in groups of three from the right. The groups are ones, thousands, millions, billions.
b) Reading and writing
Read group by group from the left, naming each group as you finish it.
So 45 302 178 is forty-five million, three hundred and two thousand, one hundred and seventy-eight.
Where a group is all zeros, say nothing for it.
c) Rounding
Look at the digit immediately after the place you are rounding to.
Five or more rounds up. Less than five leaves the digit unchanged. All digits after become zero.
Round 45 302 178 to the nearest million and you get 45 000 000. The digit after the millions place is 3.
Round from the original number every time. Rounding a number that is already rounded gives a different, wrong answer.
d) The four operations
Addition and multiplication can be done in any order. So 3 + 5 = 5 + 3, and 3 × 5 = 5 × 3.
Subtraction and division cannot. 8 − 3 is not the same as 3 − 8.
e) Combined operations
The order is: brackets, then division and multiplication left to right, then addition and subtraction left to right.
Division and multiplication rank equally. Work left to right between them, not division first.
The same applies to addition and subtraction.
f) Even, odd and prime
An even number is divisible by 2. An odd number is not.
A prime number has exactly two factors: 1 and itself.
A composite number has more than two factors.
The number 1 is neither prime nor composite, since it has only one factor.
The number 2 is the only even prime. Every other even number has 2 as a third factor.
g) Word problems
Read the question twice before writing anything.
Identify what is being asked for, and what you have been given.
Decide which operation the words point to. "Altogether" and "total" suggest adding. "Each" and "shared" suggest dividing. "How many more" suggests subtracting.
Estimate the answer, then calculate, then check the answer against the estimate.
Finally, read the answer back against the question. A number alone is not an answer.
Words to know
- Natural numbers -- the counting numbers 1, 2, 3, ... .
- Whole numbers -- the natural numbers together with zero.
- Place value -- the worth of a position in a number, such as tens or thousands.
- Total value -- a digit multiplied by its place value.
- Prime number -- a natural number greater than 1 with exactly two factors.
:::checkpoint Check yourself
- What is the total value of the 7 in 3 726 400?
- Round 6 847 291 to the nearest thousand.
- Work out 200 ÷ 5 + 4 × 6.
- Why is 1 not a prime number? :::
Bridge to practice
The exercises begin with place value and writing numbers in words, move through rounding and the order of operations, and finish with even, odd and prime numbers and word problems. For any calculation mixing operations, write out the BODMAS steps rather than working mentally, since that is where the avoidable marks are lost.