Manual of AlgebraBarnes, 1875 - 331 páginas |
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Página 36
... quotient . Division is the reverse of multiplication . In multiplication we have two factors given to find the ... Quotient . The quotient must be such a monomial as multiplied by the divisor will produce the dividend ; hence , its ...
... quotient . Division is the reverse of multiplication . In multiplication we have two factors given to find the ... Quotient . The quotient must be such a monomial as multiplied by the divisor will produce the dividend ; hence , its ...
Página 37
... quotient of terms having like signs must be + , and that of terms having unlike signs must be - EXAMPLES . ( 1. ) ( 2. ) + 16a3b3c2d + 4ab2cd = + 4a2bc - 18a2b2xyz -6abx3y - z = 3abx2y ?. ( 3. ) ( 4. ) + 15a3x2y1z8 3axyz -5a2xy ...
... quotient of terms having like signs must be + , and that of terms having unlike signs must be - EXAMPLES . ( 1. ) ( 2. ) + 16a3b3c2d + 4ab2cd = + 4a2bc - 18a2b2xyz -6abx3y - z = 3abx2y ?. ( 3. ) ( 4. ) + 15a3x2y1z8 3axyz -5a2xy ...
Página 38
... quotient . It may however be re- tained with the exponent 0. Thus , by the rule , we have , m α m -m am = a ° ; but a - am 1 ; .. = 1 . From this we infer , that , the 0 power of any quan- tity is equal to 1 , and that 1 is equal to the ...
... quotient . It may however be re- tained with the exponent 0. Thus , by the rule , we have , m α m -m am = a ° ; but a - am 1 ; .. = 1 . From this we infer , that , the 0 power of any quan- tity is equal to 1 , and that 1 is equal to the ...
Página 39
... quotient to a simpler form with- out altering its value . Such a change is called reduction . EXAMPLES . ( 1. ) ( 2. ) Yasb3c 4a2b2 r 6ab3c 2 = 4 · ab ° c airc = ac . 4 = 2a - 16-1c - 1 — 3a2b4c2 abc 15ab2c 3c 3. Reduce Ans . 3a - 1b ...
... quotient to a simpler form with- out altering its value . Such a change is called reduction . EXAMPLES . ( 1. ) ( 2. ) Yasb3c 4a2b2 r 6ab3c 2 = 4 · ab ° c airc = ac . 4 = 2a - 16-1c - 1 — 3a2b4c2 abc 15ab2c 3c 3. Reduce Ans . 3a - 1b ...
Página 40
... quotients by their proper signs . EXAMPLES . ( 1. ) 6ab - 8ax + 4a3y 36-4x + 2ay . 2a ( 2. ) 10a3x - 15x2 5х = 2a2-3x . 3. Divide 5xy + 20x3y 45axy by 5xy . Ans . 1 + 4x 9a . 4. Divide 9a2bc 12ab2c + 15abc2 by 3abc . Ans . 3a + 46 5c ...
... quotients by their proper signs . EXAMPLES . ( 1. ) 6ab - 8ax + 4a3y 36-4x + 2ay . 2a ( 2. ) 10a3x - 15x2 5х = 2a2-3x . 3. Divide 5xy + 20x3y 45axy by 5xy . Ans . 1 + 4x 9a . 4. Divide 9a2bc 12ab2c + 15abc2 by 3abc . Ans . 3a + 46 5c ...
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Términos y frases comunes
algebraic Arithmetic ax² binomial formula called clearing of fractions coefficients common difference contain contrary signs cube root Davies denominator denote the number distance dividend divisible equa equal roots equation whose roots EXAMPLES exponent expression extracting the square factors Find the cube Find the greatest Find the least Find the square Find the sum following principle following rule geometrical geometrical progression given equation greatest common divisor hence imaginary indicated irreducible fraction least common multiple logarithm Mathematics miles minuend monomial multiplying both members negative nth root number of terms operation partial fractions polynomial positive preceding problem proportion quan quotient radical sign ratio real roots Reduce remainder resulting equation roots equal second degree second member second term solved square root Sturm's Theorem substituting subtract third tion tity transposing travels unknown quantity V₁ whole number
Pasajes populares
Página 145 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Página 239 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Página 267 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 245 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Página 42 - ... the first term of the quotient ; multiply the divisor by this term and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Página 239 - In any proportion, the product of the means is equal to the product of the extremes.
Página 245 - That is, any term is equal to the first term, plus the product of the common difference by the number of preceding terms.
Página 41 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 264 - THE LOGARITHM: of a number is the exponent of the power to which it is necessary to raise a fixed number, to produce the given number. The fixed number is called the base of the system.