The Number System
Whole numbers
Use the order, identity, grouping and splitting properties of whole numbers to make arithmetic easier.
The whole numbers are 0, 1, 2, 3 and onwards for ever. Every one of them has a successor — the number one above it — so there is no largest whole number. Every one except 0 also has a predecessor, the number one below. Zero has none, because there is nothing below it in this set.
Have a play
Move along the whole numbers. Notice that each one has a next one, and that only zero has nothing before it.
Tap anywhere on the line.
Four properties worth knowing by name
Order does not matter for adding or multiplying: 8 + 5 = 5 + 8. Grouping does not matter either: (2 × 5) × 7 = 2 × (5 × 7). Adding 0 changes nothing, and multiplying by 1 changes nothing. Subtracting and dividing refuse the first two — order and grouping both matter, and 9 - 4 and 4 - 9 are nowhere near each other.
Worked example
What is 6 × 47?
Split 47 into 40 and 7.
You are allowed to split one of the numbers up, as long as you multiply every part.
Try it together
Now let us work out 8 × 25 × 5 the easy way.
You are allowed to multiply any two of them first — grouping does not change a product. So pick the pair that is kindest.
1.Start with the first two. What is 8 × 25?
Have a go
Have a go on your own: 9 × 99
Hint: 99 is one less than 100, so this is nine hundreds with nine taken off.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.