What is the Number Sentence?

If the diagram below can be represented with the addition sentence 25 + 14 = 41,

Octal addition

what mathematical sentence should represent the following diagram?

Octal subtraction

Answer

Notice how the first diagram is arranged in groups of 8, plus some units? It represents an addition in base 8. Therefore, when we add 5 + 4 = 8 + 1, we have 1 in the units place, plus an extra rod (eight units together). All in all, we have 4 rods and 1 unit represented by number 41. We can not read it as “forty-one” since forty implies four groups of 10. It is easier if we add a subscript of 8 to show that we are working in base 8, also called the octal number system:

258 + 148 = 418

The second diagram has a total of 7 groups of eight plus 4 units out of which 2 groups of eight and 7 units are crossed over. This means we are subtracting 2 groups of eight and 7 units from the total. The difference is 4 groups of eight and 5 units. The number sentence that represents this diagram is 748 – 278 = 458.

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