Using the plan shown on page 31 find these products. The single equivalent discount of two successive discounts is their sum diminished by their product. With the help of the above rule find the missing numbers in the table below. 1. When the divisor is an easy fractional part of 10 or 100. To divide a number by 2 or 3 is the same as dividing it by 10 and multiplying this quotient by 4 or 3 because 2 is of 10 and 3 is 16+21=? 16÷31=? of 10. Think 1.6X4. Write 6.4. For short, think 4X1.6. To divide a number by 81, 121, 163, 25, or 33 is the same as dividing it by 100 and multiplying the quotient by 12, 8, 6, 4, or 3. 2. When the divisor ends in one or more zeros. Cancel the zeros in the divisor and move the decimal point in the dividend as many places to the left as there are canceled zeros before you divide. 3. Dividing large numbers by large numbers. In such cases much work may be saved by dropping several of the right hand figures in both the dividend and the divisor. Usually the quotient will be accurate enough for practical purposes if one or two more places are retained in the dividend and divisor than are required in the quotient. 1. Divide 846736 by 52378, carrying the quotient to tenths. Explanation. Inspection shows that the dividend contains the divisor more than 10 times but less than 100 times. Therefore, a quotient to tenths will have 3 figures in it. Hence, the 2 right hand figures in the dividend and divisor may be dropped, which is the equivalent of dividing both terms by 100 and dropping the remainders. This makes the divisor to be used 523 and the dividend 8467. 1. How many operations do you save by the short form? 2. What % of the work is saved by the short form? 2. What % is 2,346,784 of 3,487,564 to tenths of one per cent? 3487) 2346.000 2092 2 253 80 244 09 9 710 Explanation. Inspection shows the first quotient figure to come in tenth's place. Therefore, there will be 3 quotient figures in the required result. Hence, 4 places were kept in the dividend and the divisor. Divide by the long method to see how much you save by the short form. 1. The estimated value of the 1923 corn crop in the United States at July 1 farm prices was $2,488,983,005. On July 1, 1922, this value was $1,798,022,864. Find the per cent of increase to tenths of a per cent. 2. The estimated value of the 1923 wheat crop in the United States at July 1 farm prices was $780,417,288. July 1, 1922, this value was $884,505,366. Find the per cent of decrease to tenths of a per cent. 3. The estimated 1923 cotton crop in the United States on July 1 was 11,412,000 bales, and the estimated crop for 1922 was 9,762,000 bales. The price on July 1, 1923, was $ .262 per lb. and on July 1, 1922, it was $ .204 per lb. If the average bale weighs 500 lb., find the per cent of increase of the value of the estimated 1923 crop over that of the 1922 crop. 4. The estimated wheat crop of the world for 1923 was 3,354,132,000 bu. For 1922 it was 3,298,137,000 bu. Find the per cent of increase. 5. The corn crop of the United States for 1923 was 3,021,000,000 bu. For 1922 the crop was 2,890,000,000 bu. What % is the 1923 crop of the 1922 crop? CHAPTER IV SQUARES AND SQUARE ROOTS 1. The square of a number is the product obtained by using the number twice as a factor. 9 is the square of 3 because 3X3-9. The product may be indicated by writing 2 (called the exponent) a little to the right and above the number to be squared, as 3×3=32. Such an expression is read 3 squared, or the square of 3. 2. The square root of a number is one of the two equal factors of that number. 4 is the square root of 16 because 4 is one of the two equal factors of 16. The sign of square root is √. The square root of a number may be indicated by writing the sign over the number, as √16. 3. Write in a column the squares of all the numbers from 1 to 13, and of all the numbers ending in zero between 10 and 100. 4. Recall the short method of squaring numbers ending in 5. 5. Write in three columns the squares (1) Of all integers ending in 5 from 15 to 125. (2) Of all pure decimals of two places ending in 5 from .05 to .95. (3) Of all mixed decimals of one decimal place ending in 5 from 1.5 to 12.5. Use this table when you extract square root. 6. Show by example the truth of these statements. (1) The squares of all numbers between 1 and 10 lie between 1 and 100. |