Tham khảo tài liệu 'the sat math section 1', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | THE SAT MATH SECTION If given a percentage write it in the numerator position of the number column. If you are not given a percentage then the variable should be placed there. The denominator of the number column represents the number that is equal to the whole or 100 . This number always follows the word of in a word problem. The numerator of the number column represents the number that is the percent. In the formula the equal sign can be interchanged with the word is. Examples Finding a percentage of a given number What number is equal to 40 of 50 x 40 50 100 Solve by cross multiplying. 100 x 40 50 100x 2 000 100x 2 000 100 100 x 20 Therefore 20 is 40 of 50. Finding a number when a percentage is given 40 of what number is 24 24 40 7 100 Cross multiply 24 100 40 x 2 400 40x 2 400 40x 40 40 60 x Therefore 40 of 60 is 24. Finding what percentage one number is of another What percentage of 75 is 15 15 x 75 100 Cross multiply 15 100 75 x 1 500 75x 1 500 75x 75 75 20 x Therefore 20 of 75 is 15. Ratio and Variation A ratio is a comparison of two quantities measured in the same units. It is symbolized by the use of a colon xy. Ratio problems are solved using the concept of multiples. Example A bag contains 60 red and green candies. The ratio of the number of green to red candies is 7 8. How many of each color are there in the bag From the problem it is known that 7 and 8 share a multiple and that the sum of their product is 60. Therefore you can write and solve the following equation 7x 8x 60 15x 60 15x 60 15 15 x 4 Therefore there are 7 4 28 green candies and 8 4 32 red candies. Variation Variation is a term referring to a constant ratio in the change of a quantity. A quantity is said to vary directly with another if they both change in an equal direction. In other words two quantities vary directly if an increase 142 THE SAT MATH SECTION in one causes an increase in the other. This is also true if a decrease in one causes a decrease in the other. The ratio however must
