...former zwcreasing in an irregular ratio, and the latter decreasing in an irregular ratio. If authors in writing arithmetics would observe this order, it would...understood. Let it be required, for example, to reduce T7T, T9r, |f , Jf , |f to a common denominator. First, resolve the terms of all the fractions into...

...both numerator and denominator of this complex fraction, -, by 7, we 7 1 obtain 1-; but multiplying both terms of a fraction by the same number does not change its value (Art. 84, a), .-. -= £; 5. e. T the reciprocal of ^ is £ ; and, generally, the reciprocal of any...

...21. What is the effect of dividing the numerator of a fraction? ART. 113. 23. What is the effect of multiplying or dividing both terms of a fraction by the same number? ART. 116, 117. 24. Prove that these proposition* are true. АRT. 117, Dem. 1-6. 25. How many and what...

...ij- Therefore, oto. SOLUTION 2n. — Since, by Prop. V., multiplying both numerator and denominator of a fraction by the same number does not change its value, we multiply both terms by the number which will give the required denominator, which we find to be...

...multiplying both numerator and denominator of this complex fraction, -, by 7, we obtain £ ; but multiplying both terms of a fraction by the same number does not change its value (Art. 84, a), .*. - = £; ie the reciprocal of £ is J ; and, generally, the reciprocal of any fraction...

...in the form of a fraction, the dividend being the numerator, and the divisor the denominator ; since dividing both terms of a fraction by the same number does not alter its value, it follows, that we may strike out, or cancel, any factors common to the dividend...

...in the form of a fraction, the dividend being the numerator, and the divisor the denominator ; since dividing both terms of a fraction by the same number does not alter its value, it follows, that we may strike out, or cancel, any factors common to the dividend...

...of Chain Fractions. The usual rule for the reduction of fractions is based upon the principle that dividing both terms of a fraction by the same number does not alter its value. Another mode of procedure, when the terms, without being prime numbers, are prime...

...NOTE. — Change § and | to the most convenient denomination.* • Twelfths. ILLUSTRATION. FORM. — Multiplying or dividing both terms of a fraction by the same number does not change its value ; hence if the terms of f are multiplied by 4, and the terms of | are multiplied by 3, the resulting...

...OPERATIONS. 18 — 2X3X3 — 3 18 — 18-1-6 — 3 30 ~~ fxTxT6 ~ 5' ,°r 30 ~~ 30 -5- 6 ~~ 5ISinoe dividing both terms of a fraction by the same number does not change the value expressed (Art. 141), we divide both terms by the prime factors common to them, by canceling,...