Making Formulas from Words

Understanding how to construct formulas from words is a crucial skill that you need in algebra. This task involves translating worded problems into mathematical language.
Begin with reading the word problem carefully. Identify the quantities that are being described, and assign each of these quantities a variable.
Often, the word ‘is’ can be translated into an equals sign (=) in a formula.
Words such as ‘total’, ‘sum’, ‘more than’, ‘combined’ and ‘added to’ can indicate the need to use addition (+) in your formula.
‘Difference’, ‘less than’, ‘subtracted from’ and ‘decreased by’ could suggest the use of subtraction (-).
Terms like ‘product’, ‘times’, ‘multiplied by’ and ‘of’ often mean you should use multiplication (*).
‘Quotient’, ‘divided by’ and ‘per’ indicate division (/)
Keep in mind that the order of words can influence the order of operations. For instance, ‘three less than a number x’ would be written as ‘x - 3’, not ‘3 - x’.
For quantities that change, you may need to use variables. For example, if the problem talks about ‘each’ item or ‘every’ hour, this suggests a multiplication operation.
Don’t forget to check your formula by substituting values to make sure it makes sense and solves the problem correctly.
Practice is key in mastering this skill. The more word problems you translate into formulas, the better you’ll become at recognising the mathematical operations needed.
Lastly, remember to show your working at all stages. This will aid your understanding and could gain you more marks.