## Higher Arithmetic: Designed for the Use of High Schools, Academies, and Colleges |

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acre added amount annex annuity answer approximative arithmetical progression bank becomes branches bushel called canceling cent ciphers column combinations common denominator common difference compound interest contain cost cube root decimal denominator denoting diameter diminished discount divided division divisors dollars equal Examples exponent expressed extract feet figure fourth fraction is equivalent gallons geometrical progression given gives greatest common measure half Hence inches increased individual things last term least common multiple length less means method miles mixture months multiplied nearly number of terms obtain OPERATION partial perform period person places pounds present worth prime factors principal quantity question quotient rate per cent ratio received Reduce remainder repetend RULE shillings simple SOLUTION square root subtract successive Suppose third term twice units vulgar fraction weeks wide wine wish yards

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Página 35 - Then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator...

Página 96 - Add to the first term the product of the common difference into the number of terms less one, and the sum will be the last term.

Página 164 - To raise a whole number or a decimal to any power, use it as a factor as many times as there are units in the exponent.

Página 98 - Hence, when the extremes and number of terms are given, to find the common difference, — Divide the difference of the extremes by the number of terms, less 1, and the quotient will be the common difference.

Página 173 - From the above proposition, it follows that the square of the hypotenuse, diminished by the square of one of the sides, equals the square of the other side. By means of these properties, it follows that two sides of a right-angled triangle being given, the third side can be found. Examples. 1. How long must a ladder be, to reach the top of a house, 40 feet high, when the foot of it is 30 feet from the house ? In this example it is obvious that the ladder forms the hypotenuse of a right-angled triangle,...

Página 30 - To reduce fractions to a common denominator, we have this RULE. Reduce mixed numbers to. improper fractions — compound fractions to their simplest form. Then multiply each numerator by all the denominators, except its own, for a new numerator, and all the denominators together for a common denominator. It is obvious that this process will give the same denominator to each fraction, viz : the product of all the denominators. It is also obvious that the values of the fractions will not be...

Página 139 - DISCOUNT is an allowance made for the payment of money before it is due. The present worth of a...

Página 91 - A wall was to be built 700 yards long in 29 days; after 12 men had been employed on it for 11 days, it was found they had built only 220 yards. How many more men must be put on, to finish it in the given time ? 54.

Página 91 - In how many days, working 9 hours a day, will 24 men dig a trench 420 yards long, 5 yards wide, and 3 yards deep, if 248 men, working...

Página 97 - Given the first term, last term, and common difference, to find the number of terms. RULE. — Divide the difference of the extremes by the common difference, and the quotient increased by 1 is the number of terms.