Write the ratio in lowest terms in order to decide whether the proportion is true or false.
200/240 = 250/290
To decide whether the proportion is true or false, we need to simplify the ratio 200/240 = 250/290.
To simplify the ratio, we can find the greatest common divisor (GCD) of both the numerator and denominator.
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.
The GCD of 200 and 240 is 40 because that is the greatest factor that is common to both numbers.
Dividing 200 and 240 by their GCD, we get:
200/40 = 240/40
5/1 = 6/1
Now, let's simplify the ratio 250/290.
The factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250.
The factors of 290 are 1, 2, 5, 10, 29, 58, 145, and 290.
The GCD of 250 and 290 is 5 because that is the greatest factor that is common to both numbers.
Dividing 250 and 290 by their GCD, we get:
250/5 = 290/5
50/1 = 58/1
Comparing the simplified ratios, 5/1 and 6/1, we can see that they are not equal.
Therefore, the proportion 200/240 = 250/290 is false.