Whole Numbers
1.0 Numbers · 1.1 Whole Numbers
Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 1.0 Numbers | Sub-Strand 1.1 Whole Numbers (20 lessons)
Lesson objectives
By the end of this topic, you will be able to:
- Use place value and total value of digits up to hundreds of millions
- Read and write numbers in symbols and in words up to hundreds of millions
- Round off numbers to the nearest hundreds of millions
- Classify natural numbers as even, odd, and prime
- Apply the four operations of whole numbers, including combined operations
- Identify and create number sequences
Whole Numbers
Whole numbers are the counting numbers together with zero. This topic works with large ones, up to hundreds of millions.
a) Place value and total value
The place value is what the position is worth. The total value is the digit multiplied by its place value.
In 354 067 218 the digit 5 sits in the ten millions place. Its total value is 50 000 000.
Write large numbers in groups of three from the right. It makes them readable and makes the places obvious.
b) Reading and writing
Read from the left in groups: millions, thousands, then the rest.
So 354 067 218 is three hundred and fifty-four million, sixty-seven thousand, two hundred and eighteen.
Where a group is all zeros, say nothing for it. Do not invent a word.
c) Rounding
Look at the digit just after the place you are rounding to.
Five or more rounds up. Less than five leaves the digit alone. Everything after becomes zero.
Round 354 067 218 to the nearest million and you get 354 000 000. The digit after the millions place is 0.
d) Classifying numbers
An even number is divisible by 2. An odd number is not.
A prime number has exactly two factors, itself and 1.
Every whole number is either even or odd. Only some are prime.
e) Combined operations
When several operations appear together, there is an agreed order.
Brackets first. Then multiplication and division, working left to right. Then addition and subtraction, also left to right.
Working strictly left to right gives 30, then 150, then 142. That is wrong. The multiplication must come first.
f) Number sequences
A sequence is a list of numbers following a rule.
To find the rule, look at the gap between one term and the next. Here it is 4 each time, so the rule is "add 4".
Not every sequence adds. Some multiply, as in 2, 6, 18, 54, where each term is three times the one before.
Some use a different pattern altogether. In 1, 4, 9, 16 the terms are the square numbers.
To continue a sequence, state the rule first, then apply it. Guessing the next term without naming the rule often works once and then fails.
g) Where this is used
Population figures and national budgets run into hundreds of millions. Sequences appear in savings plans, seating rows and repeating patterns of every kind.
Words to know
- Place value — the position a digit occupies in a number, determining what it represents.
- Total value — the actual amount a digit contributes, equal to the digit multiplied by its place value.
- Even number — a whole number divisible exactly by 2.
- Odd number — a whole number not divisible exactly by 2.
- Prime number — a whole number with exactly two factors: 1 and itself.
- Combined operation — an expression using more than one of the four basic operations.
- Number sequence — a list of numbers following a consistent rule.
:::checkpoint Check yourself
- What is the total value of the 7 in 47 250 000?
- Round 682 419 to the nearest ten thousand.
- Work out 30 − 4 × 6 + 10.
- Give the next two terms of 5, 11, 17, 23 and state the rule. :::
Bridge to practice
Try the exercises below — on place value, rounding, classification and order of operations.