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Numbers, units and arithmetic
Numbers, units and arithmetic

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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 ÷ one divided by two 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 ÷ one divided by two. So think of the 6 as 6 whole tomatoes.

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

equation sequence part 1 six division one divided by two equals part 2 six multiplication two equals part 3 12 full stop

Thus dividing by one divided by two is the same as multiplying by 2.

Similarly 2 ÷ one divided by four 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

equation sequence part 1 two division one divided by four equals part 2 two multiplication four equals part 3 eight full stop

Hence dividing by one divided by four is the same as multiplying by 4.

This illustrates the rule for dividing by fractions of the form one divided by n.

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