Write the following comparison as a ratio reduced to lowest terms. 25 nickels to 38 dimes?
25(5) to 38(10)
(5)(5)(5) to (2)(19)(2)(5)
(5)(5) to (4)(19)
25 to 76
To write the comparison of 25 nickels to 38 dimes as a ratio reduced to lowest terms, we need to simplify the ratio by dividing both numbers by their greatest common divisor.
First, let's find the greatest common divisor (GCD) of 25 and 38. The factors of 25 are 1, 5, and 25. The factors of 38 are 1, 2, 19, and 38. The common factor between them is 1.
Now we divide both numbers by their GCD:
25 ÷ 1 = 25
38 ÷ 1 = 38
Therefore, the simplified ratio of 25 nickels to 38 dimes is 25:38, which cannot be reduced any further.
To write the comparison as a ratio reduced to lowest terms, we need to find the greatest common divisor (GCD) of the given numbers and divide both the numerator and the denominator by it.
Step 1: Find the GCD of 25 and 38.
To find the GCD, we can factorize the numbers:
25 = 5 x 5
38 = 2 x 19
The factors of 25 are 5 and 5, and the factors of 38 are 2 and 19.
Step 2: Identify the common factors.
The only common factor between 25 and 38 is 1.
Step 3: Divide both the numerator and denominator by the GCD.
Dividing both numbers by their GCD (which is 1) gives us:
25 ÷ 1 = 25
38 ÷ 1 = 38
Therefore, the ratio of 25 nickels to 38 dimes reduced to lowest terms is:
25:38