Algebra

UK Secondary (7-11)

Build algebraic equations II

Lesson

We have already started to look at how to turn written sentences into algebraic equations. Let's continue now by looking at some more complex examples, involving more than one operation.

Remember!

- Addition "$+$+" can be expressed by words such as "more than", "sum", "plus", "add" and "increased by".
- Subtraction "$-$−" can be expressed by words such as "less than", "difference", "minus", "subtract" and "decreased by".
- Multiplication "$\times$×" can be expressed by words such as "groups of", "times", "product" and "multiply".
- Division "$\div$÷" can be expressed by words such as "quotient" and "divided by". We usually represent division using fractions instead of using the "$\div$÷" operator.
- Equality "$=$=" can be expressed by words such as "is", "equal to" and "the same as". A number sentence needs one of these symbols to be an equation!

Write down an equation in simplest form to represent "$v$`v` is $5$5 less than $3$3 lots of $u$`u`".

Think: What symbol, number or variable can we use to represent each part of the sentence?

Do: "$v$`v` is" means that $v$`v` will be on one side of the "$=$=" sign and everything else will be on the other side. "$3$3 lots of $u$`u`" means $3\times u$3×`u`, and "$5$5 less than" means we are going to subtract $5$5 from this amount (using the "$-$−" operator). So we have $v=3\times u-5$`v`=3×`u`−5, which we can write more simply as $v=3u-5$`v`=3`u`−5.

Careful!

The order of the numbers in the sentence is not necessarily the same as the order in the equation!

In the example above, "$5$5 less than" meant that $5$5 was to be *subtracted from* the following term "$3$3 lots of $u$`u`". So the equation was written as $v=3u-5$`v`=3`u`−5.

Let's watch some worked video examples:

Write an equation in simplest form for: $y$`y` is $x$`x` divided by $3$3 plus $12$12

Write an equation for: $y$`y` equals $5$5 times the sum of $x$`x` and $10$10