## The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for the Use of Schools in the United States |

### From inside the book

Page 10

Hence either of tie two

and the pr duct will still be the same . We may therefore prove multiplication by

changing the places of the

Hence either of tie two

**factors**may be made the multiplicand , or the multiplier ,and the pr duct will still be the same . We may therefore prove multiplication by

changing the places of the

**factors**, and repeating the operation . SIMPLE ... Page 28

In like manner it may be shown that every product will have as many decimal

places as there are decimal places in both the

multiplier ' under the multiplicand , and proceed in all respects as is the

multiplication of ...

In like manner it may be shown that every product will have as many decimal

places as there are decimal places in both the

**factors**. RÜLE . 122. Write themultiplier ' under the multiplicand , and proceed in all respects as is the

multiplication of ...

Page 30

0.01 ? DIVISION OF DECIMALS . Since any ANALYSIS . 125. 1. If 14.25 lb. of '

butter be divided into 3 equal shares , bow wany pounds will there be in each ? 8

) 14.25 ( 4.75 Here we wish to divide 14.25 into two

...

0.01 ? DIVISION OF DECIMALS . Since any ANALYSIS . 125. 1. If 14.25 lb. of '

butter be divided into 3 equal shares , bow wany pounds will there be in each ? 8

) 14.25 ( 4.75 Here we wish to divide 14.25 into two

**factors**, one of 12 which shall...

Page 97

Ranging the uüinbers in a line , and dividing such as are divisible by 4 , we

separate 4 , 8 and 12 , cach into two

common , and the others , 1 , % and 3 respectively . Now as the products of the

divisor ...

Ranging the uüinbers in a line , and dividing such as are divisible by 4 , we

separate 4 , 8 and 12 , cach into two

**factors**, one $ ) 3 , 4 , 8 , 12 of which , 4 , iscommon , and the others , 1 , % and 3 respectively . Now as the products of the

divisor ...

Page 109

109 employed as

number employed as

is 10 , whosc square is ( 10X10_ ) 100 , which has one figure less than the ...

109 employed as

**factors**; the cube of 1 is ( 1X1X13 ) 1 , two figures less than thenumber employed as

**factors**, and so on . The least root consisting of two figuresis 10 , whosc square is ( 10X10_ ) 100 , which has one figure less than the ...

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### Common terms and phrases

acres added Addition amount ANALYSIS answer bush bushels called cash cents Change ciphers column common compound contains cost cube cubic decimal denominator denoted diameter difference distance divide dividend division divisor dollars dolls equal evidently example expressed factors feet figures foot four fraction gain gallon give given greater half Hence hundred hundredths inches interest least left hand length less mean measure method miles months multiplicand multiply names operation payment period person pound principal proceed proportion quantity QUESTIONS FOR PRACTICE quotient ratio receive Reduce remainder right hand rods root rule share shillings side simple solid square square root subtract supposed tens tenths third tion units vulgar weight whole worth write written yard

### Popular passages

Page 82 - Multiply each payment by its term of credit, and divide the sum of the products by the sum of the payments ; the quotient will be the average term of credit.

Page 89 - The greatest common divisor of two or more numbers, is the greatest number which will divide them without a remainder. Thus 6 is the greatest common divisor of 12, 18, 24, and 30.

Page 118 - PROBLEM II. The first term, the last term, and the number of terms given, to find the common difference. RULE. — Divide the difference of the extremes by the number of terms less 1 , and the quotient will be the common diffcrenct.

Page 111 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained in the dividend...

Page 94 - It will be seen that we multiply the denominator of the dividend by the numerator of the divisor for the denominator of the quotient, and the numerator of the dividend by the denominator of the divisor for the numerator of the quotient.

Page 120 - Add together the most convenient indices to make an index less by 1 than the number expressing the place of the term sought. 3. Multiply the terms of the geometrical series together belonging to those indices, and make the product a dividend. 4. Raise...

Page 115 - 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 31 - RULE. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal places in the dividend exceed those in the divisor.

Page 2 - Los números cardinales 0: zero 1: one 2: two 3: three 4: four 5: five 6: six 7: seven 8: eight 9: nine 10: ten 11: eleven 12: twelve 13: thirteen 14: fourteen 15: fifteen 16: sixteen 17: seventeen 18: eighteen 19: nineteen 20: twenty...

Page 93 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.