Numbers, units and arithmetic
Numbers, units and arithmetic

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Numbers, units and arithmetic

3.12 Division by fractions

Before considering division of fractions, it is helpful to think about division of whole numbers.

6 ÷ 2 asks for the number of twos in 6: 6 ÷ 2 = 3, since three twos are six (3 × 2 = 6).

In a similar way, 6 ÷ is asking for the number of halves in 6. Suppose a friend is making salad decorations for plates of sandwiches. He has 6 tomatoes and wants to know how many half tomatoes this will give. This will be 6 ÷ So think of the 6 as 6 whole tomatoes.

Active content not displayed. This content requires JavaScript to be enabled.
Interactive feature not available in single page view (see it in standard view).

Each tomato contains two half-tomatoes, so 6 tomatoes contain 6 × 2 half-tomatoes. Hence

Thus dividing by is the same as multiplying by 2.

Similarly 2 ÷ is asking for the number of quarters in 2. Think of two cakes.

Each cake contains 4 quarters: the two cakes contain 8 quarters.

Expressed in figures this is

Hence dividing by is the same as multiplying by 4.

This illustrates the rule for dividing by fractions of the form .

To divide by , multiply by n (n can be any number except zero).


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 50 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, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 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 prospectus371