...5x3 3 gives = - — , which brings it to the rule. 7 x 2 Otherwise, since the multiplication of the dividend and divisor by the same number does not change the quotient (Art. 14. Cor. 1.) (Art 20.), which is the rule. 52 2x7 Or thus, •= -f- -5 = 5 -5 -- s — =5x3-^7x2...

...cancelling the same factors from both divisor and dividend. It depends on the principle (Art. 86, 2rf), that dividing both dividend and divisor by the same number does not affect the quotient. Ex. 1. Divide 8 X 3 X 10 X 63 by 4 X 5 X 7. OPERATION. We oancel 4 in 8, Siv2...

...fractions having a common denominator, equals the quotient of tJieir numerators. 2. The multiplying of both dividend and divisor by the same number does not change the value of the quotient. 102. RULES. — To divide a fraction by a fraction, 1. Reduce the fractions...

...divisor divided by any number, the quotient will be multiplied by the same number. 8. Multiplying or dividing both dividend and divisor by the same number. does not change the quotient 9. If the denomination of the divisor be less than units, the denomination of the quotient must be...

...divisor by the same number does not change the quotient. 217. It has already been shown, in Art 107, that Dividing both dividend and divisor by the same number does not change the quotient. 90 (18 90 (18+2 90 {18+6 5 90 (9 10=2x5 90 (3 30=6xS 32 (8 2x32 (2x8 5x32^5x8 4 64 (16 160 {40 4 4...

...the quotient by that number, and dividing the divisor multiplies the quotient. III. Multiplying or dividing both dividend and divisor by the same number does not change the quotient. 105. If we multiply one number by another, and then divide the product by the multiplier, we have the...

...3, which is 6, is contained in 24 one half of 8 = 4 times. ART. 75. THEOREM VI. — Multiplying or dividing both dividend and divisor by the same number, does not change the quotient. DEMONSTRATION. — This follows from the two preceding theorems; for the effects produced by multiplying...

...84756 ; 137543; 20298; 10735; 3376; 43011; 27991; 78125. Cancellation. 158. We learned in Art. 141 that dividing both dividend and divisor by the same number does not change the quotient. Hence, when both dividend and divisor contain a common factor, we may first divide them by it. This...

...Dividend or multiplying the Divisor by any number, divides the Quotient by that number. 3. Multiplying or dividing both Dividend and Divisor by the same number, does not change the Quotient. NOTE TO TEACHER. — Let the pupils be required to show the reason for the above principles, and give...

...3. Hence, rejecting the factor 3 from 72, we have 24, the quotient of 72 divided by 3. PROP. II. — Dividing both dividend and divisor by the same number does not change the quotient. Thus, 60 -H 12 = 20 threes H- 4 threes = 5. Observe that the unit three, in 20 threes -=- 4 threes,...