FRACTIONS.
Fractional parts of a cent should never be despised. They often make fortunes, and the counting of all the fractions may constitute the difference between the rich and the poor man. The business man readily understands the value of the fractional part of a bushel, yard, pound, or cent, and calculates them very sharply, for in them lies perhaps his entire profit.
TO REDUCE A FRACTION TO ITS SIMPLEST FORM.
Divide both the numerator and denominator by any number that will leave no remainder and repeat the operation until no number will divide them both.
Example. The simplest form of 36/45 is found by dividing by 9 = 4/5.
To reduce a whole number and a fraction, as 4-1/2, to fractional form, multiply the whole number by the denominator, add the numerator and write the result over the denominator. Thus, 4 X 2 = 8 + = 9 placed over 2 is 9/2.
TO ADD FRACTIONS.
Reduce the fractions to like denominators, add their numerators and write the denominator under the result.
Example. Add 2/3 to 3/4.
2/3 = 8/12, 3/4 = 9/12, 8/12 + 9/12 = 17/12 = 1-5/12. Ans.
TO SUBTRACT FRACTIONS.
Reduce the fractions to like denominators, subtract the numerators and write the denominators under the result.
Example. Find the difference between 4/5 and 3/4.
4/5 = 16/20, 3/4 = 15/20, 16/20 - 15/20 = 1/20. Ans.
TO MULTIPLY FRACTIONS.
Multiply the numerators together for a new numerator and the denominators together for a new denominator.
Example. Multiply 7/8 by 5/6.
7/8 x 5/6 = 35/48. Ans.
TO DIVIDE FRACTIONS.
Multiply the dividend by the divisor inverted.
Example. Divide 7/8 by 5/6.
7/8 X 6/5 = 42/40. Reduced to simple form by dividing by 2 is 21/20 = 1-1/20. Ans.
TO MULTIPLY MIXED NUMBERS.
When two numbers are to be multiplied, one of which contains a fraction, first multiply the whole numbers together, then multiply the fraction by the other whole number, add the two results together for the correct answer.
Example. What cost 5-1/3 yards at 18c a yard?
| 1 | 8 | c | ||||||||||||
| 5 | - | 1 | / | 3 | ||||||||||
| _ | _ | _ | _ | _ | _ | |||||||||
| 1 | 8 | x | 5 | = | 9 | 0 | ||||||||
| 1 | 8 | x | 1 | / | 3 | = | 6 | |||||||
| _ | _ | _ | _ | _ | _ | |||||||||
| 9 | 6 | c |
When both numbers contain a fraction,
First, multiply the whole numbers together,
Second, multiply the, lower whole number by the upper fraction;
Third, multiply the upper whole number by the lower fraction;
Fourth, multiply the fractions together;
Fifth, add all the results for the correct answer.
Example. What cost 12-2/3 pounds of butter at 18-3/4c per pound?
| 1 | 8 | - | 3 | / | 4 | |||||||||||||||
| 1 | 2 | - | 2 | / | 3 | |||||||||||||||
| _ | _ | _ | _ | _ | _ | _ | _ | |||||||||||||
| 1 | 8 | x | 1 | 2 | = | 2 | 1 | 6 | ||||||||||||
| 1 | 2 | x | 3 | / | 4 | = | 9 | |||||||||||||
| 1 | 8 | x | 2 | / | 3 | = | 1 | 2 | ||||||||||||
| 3 | / | 4 | x | 2 | / | 3 | = | 6 | / | 1 | 2 | = | 1 | / | 2 | |||||
| _ | _ | _ | _ | _ | _ | _ | _ | |||||||||||||
| $ | 2 | . | 3 | 7 | - | 1 | / | 2 |
Common fractions may often be changed to decimals very readily, and the calculations thereby made much easier.
TO CHANGE COMMON FRACTIONS TO DECIMALS.
Annex one or more ciphers to the numerator and divide by the denominator.
Example. Change 3/4 to a decimal. Ans..75.
We add two ciphers to the 3, making it 300, and divide by 4, which gives us.75. In the same way 1/2 =.5, or 3/4 =.75, and so on. When a quantity is in dollars and fractions of a dollar, the fractions should always be thus reduced to cents and mills.
