Numbers, units and arithmetic

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# Addition on the number line

For example, to find 8 + 3 start at 8 and move 3 units to the right.

giving 8 + 3 = 11. Adding a positive number means moving to the right along the number line.

Another way of considering the arithmetic of positive and negative numbers is to consider them as the total value of the contents of a piggy bank, belonging to a child (Thomas). The numbers on the above number line can represent the value of Thomas's piggy bank. Calculations represent transactions involving the piggy bank. When Thomas gets pocket money or gifts of money, he adds them into his piggy bank. If Thomas had £8 in his piggy bank and adds £3 (from his pocket money) the value of the piggy bank in pounds is 8 + 3 = 11.

When he spends money (on toys usually) he takes money out (subtracts). If there is not enough money in the piggy bank, he needs to borrow money. When he borrows money from his family, they note the debt on a piece of paper headed ‘IOU’ (I owe you). Thomas puts the ‘IOUs’ into his piggy bank. IOUs represent a negative amount of money (or debts).

Now suppose, at another time, Thomas's piggy bank contains an IOU for £3 when Thomas receives a gift of £5 to add to his piggy bank. £3 of this pays off the IOU and he has £2 left in the piggy bank. The transaction is represented by the calculation of the new value (in pounds) of the piggy bank

3 + 5 = 2.

How is this represented on the number line? Adding a positive number is moving to the right.

Moving 5 units to the right from −3 gets us to 2. So 3 + 5 = 2.

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