RATIO, PROPORTION, AND PARTNERSHIP RATIO 348. The ratio of one number or amount to another is the result obtained by finding how many times the first, called the antecedent, contains the second, called the consequent, as a measure. 349. The sign of ratio is the colon (:). 12 yd. Thus, the expression 12 yd. : 3 yd. denotes that the number of times that 12 yd. contains 3 yd. as a measure is to be found. is the antecedent and 3 yd. is the consequent. The expression is read, the ratio of 12 yd. to 3 yd. REMARK. The expression 12 yd.: 3 yd. is called a ratio, and may also be read 12 yd. measured by 3 yd. 350. The antecedent and the consequent of a ratio are called its terms. 351. It is evident from Section 43 that: (1) Finding the ratio is simply finding the quotient in comparative division. (2) The antecedent corresponds to the dividend and the consequent to the divisor. (3) If one term of a ratio is an amount, the other must be a similar amount. (4) The ratio is always a number. 352. A ratio may be written as a fraction whose numerator is the antecedent and whose denominator is the consequent. 353. The inverse of a ratio is the ratio resulting from an interchange of terms. Thus, the inverse of 4: 5 is 5:4. 354. It is evident that 12 bu. contains 3 bu. as many times as 12 contains 3; hence, 12 bu. : 3 bu. 12: 3, or 123. [§ 43] = The ratio of two similar amounts equals the number of units in the antecedent divided by the number of units in the consequent. 355. From Sections 86 and 87 it follows that: Multiplying or dividing both terms of a ratio by the same number does not change the value of the ratio. 356. A ratio is in its simplest form when its terms are prime to each other. Exercise 89 1. Find the ratio of 41⁄2 bu. to 2 bu. Thus, 4 bu. : 2 bu. = 412, or 21. 2. Find the ratio of 4 qt. to 2 gal. Thus, 4 qt.: 2 gal. = 4 qt.: 10 qt. 21 = 4 ÷ 10, or f. Find the missing antecedent (a), consequent (c), or 17. In a period of eight years recently, certain foodstuffs advanced in price as given below; state at sight the ratio of the first price to the second: (1) Tomatoes per can from 8 to 12. (3) Corn per can from 6 to 10%. (4) Apricots per pound from 20 to 25 ¢. (5) Lamb chops per pound from 20 to 28. 18. Find the ratio of a short ton to a long ton. 19. A cubic foot of water weighs 62.5 lb. and a cubic foot of platinum weighs 1345.625 lb.; find, correct to the nearest hundredth, the ratio of the weight of platinum to that of water. 20. The ratio of a cubic foot to a stricken bushel is about. How many cubic feet are there in a bin that holds 160 stricken bushels? PROPORTION 357. An expression of equality between two equal ratios is called a proportion. Thus, 2:36:9 is a proportion, and may be read, the ratio of 2 to 3 equals the ratio of 6 to 9. 358. Since each of the two ratios in a proportion. has two terms, a proportion has four terms; the first and fourth are called the extremes, the second and third the means, the first and third the antecedents, and the second and fourth the consequents. 359. The ratio of two similar amounts may equal the ratio of two other similar amounts; and the two ratios together form a proportion. Thus, 12 yd.: 3 yd. = $8: $2, since each ratio is 4. 360. From Section 354 we have: = 12 yd. : 3 yd. 12: 3, and $8: $28:2; therefore, the proportion 12 yd. : 3 yd. $8: $2 may be written, = 12:38:2, which is called a numerical proportion; that is, a proportion whose terms are all numbers. = = 361. The proportion 8: 12 2:3 may be written; multiplying both members of the equation by 12 × 3, we have that is, 3 x 8 = 12 × 2; therefore: In any numerical proportion the product of the means equals the product of the extremes. I. In a numerical proportion one extreme equals the product of the means divided by the other extreme. 2. In a numerical proportion one mean equals the product of the extremes divided by the other mean. Exercise 90 In these examples x stands for the missing term; find the value of x: 363. First Type. If 6 lb. of sugar cost 30, 12 lb. at the same rate would cost 60¢. The statement may be abridged thus: |