determine if 5/8 and 15/24 are equivalent ratios.
To determine if two ratios are equivalent, we need to compare them by simplifying both ratios to their simplest form.
Let's start with the ratio 5/8. To simplify it, we need to find the greatest common divisor (GCD) of the numerator (5) and the denominator (8). The GCD of 5 and 8 is 1, so the simplified form of 5/8 is already in its simplest form.
Next, let's simplify the ratio 15/24. Again, we find the GCD of the numerator (15) and the denominator (24). The GCD of 15 and 24 is 3. To simplify the ratio, we divide both the numerator and denominator by the GCD.
Dividing 15 by 3, we get 5. Dividing 24 by 3, we get 8. So the simplified form of 15/24 is 5/8.
Now, we can compare the simplified forms of the two ratios:
5/8 (simplified form of the first ratio)
and
5/8 (simplified form of the second ratio).
Since both simplified ratios are the same (5/8), we can conclude that 5/8 and 15/24 are equivalent ratios.
To determine if 5/8 and 15/24 are equivalent ratios, we need to simplify both ratios and compare them.
First, let's simplify 5/8:
To simplify 5/8, we need to find the greatest common divisor (GCD) of 5 and 8. The factors of 5 are 1 and 5, while the factors of 8 are 1, 2, 4, and 8. The only common factor between 5 and 8 is 1, meaning the GCD is 1.
To simplify the ratio, we divide both the numerator and denominator by the GCD.
5 ÷ 1 = 5
8 ÷ 1 = 8
Therefore, 5/8 is the simplified ratio.
Now let's simplify 15/24:
To simplify 15/24, we again need to find the GCD of 15 and 24. The factors of 15 are 1, 3, 5, and 15, while the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The only common factor between 15 and 24 is 3, meaning the GCD is 3.
To simplify the ratio, we divide both the numerator and denominator by the GCD.
15 ÷ 3 = 5
24 ÷ 3 = 8
Therefore, 15/24 is the simplified ratio.
Since both 5/8 and 15/24 simplify to the same ratio, which is 5/8, we can conclude that 5/8 and 15/24 are equivalent ratios.
To determine if 5/8 and 15/24 are equivalent ratios, we need to simplify both ratios and check if they are equal.
To simplify 5/8, we need to find a common factor that can be divided evenly into both the numerator (5) and the denominator (8). The greatest common factor (GCF) of 5 and 8 is 1, as there are no other common factors. Therefore, 5/8 cannot be simplified any further.
To simplify 15/24, we need to find the GCF of 15 and 24. The factors of 15 are 1, 3, 5, and 15. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The largest common factor between 15 and 24 is 3. Dividing both the numerator and the denominator of 15/24 by 3, we get 5/8.
Therefore, we have found that both 5/8 and 15/24 are equal ratios.