Algebra

NZ Level 5

Build algebraic expressions

Lesson

Algebraic expressions are applied almost everywhere in real life problems, so we need to learn how to form these expressions when situations are described to us in words.

Let's start with something simple. We know that if I had an amount $x$`x`, 2 more than that would of course be $x+2$`x`+2. So then if I said that I had $x$`x` amount of apples and my friend has $2$2 more than me, then that obviously means they have $x+2$`x`+2 apples. What if I had something like $x+47$`x`+47 apples? So you don't get confused, treat $x+47$`x`+47 as one amount at first, and add $2$2 to it. So my friend will have $x+47+2=x+49$`x`+47+2=`x`+49 apples.

Similar techniques are used in multiplication. Imagine that a big bucket holds $3$3 times as much water as a smaller bucket and the smaller one has a volume of $6m$6`m` litres. To find how much the bigger bucket holds, try to see the $6m$6`m` as one number and not as $6\times m$6×`m` at first. Then the volume must be $3\times6m=18m$3×6`m`=18`m` litres.

Write an expression for $3$3 consecutive odd numbers, the first of which is $7k+1$7`k`+1.

**Solution**

We know that consecutive odd numbers only have one pattern amongst them, and that is a difference of two. For example $3$3, $5$5, $7$7...etc.

Therefore the next odd number after $7k+1$7`k`+1 is $7k+1+2=7k+3$7`k`+1+2=7`k`+3.

Following the same logic the third number is $7k+1+2+2=7k+5$7`k`+1+2+2=7`k`+5.

So the answer is $7k+1$7`k`+1, $7k+3$7`k`+3, $7k+5$7`k`+5.

Let's have a look at these worked examples.

Write an expression for three consecutive odd numbers, the first of which is $9p$9`p`.

If Kelly is currently $x-1$`x`−1 years old, what was her age $10$10 years ago?

Generalise the properties of operations with fractional numbers and integers.