write each ratio in simplest form...
224/480
42:68
500 to 125
Divide each by the greatest common divisor.
224/32 = 7
480/32 = 15
224/480 = 7/15
it is
To write each ratio in simplest form, we need to find the greatest common divisor (GCD) of the given numbers and divide both the numerator and denominator by that GCD.
Let's find the simplest form of each ratio:
1. 224/480:
To find the GCD of 224 and 480, we can use the Euclidean algorithm. Here's how it works:
- Divide 480 by 224, which gives us a quotient of 2 and a remainder of 32 (480 ÷ 224 = 2 R 32).
- Divide 224 by 32, which gives us a quotient of 7 and no remainder (224 ÷ 32 = 7 R 0).
Since there is no remainder in the last step, the GCD is 32.
Now, divide both the numerator and denominator by the GCD (32):
- 224 ÷ 32 = 7
- 480 ÷ 32 = 15
Therefore, the simplest form of 224/480 is 7/15.
2. 42:68:
To find the GCD of 42 and 68:
- Divide 68 by 42, which gives us a quotient of 1 and a remainder of 26 (68 ÷ 42 = 1 R 26).
- Divide 42 by 26, which gives us a quotient of 1 and a remainder of 16 (42 ÷ 26 = 1 R 16).
- Divide 26 by 16, which gives us a quotient of 1 and a remainder of 10 (26 ÷ 16 = 1 R 10).
- Divide 16 by 10, which gives us a quotient of 1 and a remainder of 6 (16 ÷ 10 = 1 R 6).
- Divide 10 by 6, which gives us a quotient of 1 and a remainder of 4 (10 ÷ 6 = 1 R 4).
- Divide 6 by 4, which gives us a quotient of 1 and a remainder of 2 (6 ÷ 4 = 1 R 2).
- Divide 4 by 2, which gives us a quotient of 2 and no remainder (4 ÷ 2 = 2 R 0).
Since there is no remainder in the last step, the GCD is 2.
Divide both the numerator and denominator by the GCD (2):
- 42 ÷ 2 = 21
- 68 ÷ 2 = 34
Thus, the simplest form of 42:68 is 21:34.
3. 500 to 125:
Since "to" represents a ratio, we can rewrite the ratio as 500/125.
To find the GCD of 500 and 125:
- Divide 500 by 125, which gives us a quotient of 4 and no remainder (500 ÷ 125 = 4 R 0).
Since there is no remainder, the GCD is 125.
Divide both the numerator and denominator by the GCD (125):
- 500 ÷ 125 = 4
- 125 ÷ 125 = 1
Thus, the simplest form of the ratio 500 to 125 is 4:1.