...the ratio, for a — 6=(o+c) — (6 + c) = (o— c)— (b — c) The two terms of a ratio by quotient may be multiplied or divided by the same quantity without changing the ratio, for a am bbm Ratios by difference are sometimes called arithmetical ratios, and those by quotient...

...Ans. — a* — (2J2 — c2)a2 4. Divide y3 — y — 6* — 62c2. by y — 3 — y3 • Arts. y2 A Terms of a fraction may be multiplied or divided by the same quantity. CHAPTER II. Fractions and Proportions. SECTION I. Reduction of Fractions. 39. When a quotient is expressed...

...2J4C2_|_J2C4) by a2— &2— c2. ^lns. _a* — (262 — c2)a2 4. Divide y3 — y '•— 3y — 3 —y Terms of a fraction may be multiplied or divided by the same quantity. CHAPTER II. Fractions and Proportions. SECTION J. Reduction of Fractions. 39. Wherr a quotient is expressed...

...2a6 + 62 Division of Polynomials. 4. Divide y3 I x5 — ! — 3 + 2 x* — y5 + + + 3^3 — 3 y3 i -y Terms of a fraction may be multiplied or divided by the same quantity. CHAPTER II. FRACTIONS AND PROPORTIONS. SECTION I. Reduction of Fractions. 54. When a quotient is expressed...

...value of that quantity remains unchanged^ Also, both numerator and denominator of a fraction may be divided by the same quantity, without changing the value of the fraction ; for, dividing the numerator divides the fraction, and dividing the denominator multiplies the fraction...

...ratio, for a — b = (a + c) — (b + c) = (a — c) — (b — c). The two terms of a ratio by quotient may be multiplied or divided by the same quantity without changing the ratio, for a am 6 bm Ratios by difference are sometimes called arithmetical ratios Mid those by quotient...

...ratio, for a — b = (a -fc) — (b -fc) = (a — c) — (b — c). The two terms of a ratio by quotient may be multiplied or divided by the same quantity without changing the ratio, for a am b bm Ratios by difference are sometimes called arithmetical ratios and those by quotient...

...the fraction. In like manner it is evident that : Both numerator and denominator of a fraction may be divided by the same quantity without changing the value of the fraction. 68. We shall now apply these principles in deducing rules for the transformation or reduction of fractions....

...3200 REDUCTION OP VULGAR FRACTIONS TO DECIMALS. 117. -Ex. Reduce ^ to a decimal fraction. Since both terms of a fraction may be multiplied or divided by the same number, without altering its value, we can multiply both terms of £ by 1000. lx iaifi = ^$$£. We...

...value of that quantity remains unchanged. Also, both numerator and denominator of a fraction may be' divided by the same quantity, without changing the value of' the fraction; for, dividing the numerator divides the fraction, and dividing the denominator multiplies the fraction;...