*Ratios & Proportions: from the book 4th ed

change fraction to a ratio 5/6

answer = 5:6 steps: 1. the numerator (5) is the first listed number 2. then write the colon 3. finally, place the denominator (6) after the colon

ratio word problem Ben the camel drinks tea (so classy!). He drinks 350 liters of tea every 2 days. How many liters of tea does Ben drink every 6 days?

answer: 1050

ratio word problems You are throwing a party, and you need 5 liters of Soda for every 12 guests. If you have 36 guests, how many liters of Soda do you need?

answer: 15 liters

change fraction to ratio 19/40

answer: 19:40

change the decimal to a ratio. 0.025

answer: 1:40 0.025 = = 25 _____ then, reduce by 1000 = 25 divide 25 = 1 ______ _____ 1000 divide 25 = 40 =1:40 steps: 1. change the decimal to a fraction 2. reduce the fraction 3. the numerator (1) is the first listed number. 4. then write the colon 5. finally, place the denominator (40) after the colon.

change fraction to ratio 22/91

answer: 22:91

solve for x x:81 :: 9:27

answer: = 27 1. rewrite the proportion as a fraction x = 9 ___ ____ 81 27 2. multiply the diagonal numbers together (the one without the variable "x") 9 x 81 = 729 3. divide the answer (729) by the remaining number (27): 729 divide 27 = 27 4. so the value of x is 27.

There are 48 students studying foreign language at the community college. If the only two foreign languages offered are French and Spanish, and 28 students are studying French, which of the following represents the ratio of students studying Spanish to the total number of foreign language students? a. 2/7 b. 1/2 c. 1/3 d. 5/12

answer: d. 5/12 48 total students 28 study French 20 study Spanish the ratio of 20 to 48= 20:48 or 20 _____ 48 reduce to lowest form: 20 divide 2 =10 ______ ____ 48 divide 2 24 reduce again to lowest form 10 divide 2 = 5 ____ ____ ____ 24 divide 2 =12 answer: 5 ____ 12

solve for x: word problem John buys 3 bags of chips for $4.50. How much will it cost John to buy five bags of chips? 3:$4.50 :: 5 bags: x

answer: x = $7.50 1. rewrite the proportion as a fraction 3 = 5 ____ ____ 4.50 x 2. multiply the diagonal numbers together (the one with the variable "x") 5 x 4.50 = 22.50 3. divide the answer (22.50) by the remaining number (3). 22.50 divide 3 = 7.5 4. so, the value of x is = 7.5

solve for x 360:60 :: 6:x

answer: x = 1 1. rewrite the proportion as a fraction 360 = 6 _____ ____ 60 x 2. multiply the diagonal numbers together (the one without the variable "x") 6 x 60 = 360 3. divide the answer (360) by the remaining number (360): 360 divide 360= 1. 4. so the value of x is 1

solve for x: word problem The recipe states 4 cups of sugar will make 144 cookies. How may cups of sugar are needed to make 90 cookies? 4: 144 :: x: 90

answer: x = 2.5 1. rewrite the proportion as a fraction 4 = x _____ ____ 144 90 2. multiply the diagonal numbers together (the one without the variable "x") 4 x 90 = 360 3. divide the answer (360) by the remaining number (144): 360 divide 144= 2.5. 4. so the value of x is 2.5 cups of sugar

solve the proportion (find the value of x) 7:10: :14:x

answer: x = 20 7:10: :14:x 7/10 = 14/x 7 x 2 = 14 ____________ 10 x 2 = x 7/10 = 14/x x = 20 steps: 1. rewrite the proportion as a fraction (this might help to see the solution) 2. note that 7x2 = 14, therefore, 10x2 = 20 * multiply 14 x 10 (two diagonal numbers). The answer is 140 * 140 divide 7 = 20 (divide the remaining number) 3. so the value of x is 20.

solve the proportion (find the value of x) x:63 :: 24:72

answer: x = 21 x:63 :: 24:72 x/63 = 24/72 x/63 = 24/72 24 x 63 = 1512 1,512 divide 72 = 21 x = 21 steps: 1. rewrite the proportion as a fraction x/63 = 24/72 2. multiply the diagonal numbers: 24 x 63 = 1,512. 3. divide the answer (1, 512) by the remaining number (72): 1,512 divide 72 = 21 4. the value for x is 21

solve for x 15:x :: 3:8

answer: x = 40 1. rewrite the proportion as a fraction 15 = 3 ___ ____ x 8 2. multiply the diagonal numbers together (the one without the variable "x") 15 x 8 = 120 3. divide the answer (120) by the remaining number (3): 120 divide 3 = 40 4. so the value of x is 40.

solve the proportion (find the value of x) 240:60 :: x:12

answer: x = 48 1. rewrite the proportion as a fraction 240/60 = x/12 2. multiply the diagonal numbers together: 240 x 12 = 2,880 3. divide the answer (2,880) by the remaining number (60): 2,880 divide 60 = 48 4. so the value of x is 48 answer: x = 48 hesi hint: an example of the Foil Method is to remember "inside x inside and outside x outside." 240:60:: x: 12 60 times x :: 240 x 12 60x:: 2880 divide 60 by both sides to get x by itself x:: 48

solve for x 7 : 9 :: X : 63

answer: x = 49 1. rewrite the proportion as a fraction 7 = x ___ ____ 9 63 2. multiply the diagonal numbers together (the one without the variable "x") 7 x 63 = 441 3. divide the answer (441) by the remaining number (9): 441 divide 9 = 49. 4. so the value of x is 49.

solve for x: 7 : 5 :: 91 : x

answer: x = 65 1. rewrite the proportion as a fraction 7 = 91 ___ ____ 5 x 2. multiply the diagonal numbers together (the one without the x) 91 x 5 = 455 3. divide the answer (455) by the remaining number (7): 455 divide 7 = 65. 4. so the value of x is 65

solve for x x : 15 :: 120 : 225

answer: x = 8 1. rewrite the proportion as a fraction x = 120 ___ ____ 15 225 2. multiply the diagonal numbers together (the one without the variable "x") 120 x 15 = 1,800 3. divide the answer (1,800) by the remaining number (225): 1,800 divide 225 = 8 4. so the value of x is 8