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Q: Why are the rules for multiplying and dividing rational numbers the same?

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The rules are the same.

p/q * r/s = (p*r)/(q*s)

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The product or quotient of two numbers that have the same sign is positive. The product or quotient of two numbers with different signs is negative.

The rules for dividing negative numbers is the same as multiplying them. A negative number multiplied/divided by a negative number is positive and a negative number multiplied/divided by a positive number is negative.

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It wasn't necessary to 'create' any rules. They follow logically from the definition of exponents.

One use is shorthand for large numbers, eg the mass of the earth is 5960000000000000000000000 kg , which can be expressed as: 5.96 * 1024 kg there are also rules for multiplying / dividing exponential numbers

1. Find the value of the exponent. 2. Multiply or divide normally.

When multiplying something with exponents, you add it. When dividing something with exponents, you subtract it.

The rules are not the same.Multiplication is commutative whereas division is not.Multiplication is associative whereas division is not.

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