Express 625 as a fraction of 1000 in its lowest terms
To express 625 as a fraction of 1000 in its lowest terms, we can divide both the numerator and the denominator by their greatest common divisor, which is 125:
625 ÷ 125 = 5
1000 ÷ 125 = 8
Therefore, 625/1000, when expressed in its lowest terms, is equal to 5/8.
To express 625 as a fraction of 1000 in its lowest terms, you can simplify the fraction by finding the greatest common divisor (GCD) of 625 and 1000 and then dividing both the numerator and denominator by the GCD.
The prime factorization of 625 is 5 x 5 x 5 x 5, and the prime factorization of 1000 is 2 x 2 x 2 x 5 x 5 x 5.
The common factors between the two numbers are 5 x 5 x 5. Therefore, the GCD is 5 x 5 x 5 = 125.
Dividing both the numerator and denominator by 125, we get:
625 ÷ 125 = 5
1000 ÷ 125 = 8
Therefore, 625/1000 in its lowest terms is 5/8.
To express 625 as a fraction of 1000 in its lowest terms, we need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD.
Step 1: Find the GCD of 625 and 1000.
To find the GCD, we can use the Euclidean algorithm. We start by dividing the larger number (1000) by the smaller number (625).
1000 ÷ 625 = 1 remainder 375
Next, we divide the previous divisor (625) by the remainder (375).
625 ÷ 375 = 1 remainder 250
Continuing this process, we divide the previous divisor (375) by the remainder (250).
375 ÷ 250 = 1 remainder 125
Finally, we divide the previous divisor (250) by the remainder (125).
250 ÷ 125 = 2 remainder 0
Since the remainder is 0, the GCD of 625 and 1000 is 125.
Step 2: Divide both the numerator and denominator by the GCD.
To express 625 as a fraction in its lowest terms, we divide both the numerator and denominator by the GCD (125).
625 ÷ 125 = 5
1000 ÷ 125 = 8
Hence, 625/1000 in its lowest terms is 5/8.