EXAMPLES. 1. If 37 yards of cloth cost £.40 49, what will 1 yard cost? £. s. d. S. d. 37)40 4 9- (1 1 9 Answer. 37 33. 20 37)64(1 37 27 12 37)333(9 333 2. If 47 bags of Indigo weigh 12Cwt. 1gr. 266. 4oz. what does each weigh? Ans. 1gr. 1lb. 12oz. 3. If 19 degrees on the earth's surface be 1321 miles, 2fur. 26 rods, what is the length of 1 degree? Ans. 69m. 4fur. 14rods. 4. If 135 solar years be 49307 days, 17h. 8m. 15s. how long are the years? Ans. 365d. 5h. 48m. 57s. 5. Divide .184 3 4, between 12 men, and 16 women; and give the men twice as much as the women. Men.. £• S. d. In the last example, I divided the sum by the number of simple shares, which was 40; (for the men had 12 double shares, and the women 16 single shares, which make 40 single shares) and the quotient was a woman's share; which being doubled, gave a man's. share. DECIMAL FRACTIONS. Decimal Fractions are set down in the same form, and managed in the same manner, as whole numbers. The denominator of a decimal fraction is always 10, 100, 1000, &c. that is, an unit with a number of cyphers annexed; therefore, the denominator needs not to be set down, for the numerator; with a point at the left hand, to distinguish it from a whole number, is sufficient to express the value of a decimal; thus, To is written,5; is written,42, &c.-But if the numerator has not so many places, as the denominator has cyphers, prefix so many cyphers at the left hand as will make up the defect; thus, is written,02; is written ,00036, &c. 5 36 42 Decimal fractions decrease from the left hand towards the right, in the same proportion as whole numhers increase towards the left; as may be seen 3 4 following Table : 7 5 4 in the Ten thousandth parts. Millionth parts. Tens. Units. Tenth parts. Thousandth Hundredth parts. parts. Thousands. Hundreds. in Tens of thousands. From this table it is evident, that, in decimals, as. well as in whole numbers, each figure takes its value by its distance from units place if it be in the first place after units, it signifies tenths; if in the second place, hundredths, &c. therefore every single figure, expressing a decimal, has, for its denominator, an unit with so many cyphers as its place is distant from units; thus,,2 (in the decimal part of the table) is ;,03 is 3, &c. And if a decimal be expressed by several figures, the denominator is 1, with so many cyphers as the lowest figure is distant from units' place; thus, ,146 is 146;,0083 is thus,,146 8:3 100001 &c. The value of decimals cannot be altered, by placing. cyphers at the right hand, because every significant. figure possesses the same place it did before: thus, ,5,50,500 are all of the same value, or equal to . But cyhers placed at the left hand of a decimal, alter its value, by removing the significant figures farther from units place; every cypher depressing it to of the value it had before; thus, ,3,03,003 express decimals of different values, ,3 being 3,03 To and ,003 TOO. 3 A mixed number, viz. a whole number with a decimal annexed, is equal to an improper fraction, whose numerator is all the figures of the mixed number taken together, and the denominator, that of the deci mal part; thus, 23,764 is equal to 200 Addition of Decimals. RULE. t: Place the numbers, whether mixed or pure decimals, in such order, that figures of the same value may stand directly under each other. 2. Add them together, as in whole numbers, and point off so many figures in the sum, for decimals,, as are equal to the greatest number of decimal places in any of the given numbers. 4. Required the sum of 7268,45321-3,600599 -20--,00010094-276,3375, and 3,8. 5. What is the sum of 8000,2368-800,04342 80,00963-6,86634, and 1,7369? Subtraction of Decimals. RULE. Place each figure of the less number directly under those of the same value in the greater; then subtract as in whole numbers, and point off the decimals, as in addition.. Rem. 78726,7778. 4. From 1000 take 99,995 5. -Rem. 73325,76127.. 6. From 8,00035 take ,01036. Rem. 7,98999.. Multiplication of Decimals. RULE. 1. Place the factors, whether they be pure decimals or mixed numbers, in the same order, and multiply them in the same manner as whole numbers. 2. Point off so many figures at the right hand of the product, for decimals, as there are decimal places in both factors; but if there be not so many places, supply the defect by prefixing cyphers at the left/ hand |