Write the ratio in lowest terms in order to decide whether the proportion is true or false.
150/210 = 280/340
To decide whether the proportion is true or false, we need to simplify the ratio on each side of the equation and then compare them.
First, let's simplify the ratio 150/210:
The greatest common divisor (GCD) of 150 and 210 is 30, so we can divide both numerator and denominator by 30:
150 ÷ 30 = 5
210 ÷ 30 = 7
Therefore, 150/210 simplifies to 5/7.
Next, let's simplify the ratio 280/340:
The GCD of 280 and 340 is 20, so we can divide both numerator and denominator by 20:
280 ÷ 20 = 14
340 ÷ 20 = 17
Therefore, 280/340 simplifies to 14/17.
Now, we compare the simplified ratios: 5/7 and 14/17.
Since these ratios are not equal (5/7 ≠ 14/17), the proportion 150/210 = 280/340 is false.