Final answer:
Both ratios, 21:45 and 63:135, are equivalent to 7:15 after being simplified by dividing both terms of each ratio by their respective greatest common divisors.
Step-by-step explanation:
First, let's see if the ratio 21:45 is equivalent to 7:15. To determine this, we can simplify the ratio 21:45 by dividing both terms by their greatest common divisor. In this case, the greatest common divisor of 21 and 45 is 3. When we divide both 21 and 45 by 3, we get:
21 ÷ 3 = 745 ÷ 3 = 15
Therefore, the simplified form of the ratio 21:45 is 7:15, which means that the ratio is indeed equivalent.
Now, let's examine whether the ratio 63:135 is equivalent to 7:15. Again, we simplify the ratio by finding the greatest common divisor of 63 and 135, which is 9. Dividing both terms of the ratio by 9 yields:
63 ÷ 9 = 7135 ÷ 9 = 15
Thus, the ratio 63:135 simplifies to 7:15, showing that this ratio is also equivalent.