Therefore the number required=101. Ex. 4. What number divided by 13 will produce 10? This question in other words is the following: "What is the product of 13 and 10?" The product of 13 and 10, (the least common multiple of 4, 38, and 3, =38 × 2 × 3) (11 × 19 × 3+175 × 2 × 3-2 × 38 × 2) 228 305 = 228 305 Miscellaneous Questions and Examples on Arts. (58—79). 1.. 1. Define a fraction; what is the distinction between a Vulgar and a Decimal fraction? How many different kinds of Vulgar fractions are there? Give an example of each kind. 2. Find the sum and difference of and the sum of 51, of 31, and 2÷4. of 72, and 12 divided by 21; 5. The difference of two numbers is 15; the greater number is 2011: find the smaller number. II. 1. If the numerator and denominator of a fraction be both multiplied or both divided by the same number, the value of the fraction is not altered: prove this by means of an example. 2. What number subtracted from 411 leaves 191? and what number multiplied by 2 of produces 31⁄2 of ? 3. When is a fraction said to be in its lowest terms? Reduce the fractions 13298 and 395489 to their lowest terms. 1. Shew by an example that multiplying the numerator of a fraction by any number, is the same in effect as dividing the denominator by that the remainder add the quotient of divided by 23, the sum will be 1. Define a Vulgar fraction; an improper fraction; and the terms numerator and denominator of a fraction. Prove by means of an example the rule for the multiplication of fractions; and multiply the sum of of and 13 by the difference of and 2. Reduce to their most simple forms the following expressions: (1) ××8÷ths of (72+§). (2) +20. 15 3. What number added to 2 of (3+}− +}) makes 31? and what number divided by 1 of of will give ? 315 4. If I pay away of my money, then of what remains, and then of what still remains; what fraction of the whole will be left? 5. Explain the method of 'comparing' fractions. Compare the product and quotient of the sum and difference of 53 and 51. V. 1. State the rules for multiplying and dividing one fraction by another; and prove them by means of an example. 2+3 4+3 Divide by ; and multiply the sum of 1, 1, and & by the 4+5 5+5 difference of and, and divide the product by 1 of 11. 2. Reduce to their simplest forms 41 Find the least fraction which added to the sum of 2, 7, and 12, make the result an integer. shall 4. Find the sum of the greatest and least of the fractions, and ; the sum of the other two; and the difference of these sums. |