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Rh 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, $$3 : 6 = \frac{1}{2}$$, or $$6 : 12 = \frac{1}{2}$$, or $$1 : 2 = \frac{1}{2}$$.

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:

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 $$\frac{2}{5}$$ and the other boy gets 3 of the 5, or $$\frac{3}{5}$$.

$$\frac{2}{5} \text{ of } 30 = 12$$$$\frac{3}{5} \text{ of } 30 = 18$$12 cents and 18 cents.

The ratio $$8:4 = 2$$.The ratio $$12 : 6 = 2$$.

Thus the two ratios being equal to the same number, are equal to each other, and may be written $$8 : 4 = 12 : 6$$.

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 $$\times$$ in the following:

Find the missing term: