Which ratio is the same as 2/3
6/12
8/12
10/12
9/12
Done ->
6/12
To find a ratio that is the same as 2/3, we need to simplify the given options.
To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD.
The GCD of 2 and 3 is 1.
Let's simplify the options:
6/12:
The GCD of 6 and 12 is 6.
Dividing both numerator and denominator by 6, we get 1/2.
8/12:
The GCD of 8 and 12 is 4.
Dividing both numerator and denominator by 4, we get 2/3.
This is the same as the original ratio 2/3.
10/12:
The GCD of 10 and 12 is 2.
Dividing both numerator and denominator by 2, we get 5/6.
9/12:
The GCD of 9 and 12 is 3.
Dividing both numerator and denominator by 3, we get 3/4.
Therefore, the ratio 8/12 is the same as 2/3.
Done ->
To find the ratio that is the same as 2/3, we can compare the numerators and denominators of 2/3 with the options provided.
If we simplify 2/3, we can multiply both the numerator and denominator by the same number to find an equivalent fraction that is easier to compare.
Since the denominator (3) can be evenly divided by 3, we can simplify the fraction by dividing both the numerator and denominator by 3:
2 ÷ 3 = (2 ÷ 3) / (3 ÷ 3) = 2/9
Now, let's compare this simplified fraction to the options provided:
6/12 can be further simplified by dividing both the numerator and denominator by 6: 6 ÷ 6 = 1 and 12 ÷ 6 = 2, so 6/12 is equivalent to 1/2.
8/12 can be further simplified by dividing both the numerator and denominator by 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8/12 is equivalent to 2/3.
10/12 can be further simplified by dividing both the numerator and denominator by 2: 10 ÷ 2 = 5 and 12 ÷ 2 = 6, so 10/12 is equivalent to 5/6.
9/12 can be further simplified by dividing both the numerator and denominator by 3: 9 ÷ 3 = 3 and 12 ÷ 3 = 4, so 9/12 is equivalent to 3/4.
Comparing the simplified fraction 2/3 with the options, we see that 2/3 is equivalent to 8/12.
So, the ratio that is the same as 2/3 is 8/12.