Q&A for How to Simplify a Ratio

Common mistakes when calculating ratios often arise from misinterpreting the wording of a problem. When dealing with ratios, students may encounter errors in determining which term should be the numerator and which should be the denominator. For instance, consider the question "What's the ratio of the length to the width?" In this case, the first term mentioned (length) should be the numerator, and the subsequent term (width) becomes the denominator. So, the correct ratio is length divided by width, or expressed as L/W. For practical understanding, let's take another example: "What's the ratio of the number of pigs to the total number of animals on a farm with 10 animals?" In this scenario, the number of pigs should be in the numerator, while the total number of animals serves as the denominator. This ensures that the ratio accurately represents the number of pigs in relation to the total number of animals. One common mistake students make is not discerning which term corresponds to the numerator and which to the denominator. This lack of clarity can lead to inaccurate ratios. Therefore, it is crucial to carefully identify the order in which the terms are presented in the problem and assign them correctly as the numerator or denominator accordingly.

Multiply both terms by 5. The ratio becomes 8 : 35.

9 + 2 = 11. 55 ÷ 11 = 5. 5 x 9 = 45 points. 5 x 2 = 10. So the two scores are 45 and 10, which are in the ratio of 9:2.

You are trying to find a number whose relationship to 6 is the same as 3's relationship to 2. It's a question of "proportion," which means setting one ratio equal to another -- in this case, 2:3 = 6:x ("two is to three as six is to what?"). Set it up as 2/3 = 6/x. Solve for x by cross-multiplying: (2)(x) = (3)(6). Then 2x = 18, and x = 9, the number you're looking for.

Find the greatest common divisor of those three numbers, divide it into each of them, and the three quotients will form the simplified ratio. The GCD is 8.

You need to make the value of y to be same, so: x:y = 2x3 : 5x3 = 6:15, y:z = 3x5 : 8x5 = 15:40. Combine these two ratios and you will get 6:15:40.

x - y = 20, so x = y + 20. x/y = (y + 20) / y = 7/3. Cross-multiply that last equation: (3)(y + 20) = (7)(y). So 3y +60 = 7y. Then 60 = 4y, and y = 15. So x = y + 20 = 15 + 20 = 35. (To check: x/y = 35/15 = 7/3.)

Multiply each term by 3 to get rid of the fraction in the first term. The ratio becomes 1:12.

You can't simplify it, because there is no number that will divide evenly into all three of those terms.