The first principles of algebra, for the use of the boys of the Royal hospital schools, Greenwich1845 |
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Σελίδα 27
... minator of a fraction ( Art . 6 ) , and as = b , so a abc 8xyz likewise EC , ab -4xz -56xy - 2y ; = 8y , 7x - = since in each case the dividend is equal to the product of the divisor and quotient , as it ought to be . 32. A multiplier ...
... minator of a fraction ( Art . 6 ) , and as = b , so a abc 8xyz likewise EC , ab -4xz -56xy - 2y ; = 8y , 7x - = since in each case the dividend is equal to the product of the divisor and quotient , as it ought to be . 32. A multiplier ...
Σελίδα 37
... minator of a fraction . If the dividend is not exactly divisible by the divisor , or there are few or no quantities common to both ; this mode of expressing the result is generally more convenient than that of actually dividing each ...
... minator of a fraction . If the dividend is not exactly divisible by the divisor , or there are few or no quantities common to both ; this mode of expressing the result is generally more convenient than that of actually dividing each ...
Σελίδα 38
... minator by their greatest common measure or divisor . A fraction whose numerator and denominator consist of one term only , as 4ar 7ax y z ,, may easily In this case the be reduced to its lowest terms . greatest common divisor is at ...
... minator by their greatest common measure or divisor . A fraction whose numerator and denominator consist of one term only , as 4ar 7ax y z ,, may easily In this case the be reduced to its lowest terms . greatest common divisor is at ...
Σελίδα 39
... minator . Multiply each numerator of the given fractions , into all the denominators except its own for new numerators , and all the denominators together , for a common denominator ; as in com- mon arithmetic . x y 2 Reduce , α b с ...
... minator . Multiply each numerator of the given fractions , into all the denominators except its own for new numerators , and all the denominators together , for a common denominator ; as in com- mon arithmetic . x y 2 Reduce , α b с ...
Σελίδα 40
... minator . Ꮖ Ex . - Reduce and minator . — y 2 to a common deno- 2y This is done immediately , by multiplying the X numerator and denominator of the fraction by 2 ; when the fractions become and 2 2y y 2x 2y EXAMPLES . a b 1. Reduce to ...
... minator . Ꮖ Ex . - Reduce and minator . — y 2 to a common deno- 2y This is done immediately , by multiplying the X numerator and denominator of the fraction by 2 ; when the fractions become and 2 2y y 2x 2y EXAMPLES . a b 1. Reduce to ...
Συχνά εμφανιζόμενοι όροι και φράσεις
1st equation 2nd equation a+b+c a²+b² algebraical algebraical quantities apples arithmetical progression ax³ boys coefficient common arithmetic common denominator common difference contained cube root Diff Divide dividend and divisor division equa equal Extract the square farthing Find 2 numbers find the numbers Find the sum Find the value frac fractions geometrical progression given equations gression known last example last term least common multiple left hand term letters lowest terms means minator Mult multiplicand negative quantity nth root number of terms numerator and denominator placed positive quantity quadratic equation quantities are proportionals question quotient ratio Reduce remainder represented ROYAL HOSPITAL SCHOOLS Rule signifies SIMPLE EQUATIONS simple form square root substituting subtracted surd taken tion tities unity unknown quantities Vulgar Fractions x²y ах х х ха
Δημοφιλή αποσπάσματα
Σελίδα 116 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Σελίδα 91 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans.
Σελίδα 118 - If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents.
Σελίδα 91 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.
Σελίδα 23 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Σελίδα 23 - The square of the sum of two quantities is equal to the square nf the first, plus twice the product of the first by the second, plus the square of the second.
Σελίδα 23 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second.
Σελίδα 1 - The Sign of Subtraction, — , is read minus. It denotes that the quantity to which it is prefixed is to be subtracted. Thus, a — b, denotes that b is to be subtracted from a.
Σελίδα 128 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Σελίδα 62 - First, if necessary, clear of fractions ; then transpose all the terms containing the unknown quantity to one side of the equation, and the known quantities to the other.