Geometry. 184. QUADRILATERALS. 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. it? Which is 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 angles. right 9. Tell as nearly as you can the size of each angle of each figure. 185. MISCELLANEOUS REVIEW. 1. The difference of two numbers is 37411; the smaller number is 24317. What is the larger number? * 2. The difference of two numbers is a; the smaller number is b. What is the larger number? 3. James had a certain number of dollars and John had three times as many; together they had 196 dollars. How many had each? (x+3x=196) † 4. William had a certain number of marbles; Henry had twice as many as William, and George had twice as many as Henry; together they had 161. How many had each? (x+2x+4x=161) † (x + x + 30 = 140) † 5. Divide 140 dollars between two men, giving to one man 30 dollars more than to the other. 6. By what integral numbers is 30, (2 × 3 ×5), exactly divisible besides itself and 1? 7. By what is abc, (a × b × c), exactly divisible besides itself and 1? (1) How many times is a contained in abc? (2) How many times is b contained in abc? (3) How many times is c contained in abc? (4) How many times is ab contained in abc? (5) How many times is ac contained in abc? (6) How many times is bc contained in abc? Observe that a number composed of three different prime factors has exact integral divisors. 8. Change to 60ths. Is more or less than f? 9. Change to 100ths. 10. Change to 100ths. Change to 100ths. *The difference of two numbers is 5; the smaller number is 4. What is the larger number? + See page 78. RULE. Reduce the fractions if necessary to equivalent fractions having a common denominator, find the difference of their numerators, and write it over the common denominator. (b) Find the sum of the six differences. Fractions. 187. To subtract one mixed number from another when the fraction in the subtrahend is greater than the fraction in the minuend. Operation. 58% = 5924 Difference 2514 is greater than 24, therefore we take I unit from the 8 units, change it to 24ths, and add it to the 9 24ths. #+2=11. }}-1} = 11. 2 units from 7, (8 − 1), units = Junits. 3 tens from 5 tens = 2 tens. (a) Find the sum of the ten differences. 1. Observe that by the first operation we obtain 1; that in 12 there are 6 times as many parts as there are in and that the parts are of the same size as those in 4. 2. Observe that by the second operation we obtain ; that in there are the same number of parts as there are in 4, and that the parts are 6 times as great as those in. Note 1. The 7 of may be regarded as a dividend; the 24, as a divisor, and itself, as a quotient. In . we have a dividend 6 times as great as that in, the divisor remaining unchanged. In 1, we have a divisor 1 sixth as great as that in , the dividend remaining unchanged. Multiplying the dividend or dividing the divisor by any number, multiplies the quotient by the same number. Note 2.- The 7 of may be regarded as the antecedent of a couplet; the 24, as itself as the ratio. Multiplying the antecedent or dividing the consequent of any couplet multiplies the ratio by the same number. the consequent, and RULE. To multiply a fraction by an integer, multiply its numerator or divide its denominator by the integer. (a) Find the sum of the twelve products. (b) Find the sum of the twelve products. |