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times, calling them 1 and 5 the first time, and adding a cypher to each the next time.

What is the product of 13 by 3?

Place 3 opposite 1, then opposite 13 (found be. tween the large 1 and 2) is 39, the answer.

What is the product of 50 by 4?

Place 4 opposite 1: now we must call the large 5 50 : opposite it is 200, the answer.

What is the product of 24 by 3?

Place 3 opposite 1: then opposite 24 (found between the large 2 and the large 3) is 72, the answer.

What is the product of 3 multiplied by 2 (two tenths)?

Now we must call the large 2, two tenths. Place it opposite 1: then opposite 3 is :6, (six tenths,) the

answer.

DIVISION.

RULE.- Find the divisor on the circular. Place il opposite 1: then opposite the dividend, found also on the circular, is the quotient on the fixed part.

Example.—2 is in 8, how many times ?
Place 2 opposite 1: then opposite 8 is 4, the

answer.

3 is in 12, how many times?

Place 3 opposite 1: then opposite 12 is 4, the

answer.

How many times 4 in 14?

Place 4 opposite 1: then opposite 14 is 3 and five tenths, (35,) the answer.

Note.—Whenever a divisor is placed opposite 1, all the numbers and parts of numbers on the circular are divided by it. The quotients are on the fixed part.

Example. ---Place the divisor 2 opposite 1: now opposite 2 is i, opposite 12 is 6, opposite 4 is 2, opposite 6 is 3, opposite 14 is 7, opposite 24 is 12, opposite 125 is 62.5, opposite 75 is 37.5, &c.

To MULTIPLY BY ONE NUMBER AND DIVIDE BY ANOTHER

BY ONE SIMPLE PROCESS.

RULE.--Place the multiplier on the circular opposite the divisor: then, opposite the multiplicand is the result.

Example.—What is the result of 22 multiplied by 13 and divided by 14?

Place 13 opposite 14: then opposite 22 is 20 4+ the answer.

FRACTIONS.

To CHANGE AN IMPROPER FRACTION TO A WHOLE OU

MIXED NUMBER.

RULE.—Place the rfumerator found on the circular opposite the denominator: then opposite 1 is the

answer.

Example.-A man spending of a dollar per day, in 83 days would spend of a dollar. How much would that be?

Place 83 opposite 6: then opposite 1 is $13 83, the answer.

In of a dollar how many dollars ?
Place 8 opposite 4: then opposite 1 is $2, the

answer.

TO REDUCE A MIXED NUMBER TO AN IMPROPER

FRACTION.

Rule.---Place the mixed number opposite 1: then opposite the denomination to which you wish it 'reduced is the answer.

Example.-In 1612 of a dollar, how many 12ths of a dollar ?

Place 16 opposite 1: then opposite 12 is the number of 12ths in 1613, viz., 197=137, the answer.

TO REDUCE A FRACTION TO ITS LOWEST AND ALL ITS

TERMS.

RULE.—Place the numerator found on the circular opposite the denominator: then all the numbers standing directly opposite each other, are other terms of said fraction, and the lowest of said numbers are its lowest terms.

Reduce 1 to its lowest terms.

Place 12 opposite 16: now 9 is opposite 12 (1) 6 is opposite 8 (8,) and 3 is opposite 4 (iv) the

answer.

TO DIVIDE A FRACTION BY A WHOLE NUMBER.

RULE.- Place the whole number found on the cir: cular opposite 1: then opposite the denominator is a number, which, placed opposite the numerator, is the

answer.

Example.--If 2 yards of cloth cost of a dollar, how much is that per yard? a.cat

2 is in how many times? Place 2 opposite 1: then opposite 3 is 6. Now place this opposite 2, and it will read , the answer=

2 is in ] how many times ?

Place 2 opposite 1: opposite 8 is 16. This, placed opposite 7, makes to, the answer.

TO MULTIPLY A WHOLE NUMBER BY A FRACTION, OR

A FRACTION BY A WHOLE NUMBER.

RULE.- Place the numerator found on the circular opposite the denominator : then opposite the whole number is the answer.

N. B.-Whenever a numerator is placed opposite a denominator, all the numbers on the circular are that fractional part of the numbers opposite them.

Example.- Place 3 opposite 4: this is . Now the 3 is of 4; 6 stands opposite 8, being of 8; 9 is opposite 12; 12 is opposite 16, &c., &c. Now move the circular until 3 is opposite 5: now all the numbers on the circular are of those opposite them.

Note.—Whenever a numerator is placed opposite a denominator, thereby forming a vulgar fraction, the decimal of said vulgar fraction is opposite 1; hence,

TO REDUCE VULGAR FRACTIONS TO DECIMAL

FRACTIONS.

RULE.- Place the numerator found on the circular opposite the denominator : then opposite 1 is the decimal fraction.

Example.—What is the decimal off?
Place 3 opposite 4: now opposite 1 is •75, the

answer.

What is the decimal of ?
Place 7 opposite 8: opposite 1 is 875.

TO REDUCE DECIMAL FRACTIONS TO VULGAR

FRACTIONS.

RULE.- Place the decimal found on the circular opposite 1: then any two figures standing directly opposite each other is the answer.

Example.- What is the vulgar fraction equivalent to the decimal •5 ?

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