## Introduction to the National Arithmetic: On the Inductive System : Combining the Analytic and Synthetic Methods with the Cancelling System : in which the Principles of Arithmetic are Explained and Illustrated in a Familiar Manner : Designed for Common Schools |

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acres addition amount answer barrel Boston Bought bushels called cents Change cloth common compound contains contents continued cords cost cube decimal denominator diameter difference Divide dividend division divisor dollars edition English equal examined farthings feet feet long figure five following RULE four fourth fraction gain gallons give given Greenleaf's hand Hence hogshead hundred improper inches interest John June land less lowest MEASURE method miles mixed months Multiply National Arithmetic Note OPERATION paid pair payment pence performed pounds principal proportion pupil quantity quarters quarts question quotient Received Reduce remainder rods RULE School seven share shillings side sold square square root subtract teachers third thousand thousandths tion tons units weeks weight whole number wide wood write yards

### Popular passages

Page 24 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

Page 133 - Multiply each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, and write...

Page 140 - CUBE is any number multiplied by its square. To extract the cube root, is to find a number which, being multiplied into its square, shall produce the given number. RULE.

Page 79 - To find the value of a fraction in the known parts of the integer, as of coin, weight, measure, fyc.

Page 77 - Or, multiply each numerator into all the denominators except its own for a new numerator ; and all the denominators into each other for a common denominator.

Page 26 - Multiply the whole number by the numerator of the fraction, and divide the product by the denominator ; or divide the whole number by the denominator of the fraction, and multiply the quotient by the numerator.

Page 120 - RULE.—Multiply each payment by the time at which it is due; then divide the sum of the products by the sum of the payments, and the quotient will be the equated time.* • , EXAMPLES.

Page 142 - ... under the last ; under all, set the cube of the last quotient figure, and call their sum the subtrahend. 7. Subtract the subtrahend from the dividend, and to the remainder bring down the next period for a new dividend, with which proceed as before, and so on, till the whole is completed. NOTE 1 . The same rule must be observed for continuing the operation, and pointing for decimals, as in the square root.

Page 91 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.