Question Which ratio is equivalent to 5/4? 20/30 24/30 30/20 30/24
To determine which ratio is equivalent to 5/4, we need to simplify 5/4 and then compare it to the given options.
To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and denominator and divide both by this common factor.
For 5/4, the GCD of 5 and 4 is 1 (since there are no common factors other than 1). Dividing both 5 and 4 by 1, we get:
5 ÷ 1 = 5
4 ÷ 1 = 4
So, 5/4 cannot be simplified further.
Now, we can compare 5/4 with each of the given options:
1. 20/30:
To simplify 20/30, we find the GCD of 20 and 30. The GCD of 20 and 30 is 10. Dividing both 20 and 30 by 10, we get:
20 ÷ 10 = 2
30 ÷ 10 = 3
So, 20/30 is equivalent to 2/3, not 5/4.
2. 24/30:
To simplify 24/30, we find the GCD of 24 and 30. The GCD of 24 and 30 is 6. Dividing both 24 and 30 by 6, we get:
24 ÷ 6 = 4
30 ÷ 6 = 5
So, 24/30 is equivalent to 4/5, not 5/4.
3. 30/20:
To simplify 30/20, we find the GCD of 30 and 20. The GCD of 30 and 20 is 10. Dividing both 30 and 20 by 10, we get:
30 ÷ 10 = 3
20 ÷ 10 = 2
So, 30/20 is equivalent to 3/2, not 5/4.
4. 30/24:
To simplify 30/24, we find the GCD of 30 and 24. The GCD of 30 and 24 is 6. Dividing both 30 and 24 by 6, we get:
30 ÷ 6 = 5
24 ÷ 6 = 4
So, 30/24 is equivalent to 5/4.
Therefore, the ratio equivalent to 5/4 is 30/24.