FRACTIONS AND MIXED NUMBERS Machinery's Handbook, 31st Edition
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Dividing Fractions and Mixed Numbers To Divide Common Fractions: 1) Take the reciprocal of the dividing fraction; 2) multi- ply the numerators and denominators; and 3) convert improper fractions to mixed num- bers, if necessary. To Divide Mixed Numbers: 1) Convert the mixed numbers to improper fractions; 2) take the reciprocal of the dividing fraction; 3) multiply numerators and denominators; and 4) convert improper fractions to mixed numbers, if necessary. Examples, Division of Fractions 2 7 5 21 2 7 21 5 2 21 7 5 × 2 21 7 5 ÷ = × = = = 42 35 6 5 10 3 14 5 10 3 5 14 50 42 3 2 1 3 ÷ 4 5 4 5 = = × = = × × ÷ × = = 25 21 5 21 2 7 21 5 42 35 6 5 10 3 14 5 10 3 5 14 50 42 3 2 1 3 ÷ ÷ = × = = = × = = ÷ 25 21 Decimal Numbers.— Decimal fractions are fractional parts of a whole whose implied de- nominators are multiples of 10. A decimal fraction of 0.1 has a value of 1/10, 0.01 has a value of 1/100, 0.001 has a value of 1/1000, and so on. Thus, the value of the digit in the first place right of the decimal point is expressed in tenths, a digit two places to the right is expressed in hundredths, a digit three places to the right is expressed in thousandths, and so on. Because the denominator is implied, the number to the right of the decimal point indicates the numerator of the decimal frac tion. For example, 0.125 is equivalent to 125/1000. In industry, most decimal fractions are expressed in terms of thousandths rather than tenths or hundredths. For example, a decimal fraction of 0.2 is written as 0.200 and read as “200 thousandths” rather than “2 tenths”; a value of 0.75 is written as 0.750, and read as “750 thousandths” rather than “75 hundredths.” In the case of four place decimals, the values are expressed in terms of ten-thousandths. So a value of 0.1875 is read as “1875 ten-thousandths.” Just as a mixed number is the sum of a whole number and a fraction, a decimal number greater than 1 has a whole and a decimal part. For example, 10.125 = 10 125 ⁄ 1000 , which is read as “10 and 125 thousandths.” Adding or Subtracting Decimal Numbers: To add or subtract decimal numbers, align the decimal points and add or subtract the digits as usual. The decimal point in the answer is aligned with the decimal points in the numbers added or subtracted. Examples, Adding Decimal Fractions 0.125 1.0625 2.50
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Examples, Subtracting Decimal Fractions 1.750 –0.250 1.500 2.625 –1.125 1.500
1.750 0.875 0.125 2.0005 4.7505
0.1875 3.8750
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Multiplying Decimal Numbers: In setting up decimal multiplication, the decimal points do not have to be aligned. Long multiplication is done as usual, but the decimal point in the answer is placed so that the number of digits on its right is the same as the total number of digits on the right of the numbers multiplied. Examples, Decimal Number Multiplication 24035 008 192280 . . . three decimal places two decimal places × five decimal places 6002 41 3 . . three decimal places one decimal place ×
18006 60020
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2400800 247.8826
four decimal places
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