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 ÷ 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.

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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).

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