Determine whether the ratios are equivalent.
10 / 17 and 30 / 51
10*51 = 17*30
so, yes
Well, let's see if these ratios are equivalent. To do that, we need to simplify both fractions.
The first ratio, 10/17, cannot be simplified any further.
The second ratio, 30/51, can be simplified by dividing both the numerator (30) and denominator (51) by their greatest common divisor, which is 3. Doing so, we get 10/17.
So, after simplifying, both ratios are 10/17, which means they are indeed equivalent! It's like they're twins separated at birth.
To determine whether the ratios 10/17 and 30/51 are equivalent, we can simplify both ratios to their simplest form.
First, let's simplify the ratio 10/17:
Find the greatest common divisor (GCD) of 10 and 17, which is 1.
Divide both the numerator and the denominator by the GCD:
10 ÷ 1 = 10
17 ÷ 1 = 17
So, the simplified form of 10/17 is also 10/17.
Next, let's simplify the ratio 30/51:
Find the GCD of 30 and 51, which is 3.
Divide both the numerator and the denominator by the GCD:
30 ÷ 3 = 10
51 ÷ 3 = 17
So, the simplified form of 30/51 is 10/17.
Since both ratios simplify to 10/17, we can conclude that the ratios 10/17 and 30/51 are equivalent.
To determine if two ratios are equivalent, we need to check if the simplified forms of the two ratios are equal.
Step 1: Simplify the first ratio, 10/17
To simplify a fraction, we divide the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 10 and 17 is 1, so we cannot simplify this ratio further.
Step 2: Simplify the second ratio, 30/51
To simplify this ratio, we need to find the GCD of 30 and 51.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The factors of 51 are 1, 3, 17, and 51.
The largest common factor between 30 and 51 is 3.
Dividing both the numerator and denominator of the fraction 30/51 by 3, we get:
30 ÷ 3 / 51 ÷ 3 = 10 / 17
Step 3: Compare the simplified ratios
After simplification, both ratios are 10/17. This means that the ratios 10/17 and 30/51 are equivalent.