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Deriving expressions

Sometimes we need to use a word based problem to write an expression.

If my rectangular garden is twice as long as it is wide, how can I express the area without knowing the side lengths?

We can turn statements like this into algebraic expressions.

Choose $$x$$ to represent the width of the garden. Then the length is $$2x$$. The area of a rectangle is the product of its side lengths, so the area is $$2x \times x = 2x^2$$.

The first thing to do is to represent the most basic quantity in the statement using a letter. Then write out any other quantities in terms of this letter. Work through the statement and "build up" the expression, remembering to use brackets if necessary.

I think of a number and add ten. Then I double the result. Give an expression for the new number in terms of the old one.

If we represent the original number using $$n$$, the first thing we do is to add $$10$$ to get to $$n+10$$. Then we multiply the entirety of this by $$2$$, to get $$2(n+10)$$.