Equivalent Proportions Test! Math Trivia

Explanation
The given answer "yes" is correct because the ratio of 5 to 4 is equivalent to the ratio of 35 to 28. This can be determined by dividing both sides of the first ratio by the greatest common divisor, which in this case is 1. Therefore, the ratios are equal and the answer is "yes".

Explanation
The statement "4/3 = 24/30" is incorrect. The fraction 4/3 is not equal to the fraction 24/30. In order to determine if two fractions are equal, we need to find their simplest form. Simplifying 4/3 gives us 1 1/3, while simplifying 24/30 gives us 4/5. Since 1 1/3 is not equal to 4/5, the answer is "no".

Explanation
The given equation 6/5 = 24/20 is true because both sides of the equation simplify to the same value. When we simplify 6/5, we get 1.2. Similarly, when we simplify 24/20, we also get 1.2. Therefore, both sides of the equation are equal, making the statement "yes" correct.

Explanation
The given answer "yes" is correct because the ratio of 11:3 is equivalent to the ratio of 33:9. This can be determined by multiplying the numerator and denominator of the first ratio by the same number (3), which gives us 33:9. Therefore, the two ratios are equal and the answer is "yes".

Explanation
The given question asks to identify the proportions that are equal to 8/9. To determine this, we need to simplify each proportion and check if it equals 8/9. Simplifying 16/18 gives us 8/9, so it is equal to the desired proportion. Simplifying 56/81 results in a different value, so it is not equal to 8/9. Similarly, simplifying 24/27 gives us 8/9, so it is correct. Lastly, simplifying 80/90 gives us a different value, so it is not equal to 8/9. Therefore, the correct answers are 16/18, 24/27, and 80/90.

Explanation
The given question asks for proportions that are equal to 5 to 4. Among the options provided, the proportions 15 to 12 and 25 to 20 are equal to 5 to 4. In both cases, if we divide the first number by the second number, we get a ratio of 5/4. Therefore, these two options are correct answers.

Explanation
The given answer "yes" is correct because the ratio of 3 to 2 is equivalent to the ratio of 18 to 12. When both ratios are simplified, they both reduce to 3:2, indicating that they are proportional. Therefore, the answer is "yes" as the two ratios are equal.

Explanation
The proportions that are equal to 4/5 are 12 to 15 and 36/45. In the first proportion, 12 is 4/5 of 15. In the second proportion, 36 is also 4/5 of 45. The other options, 15/18 and 20/30, are not equal to 4/5.

Explanation
The given equation states that 6/5 is equal to 36/30. This is true because both fractions can be simplified to 6/5, indicating that they are equivalent.

Explanation
All the given proportions can be simplified to a ratio of 12 to 10. The ratio 24 to 20 can be simplified by dividing both numbers by 2, resulting in a ratio of 12 to 10. Similarly, the ratio 6 to 5 can be simplified by multiplying both numbers by 2, resulting in a ratio of 12 to 10. The ratio 30 to 25 can be simplified by dividing both numbers by 5, resulting in a ratio of 6 to 5. Finally, the ratio 60 to 50 can be simplified by dividing both numbers by 10, resulting in a ratio of 6 to 5. Therefore, all the given ratios are equal to 12 to 10.