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

### From inside the book

Page 73

In the first example , the

of the prices , as 12 to 18 , or 1 = 1,5 ; and in the second , the

as 2 to 11 , or y = 5.5 , and the

In the first example , the

**ratio**of the quantities is as 4 to 6 , o f = 1.5 ; and the**ratio**of the prices , as 12 to 18 , or 1 = 1,5 ; and in the second , the

**ratio**of the times isas 2 to 11 , or y = 5.5 , and the

**ratio**of the distances , as 3 to 16.5 , or 16.5 = 5.5 . Page 74

Now , if we invert the first

, and consequently a proportion : i . e . 8 : 7 :: 6 : 3 , or 8 : 6 :: 4 : 3 . By the

question , the proportion would stand , 8 : 6 :: 4 : 6 ; then 8 4X6 , and r33 . Ans .

Where ...

Now , if we invert the first

**ratio**, it becomes , 8 to 43 ; me we have two equal**ratios**, and consequently a proportion : i . e . 8 : 7 :: 6 : 3 , or 8 : 6 :: 4 : 3 . By the

question , the proportion would stand , 8 : 6 :: 4 : 6 ; then 8 4X6 , and r33 . Ans .

Where ...

Page 120

The multiplier or divisor , by which the series is produced , is called the

. A person bought 6 brooms , giving 3 cents for the first ; 6 cents for the second ,

12 for the third , and so on , doubling the price to the sixth ; what was the price of

...

The multiplier or divisor , by which the series is produced , is called the

**ratio**. 281. A person bought 6 brooms , giving 3 cents for the first ; 6 cents for the second ,

12 for the third , and so on , doubling the price to the sixth ; what was the price of

...

Page 121

Had the

the sum of the series as the

difference between the first terma and the product of the last term by the

Hence ...

Had the

**ratió**been other than 2 , the remainder would have been as many timesthe sum of the series as the

**ratio**, less 1 , and the remainder is always thedifference between the first terma and the product of the last term by the

**ratio**.Hence ...

Page 128

What is the

multiplicaTerms are given , how do you find tion of duodeciinals ? How are all the

common difference ? How the denominations less iban a foot to be number of

terras 1 ...

What is the

**ratio**1 means ? When the first and last What is the rule for themultiplicaTerms are given , how do you find tion of duodeciinals ? How are all the

common difference ? How the denominations less iban a foot to be number of

terras 1 ...

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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.