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!
Example
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=3u−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=3u−5.
Let's watch some worked video examples:
Question 1
Write an equation in simplest form for: $y$y is $x$x divided by $3$3 plus $12$12
Question 2
Write an equation for: $y$y equals $5$5 times the sum of $x$x and $10$10