Language, notation and formulas
Language, notation and formulas

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Language, notation and formulas

2.6.1 Arithmetical symbols

You will have already met the symbols for the basic arithmetical operations, which are +, −, × and ÷, but you may not have met some of the alternative ways of writing × and ÷.

To recap, the main symbols for arithmetical operations are:

There are other alternatives to × and * for multiplication. Sometimes, provided there is no risk of ambiguity, no symbol is used, just as sometimes the words ‘multiplied by’ or ‘times’ can be omitted in speech: for example, two fours or five fives means two times four or five times five, respectively. So, instead of writing 3 × (4 + 5), you can just write 3(4 + 5) and save one symbol. Mathematicians like to be as concise as possible! Brackets avoid ambiguity in mathematical expressions.

An alternative to ÷ and / for division is a fractional notation: for example, means ‘add three and six, and then divide by four’. The slash symbol / is sometimes used for fractions: thus, three-quarters may be written as 3/4. Many calculators use this notation to display fractions.

Example 4

What do the following expressions mean?

  • (a) 5/(3 + 2)

  • (b) 5/3 + 2

  • (c) 4(8 − 5)

Answer

  • (a) Divide 5 by the sum of 3 and 2. (This gives 1.)

  • (b) Divide 5 by 3 and then add to 2, or added to 2. (This gives .)

  • (c) Multiply 4 by the difference between 8 and 5. (This gives 12.)

MU120_4M6

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has over 40 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus