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# What is a comparison of two quantities by division?

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A comparison of two quantities by division is known as a ratio. A ratio is expressed as a number of one item compared to a corresponding number of another item.

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According to PurpleMath, there are three common notations to express ratios. One method expresses the ratio in words; for example, if there are 35 people at a party, of which 15 are men and 20 are women, then the ratio of men to women is "15 to 20." This can also be expressed in odds notation as "15:20" or in fractional notation as "15/20." As the total number increases or decreases by a certain scale factor, the items on both sides of the ratio increase or decrease by the same scale factor. For example, if the number of total people at the party were multiplied by a factor of two and there were 70 people at the party, the ratio of men to women would be 2*15 : 2*20, or 30:40. Ratios are used in setting up proportions, which are equations used to calculate the amount of one item if the other item is known.

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John Napier is said to have invented the mathematical function known as division. His calculations were further developed by Henry Briggs.

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Matrix division means multiplying one matrix by the inverse of another matrix. Matrix A "divided by" matrix B is equivalent to matrix A multiplied by the inverse of matrix B. Mathematicians usually use the term "multiplying by the inverse" rather than "dividing" when working with matrices.

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To perform long division, start by writing the number you want to divide. Make a division box over the number, and write the number you are dividing by the number by to the left of the box. Proceed digit by digit, dividing the outside number by the inside.

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The symbol representing long division does not actually have a name. It is usually simply referred to as a "long division symbol" or a "division bracket."

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