11. 6 7 5 12 × 9 × 49 × 25 7 × 18 × 3 We take the factor 2 out of 12 and 18; the factor 7 out of 7 = 210 and 49; the factor 5 out of 5 and 25; and cancel the factor 9 from both dividend and divisor. The factors remaining in the dividend are 6, 7, and 5. 6×7×5= 17. (108 x 32 x 8) ÷ (36 x 6 x 24) = ? 18. Divide 25 × 2 × 72 × 19. (11 X 3 X 15 X 14) ÷ 14 by 6 × 9 × 120. 2 × 5 × 54 = ? 10 × 6 22. What is the quotient of 4 × 9 × 17 × 80 divided by 17 X 90? 23. (16 × 24 × 33 × 34) ÷ (11 × 4 × 8 × 17) = ? 24. Divide 36 × 27 × 49 × 38 × 50 by 70 X 18 X 15. 25. (28 x 38 x 48)÷ (14 X 19 X 24 X2 X2)=? 26. What is the quotient of 36 × 48 × 16 divided by 27 × 24 X 8? 20 and 21 are dividends and 4 and 7 are divisors. The result is the same whether we make each division separately and then multiply the quotients, or divide the product of the dividends by the product of the divisors. In many cases the latter way is easier, because we may use cancellation; e.g. (18÷7) X (28÷24) × (210÷15): Find results: t 42 = 18×28×210 = 42. Ans. 1. (12 ÷ 11) × (22 ÷ 5) × (35 ÷ 6) × (15 ÷ 2) 2. (20÷6) × (55 ÷ 10) × (42 ÷ 11) 3. (39 ÷ 13) × (35 ÷ 21) × (12 ÷ 7) × (21 ÷ 3) 5. (27 18) × (35 ÷ 75) × (25 ÷ 12) × (12 ÷ 7) 7. (5210) X (34 ÷ 13) × (125 ÷ 10) 8. (26 ÷ 20) × (68 ÷ 13) × (125 ÷ 35) 9. (7017) X (68 ÷ 24) × (35 ÷ 7) 10. 75 X 108 X 18 11. 48 X 4 X 17 X 20 12. Multiply the quotient of 29 divided by 12 by the quotient of 84 divided by 29. 13. (26 × 5 × 54) ÷ (13 × 5 × 6) = ? 14. Divide 5 X 45 X 7 X 20 by 49 X 5 X 4 X 9. 15. Divide 5 × 51 × 7 × 9 × 4 by 17 × 20 × 12 × 7 X 2. 16. Divide 25 × 2 × 72 × 14 by 6 × 9 × 120. MULTIPLICATION OF FRACTIONS Written 1. Multiply: a. 1, §, and 7. b. 1, §, and 1. Each of these fractions indicates what operation? Since all the numerators are dividends and all the denominators are divisors, we may find the result by dividing the product of the numerators by the product of the denominators, as on page 76, using cancellation when possible: Any integer may be expressed as a fraction by writing it as a numerator with 1 for a denominator; e.g. 5 is the same as ; 19 is the same as ; X7X15 is the same as 1 × 1 × 15. = of 4 X The word of, between fractions, means the same as the sign of multiplication; e.g. of 1 = 3 × 1 × 16. 2. How many 12ths are there in of? How many 6ths? 3. How many 12ths are there in ? ? 4. How many 12ths are there in 1 of 。 6. How many halves are there in of ? of = √ = }· 7. What else is shown in this figure? Look at Fig. 2 and answer: 1. A, B, C, and D together are what part of Fig. 2? 2. A is what part of? 3. A is what part of Fig. 2? 4. A and E together are what part of Fig. 2? 5. A is what part of ? of 1 = ? 6. A+B+C = what part of? A + B + C = what part of Fig. 2?of= ? NOTE.-Feet and inches are sometimes indicated by marks, thus: 7' stands for 7 feet; 6" stands for 6 inches. What does 7" stand for? '? From Fig. 3 answer the following questions: 1. How many parts like K are there in the square inch? 2. What part of a square inch is K? 3. What is the length of K? The breadth? The area? 4. The top row of oblongs is what part of the square inch? K is what part of that row? of? · 5. The left-hand column of oblongs is what part of the square inch? K is what part of the column? of 1 = ? In Figure 4: 1. M (the unshaded part) is how long? How wide? What is its area? 2. K is what part of the square inch? M contains how many parts like K? M is what part of the square inch? What does Fig. 5 show? Divide two opposite sides into fourths and the other two sides into thirds. Connect the opposite division K FIG. 3 points. Show that: (a) X = + (b) & × 1 == } Show as many other facts as you can by that figure. TO THE TEACHER. - Many exercises similar to the preceding may be given to interest children and make the topic real to them. We must remember, however, that these are mere graphic verifications of the rule for multiplication of fractions. They neither prove nor derive the principle. The authority for every operation in fractions is found in the principles of division and the relation of dividend, divisor, and quotient. |