Ratio: Simplify And Divide Into Ratio

The simplest form of a ratio is obtained by dividing both terms of the ratio by their greatest common divisor. In this case, the greatest common divisor of 12 and 18 is 6. Dividing both terms by 6 gives us 2 and 3, resulting in the simplest form of the ratio being 2:3.

The ratio 21:49 can be simplified by dividing both numbers by their greatest common divisor, which is 7. When we divide 21 by 7, we get 3, and when we divide 49 by 7, we get 7. Therefore, the simplified ratio is 3:7.

The ratio 20:45 can be simplified by dividing both numbers by their greatest common divisor, which is 5. By dividing 20 by 5, we get 4, and by dividing 45 by 5, we get 9. Therefore, the simplified ratio is 4:9.

The simplest form of a ratio is when the two numbers have no common factors other than 1. In this case, the ratio 13:27 is already in its simplest form because 13 and 27 do not share any common factors other than 1. Therefore, the answer is 13:27.

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The given question asks to divide 121 into the ratio of 3:6:2. To find the parts of the ratio, we add the parts together (3+6+2=11) and then divide 121 by this sum (121/11=11). Now, we multiply each part of the ratio by 11 to find the actual values. Thus, the answer is 33:66:22, which represents the division of 121 into the ratio of 3:6:2.

The given ratio 36:18:42 can be simplified by dividing all the numbers by their greatest common divisor, which is 6. Dividing 36 by 6 gives us 6, dividing 18 by 6 gives us 3, and dividing 42 by 6 gives us 7. Therefore, the simplified ratio is 6:3:7.

The ratio 5:3 means that the total value is divided into 5 parts and 3 parts. To find the value of each part, we divide 32 by the sum of the parts, which is 5+3=8. 32 divided by 8 is 4. Therefore, each part is equal to 4. Multiplying 4 by 5 gives us 20, and multiplying 4 by 3 gives us 12. So, the correct answer is 20:12.

The given ratio 21:42 can be simplified by dividing both numbers by their greatest common divisor, which is 21. When we divide 21 by 21, we get 1, and when we divide 42 by 21, we get 2. Therefore, the simplified ratio is 1:2.

The given question asks to divide 45 into a 2:7 ratio. This means that the total ratio is 2+7=9 parts. To find the value of each part, we divide 45 by 9, which gives us 5. Therefore, each part is equal to 5. Multiplying 5 by 2 and 7 gives us 10 and 35, respectively. So, the correct answer is 10:35.

The given answer is correct because when we divide 144 into a 3:4:5 ratio, we can calculate the parts by dividing 144 by the sum of the ratio parts, which is 3+4+5=12. Then, we multiply each part by the corresponding ratio to find the values. In this case, 144 divided by 12 is 12. Therefore, the parts are 3 parts of 12, which is 36, 4 parts of 12, which is 48, and 5 parts of 12, which is 60. So, the correct answer is 36:48:60.