As we can multiply or divide both terms of a fraction by the same number without changing its value, so we can multiply or divide both terms of a ratio by the same number without changing its value. Thus, , or , or .
The term antecedent is another name for numerator or dividend; the term consequent is another name for denominator or divisor.
Find the value of the following ratios:
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2.
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3.
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4.Divide 30 cents between two boys in the ratio of 2 to 3.
Each time a division is made, 5 cents are taken, of which the first boy gets 2 of the 5, or and the other boy gets 3 of the 5, or .
12 cents and 18 cents.
The ratio .The ratio .
Thus the two ratios being equal to the same number, are equal to each other, and may be written .
A proportion is an equality of ratios.
The first and last terms of a proportion are called the extremes.
The second and third terms of a proportion are called the means.
The test of a proportion is to have the product of the means equal the product of the extremes. Thus the product of the means divided by either extreme will give the other extreme; and the product of the extremes divided by either means will give the other mean.
Find the missing term, which is represented by in the following:
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Multiply the means and divide by the given extreme.
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Multiply the extremes and divide by the given mean.
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Find the missing term:
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