(a) Find the sum of the twenty-five fractions.* 179. To add common fractions. RULE.-Reduce the fractions if necessary to equivalent f having a common denominator, add their numerators, and wr sum over the common denominator. EXAMPLE. Add 1, 3, and 3. (1) The 1. c. m. of 45, 30, and 60, is 180. NOTE.-If the work that precedes this article has been wel no explanation of the foregoing will be necessary. Pupil already learned (presumably before using this book) (1) that fr may be reduced to higher terms, (2) that two or more fractions denominators are not alike may be reduced to higher terms wi denominators, (3) that a common denominator of two or fractions with unlike denominators, is a common multiple given denominators, and (4) that in reducing a fraction to terms the numerator and denominator must be multiplied same number. The simple problem of adding 44 180ths, 102 and 159 180ths, is not unlike the problem of adding 44 appl apples, and 159 apples. (For a continuation of this work, see page 91.) *This work may be omitted until the subject of fractions is reviewed. The above expressions are read, a divided by b; x divided by 4; 6 divided by cd. Observe that to reduce a fraction to its lowest terms we have only to strike out the factors that are common to its numerator and denominator. x 1. and y ab a2d Since the common denominator n exactly divisible by each of the given d ators, it must contain all the prime found in either of the given denominators. The new deno must therefore be a xa xbx d = a2bd; a2bd ÷ ab = ad; a'd=b. Give any values you please to a, b, d, x, and y, and *Since the numerical values of the letters are unknown, each must be as prime to all the others. The prime factors, then, in the first denomina and b; in the second, a, a, and d. GEOMETRY. 184. QUADRILaterals.—Review. 1. All the geometrical figures on this page are quadrilaterals; that is, each has four sides. 2. The first four figures are parallelograms; that is, the opposite sides of each figure are parallel. 3. The first two figures are rectangular; that is, their angles are right angles. 4. The first and third are equilateral; that is, the sides are equal. 5. There is one equilateral rectangular parallelogram. Which is it ? 6. There is one equilateral parallelogram that is not rectangular. Which is it? 7. There is one rectangular parallelogram that is not equilateral. Which is it? 8. The sum of the angles of each figure on the page is ...... right angles. 9. Tell as nearly as you can the size of each angle of each figure. a Square. a b 1 d Oblong. a 2 C Rhombus. b 3 three times as many; together they had 196 dollars many had each? (x + 3 x = 196) † 4. William had a certain number of marbles; He twice as many as William, and George had twice as Henry; together they had 161. How many had (x + 2x + 4 x = 161)† 5. Divide 140 dollars between two men, giving to 30 dollars more than to the other. ( x + x + 30 1. 6. By what integral numbers is 30, (2 × 3 × 5), divisible besides itself and 1 ? 7. By what is abc, (a × b × c), exactly divisible itself and 1? (1) How many times is a contained in abc? Observe that a number composed of three different exact integral divisors. factors has 8. Change to 60ths. 9. Change to 100ths. 10. Change to 100ths. Is more or less than 37 ? Change to 100ths. Change to 100ths. *The difference of two numbers is 5; the smaller number is 4. Wh larger number? + See page 78. |