Algebra
Letters for numbers
Write simple algebraic expressions and work out their value.
A letter in maths is a number you have not been told yet. Write n for how many sweets are in a bag and you can talk about two bags, or five more sweets, or half the bag, long before anyone says how many are actually in there. That is the whole trick: the letter holds the place, and anything you would do to a number you can do to it.
The multiplication sign goes missing
In algebra 3 × n is written 3n, with the number in front and no sign between them. Nothing else is left out: 3 + n stays 3 + n, and n - 3 stays n - 3. So 3n and n + 3 are two different things, and reading one as the other is the commonest slip there is.
Have a play
The scale is level. Move the weights about and see what keeps it that way.
Worked example
A crate holds 12 bottles. Write an expression for the number of bottles in k crates, then find its value when k = 5.
One crate is 12 bottles, so k crates is 12 multiplied by k.
You cannot work out a number yet, because k has not been given one — but you can say exactly what to do with it the moment it arrives.
Multiply before you add or take away
In 6n - 5 the 6n is worked out first and the 5 comes off afterwards. Doing it the other way round gives a different answer, so when you substitute a number, do the multiplying first and only then the adding or subtracting.
Try it together
Now one together. A number machine takes a number n, multiplies it by 6, and then takes away 5.
Build the expression first and use it second. Building it is the part worth slowing down for.
1.Write 6 multiplied by n the way algebra writes it, with no multiplication sign.
Have a go
Have a go on your own. If m = 8, what is the value of 5m + 3?
Hint: Work out 5m first, then add on the 3.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.