Ratios- introduction

Before getting into the topic,try this question: The owner of a pet store sells only two types of pets: donkeys and  mountain lions. In the store the ratio of donkeys to lions is 3:7. What do you know? For every 3 donkeys you have 7 lions. When you get a ratio, it actually contains a lot of information.The simplest level: The store has more lions than donkeys. That can be useful information. Next thing that should pop in your head: what fraction/percent of the total animals are donkeys? (Careful, if you say 3/7, you fell for the most common ratio trap. Ratios compare parts to parts. To get a fraction or percent of the total, we must first add these parts.The relative total is the sum of the relative parts: in this case 3+7=10). So the fraction/percent that are donkeys: 3/10, or 30%. 70% of these animals are lion. So when you are given a ratio of the parts, you can also tell percentages of the total. Also you can give relative percents between animals themselves. There are 133% more lions than donkeys, which is the same as saying 233% the number of donkeys is the number of lions. The inverse of that:There are approximately 57% fewer donkeys than lions (4/7 is approximately 57%), which is the same as saying the number of donkeys is 43% the number of lions. Note that we’re working from ratio to these percentages, but you can also work from the percentages to the ratio. When you are given a relative value between items, you can typically tell every relative value between them. Another question: which of the following could be the number of donkeys in the pet store? -82 -83 -84 -85 -86 Because we’re dealing with discrete (that is, countable in whole number) items just by knowing the ratio, we know something about the possible number of donkeys. And lions. And the total number of animals. Remember, whenever you have a ratio, you also have an ‘unknown multiplier’—some value that you can multiply each relative value of the ratio to get the actual values of those items. Let’s call the unknown multiplier ‘m’ ( avoid using x for the multiplier, because a lot of students  solve for ‘x’ and forget they aren’t done with the problem) So the ratio in actual values is 3m:7m (which simplifies to the 3:7 we’re given). Now let’s consider the possibilities for this ratio. The simplest case is we have 3 donkeys, 7 lions, and 10 total animals. That is, the unknown multiplier is 1. It’s a great idea to pick those values on a problem that can be solved with smart numbers, but otherwise, just realize the unknown multiplier is virtually never ‘1’. What other possibilities might we have?The donkeys are in multiples of 3, the lions in multiples of 7, and the total in multiples of 10. In the question above, the only choice that was a multiple of 3 is 84. Which of the following could be the positive difference between the number of donkeys and the number of lions? -42 -46 -50 -64 -66 Look at the chart again, replacing the ‘total’ column with ‘difference’:The unknown multiplier also applies to the difference between the parts of your ratio. 7-3=4, so our final difference must be a multiple of 4. The only answer that was a multiple of 4 was 64. Also, we can use a ratio to set up an equation (useful in solving a system of equations). If the ratio of D:L is 3:7, then D/L = 3/7, or 7D=3L Your job is to recognize which facts are useful in the problem you’re solving, but in order to do that it’s important to understand what information is even available to you when the CAT gives you what looks like a boring two or three number ratio.     ratio and proportion cat level questions ratio and proportion cat concepts ratio and proportion cat preparation ratio and proportion for cat pdf ratio and proportion tricks for cat ratio and proportion problems and solutions for cat ratio and proportion difficult questions ratio and proportion concept pdf