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MULTIPLICATION OF FRACTIONS.

38. To multiply fractions. Multiply all the numerators together for the numerator, and all the denominators for the denominator, suppressing such factors as are common to both numerator and denominator.

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For additional exercises, add the fractions in the last set.

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SUBTRACTION OF FRACTIONS.

37. To subtract one fraction from another. Reduce them if necessary to the same denominator; then subtract the one numerator from the other, and under the difference write the common denominator.

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MULTIPLICATION OF FRACTIONS.

38. To multiply fractions. Multiply all the numerators together for the numerator, and all the denominators for the denominator, suppressing such factors as are common to both numerator and denominator.

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a

(13.) (++)× L. C. M. of denominators. Ans. 11a.

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39. To divide one fraction by another. Invert the divisor, and proceed as in Multiplication.

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27

CHAPTER IV.

EQUATIONS OF THE FIRST DEGREE.

40. An equation is a statement of equality between two quantities. Thus axb-x is an equation of which ax is the one side or member, and b - the other. In this equation it is asserted that the unknown quantity x is so connected with the two known quantities a and b, that the sum of a and x is the same as the excess of b above x.

A simple equation is one which contains only one power of the unknown quantity; if it contain more than one, it is compound.

An equation is said to be of the first, second, third, or nth degree, according as the highest power of the unknown. quantity in it is the first, second, third, or nth power.

To solve an equation, or to find the value of the unknown quantity, it is necessary to separate it from all the other quantities with which it may be connected, so that it may stand alone on one side of the equation and its value on the other.

Axiom 1. If equals, or the same be added to equals, the wholes are equal.

2. If equals, or the same be taken from equals, the remainders are equal.

3. If equals be multiplied by the same or by equals, the products are equal.

4. If equals be divided by the same or by equals, the quotients are equal.

General Principles.-1. Any quantity may be transposed from the one side of an equation to the other by changing its sign.

2. A coefficient or multiplier may be removed by dividing both sides of the equation by it.

3. An equation may be cleared of fractions by multiplying both sides by all the denominators, or by their least common multiple.

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