A RATIO is another name for a division problem. The RATIO of A to B means A/B or A divided by B or A:B (read A to B). Example: 2ft.:3yd. = 2ft.:9ft. = 2:9 Ans. Note: In RATIO problems always compare like measurements :RA A PROPORTION is an equation of 2 equal ratios. To solve a proportion cross multiply and divide. Example: x 8 - = -- 5 10 10x = 40 cross multiply x = 4 divide both sides by 10 :RA There are two types of proportions: DIRECT proportions and INDIRECT proportions. DIRECT PROPORTIONS - as the first quantity increases the second increases, or as the first quantity decreases the second decreases. Specific Cases: Changing feet to miles, pounds to ounces, inches on a map to miles, cost of food - the more you have of the first item the more you have of the second. :RA Example: If a articles cost b cents, how many articles can you buy for $1.00? Note: Unknown articles = y, $1.00 = 100 cents. DIRECT PROPORTION articles cents a b - = --- y 100 by = 100a y = 100/b articles :RA INVERSE PROPORTIONS - as the first quantity increases the second decreases, or as the first decreases the second increases. They vary in opposing direction. Specific Cases: More people spending time on a job - less time the job takes, the more pulleys - the less effort to raise a load, the more fuel efficient the car - the less gas it uses. :RA Example: If a supply of food will last b boys, d days, then how long will it last n boys? Note: y = unknown boys. One fraction will need to be INVERTED. INVERSE PROPORTION boys (not =) days boys days b d b y - not = - use: - = - n y n d ny = bd y = bd/n y = bd/n days Ans. :RA Example: If n pads can be bought for $5, how many pads can be bought for d dollars? y = the unknown pads DIRECT PROPORTION pads $ n 5 - = - y d 5y = nd dn x = -- pads Ans. 5 :RA Example: On a certain map, two towns are 2.5 inches apart. If the actual distance is 20 miles, how many inches on the map represent 1 mile of actual distance. :RA y = unknown inches DIRECT PROPORTION map (in) actual (miles) 2.5 20 --- = -- y 1 20y = 2.5 25 y = --- 200 y = 1/8 mile Ans. :RA Example: A sum of $600 is to be divided into 3 parts in the ratio 3:5:7. Find the largest part. y = the common multiplier, 3y = smallest part 5y = second part 7y = largest part Therefore 3y + 5y + 7y = 600 15y = 600 y = 40 7y = 7(40) = $280 Ans. :RA Example: A pulley having a 9" diameter is being driven at 1000 rpm. It is desired to belt it to another pulley which is to run at 600 rpm. Find the diameter of the second pulley. INVERSE PROPORTION diameter (in.) rpm 9 600 - = ---- y 1000 600y = 9000 y = 15 in. Ans. :RA Example: If 10 men take 6 hours to do a certain job, how long would it take 12 men to do the same job? y = unknown hours INVERSE PROPORTION men hours 10 y -- = - 12 6 12y = 60 y = 5 hr. Ans. :ET :ET
