Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

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 : opposite it is 200, the answer.

50:

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 it 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, (3.5,) 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 1, 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 numerator 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 3 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 16 of a dollar, how many 12ths of a dollar?

Place 16 opposite 1: then opposite 12 is the number of 12ths in 161⁄2, viz., 197—197, 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.

[ocr errors]

Reduce to its lowest terms.

Place 12 opposite 16: now 9 is opposite 12 (†)

6 is opposite 8 (§,) and 3 is opposite 4 (,) the

answer.

TO DIVIDE A FRACTION BY A WHOLE NUMBER.

RULE.-Place the whole number found on the circular 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?

o t 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 7, 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 of ?

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?

« ΠροηγούμενηΣυνέχεια »