# University Arithmetic: Embracing the Science of Numbers, and General Rules for Their Application

A.S. Barnes, 1870 - Arithmetic - 466 pages

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### Contents

 Least Common Multiple 109111 109 COMMON FRACTIONS 115 Reduction of Common Fractions 124132 124 Reduction of Denominate Fractions 132135 132 Subtraction of Common Fractions 140145 140 Multiplication of Common Fractions 145148 145 Complex Fractions 152 DECIMAL FRACTIONS 164 Addition of Decimals 170173 170 Contractions in Multiplication 177179 177 Contractions in Division 184186 184 Reduction of Denominate Decimals 190191 190 Addition of Repeating Decimals 201 Compound Ratio 207 Single Rule of Three 214220 214
 Annuities 279281 279 Alligation 295 Customhouse Business 202206 302 General Average 308310 308 Arbitration of Exchange 820822 320 ARITHMETICAL PROGRESSION 339 Definition of c 344 MENSURATION 370 Gauging 381383 381 Questions in Natural Philosophy 392398 392 APPENDIX 399 Linear Units 408409 408 Units of Weight 414416 414 Books and Paper 420 Answers 433466 433

### Popular passages

Page 177 - To multiply a decimal by 10, 100, 1000, &c., remove the decimal point as many places to the right as there are ciphers in the multiplier ; and if there be not places enough in the number, annex ciphers.
Page 106 - Divide the product of the remaining factors of the dividend by the product of the remaining factors of the divisor, and the result will be the quotient.
Page 145 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 335 - Take three times the square of the root just found for a divisor, and see how often it is contained in the dividend, and place the quotient for a second figure of the root. Then cube the figures of the root thus found, and if their cube be greater than the first two periods of the given number, diminish the last figure ; but if it be less, subtract it from the first two periods, and to the remainder bring down the first figure of the next period, for a new dividend.
Page 113 - Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Page 109 - The Least Common Multiple of two or more numbers is the least number which is a multiple of each of them; thus, 12 is the least common multiple of 2, 3, and 4.
Page 326 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. 5. Double the whole root already found for a new divisor, and continue the operation as before, until all the periods are brought down.
Page 280 - RULE. Divide the given sum by the amount of \$1. for the given rate and time ; and the quotient will be the present worth.
The text passage is a table of contents from a 19th-century arithmetic textbook, listing various chapters and sections on arithmetic topics.
no_question

the text does not contain any mathematical questions or answers. it is simply a table of contents listing the chapter and section titles of an arithmetic textbook. there are no specific problems or calculations presented.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# University Arithmetic: Embracing the Science of Numbers, and General Rules for Their Application

A.S. Barnes, 1870 - Arithmetic - 466 pages

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 Least Common Multiple 109111 109 COMMON FRACTIONS 115 Reduction of Common Fractions 124132 124 Reduction of Denominate Fractions 132135 132 Subtraction of Common Fractions 140145 140 Multiplication of Common Fractions 145148 145 Complex Fractions 152 DECIMAL FRACTIONS 164 Addition of Decimals 170173 170 Contractions in Multiplication 177179 177 Contractions in Division 184186 184 Reduction of Denominate Decimals 190191 190 Addition of Repeating Decimals 201 Compound Ratio 207 Single Rule of Three 214220 214
 Annuities 279281 279 Alligation 295 Customhouse Business 202206 302 General Average 308310 308 Arbitration of Exchange 820822 320 ARITHMETICAL PROGRESSION 339 Definition of c 344 MENSURATION 370 Gauging 381383 381 Questions in Natural Philosophy 392398 392 APPENDIX 399 Linear Units 408409 408 Units of Weight 414416 414 Books and Paper 420 Answers 433466 433

### Popular passages

Page 177 - To multiply a decimal by 10, 100, 1000, &c., remove the decimal point as many places to the right as there are ciphers in the multiplier ; and if there be not places enough in the number, annex ciphers.
Page 106 - Divide the product of the remaining factors of the dividend by the product of the remaining factors of the divisor, and the result will be the quotient.
Page 145 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 335 - Take three times the square of the root just found for a divisor, and see how often it is contained in the dividend, and place the quotient for a second figure of the root. Then cube the figures of the root thus found, and if their cube be greater than the first two periods of the given number, diminish the last figure ; but if it be less, subtract it from the first two periods, and to the remainder bring down the first figure of the next period, for a new dividend.
Page 113 - Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Page 109 - The Least Common Multiple of two or more numbers is the least number which is a multiple of each of them; thus, 12 is the least common multiple of 2, 3, and 4.
Page 326 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. 5. Double the whole root already found for a new divisor, and continue the operation as before, until all the periods are brought down.
Page 280 - RULE. Divide the given sum by the amount of \$1. for the given rate and time ; and the quotient will be the present worth.
user
The text passage is a table of contents from a 19th-century arithmetic textbook, listing various chapters and sections on arithmetic topics.

TYPE: NO_QUESTION

The text does not contain any mathematical questions or answers. It is simply a table of contents listing the chapter and section titles of an arithmetic textbook. There are no specific problems or calculations presented.