26/48-19/100
Since the common denominator is 4800, it would be easier to convert these fractions to decimals.
To evaluate the expression 26/48 - 19/100, we need to find a common denominator for the two fractions.
The prime factorization of 48 is 2^4 * 3, and the prime factorization of 100 is 2^2 * 5^2.
To find the least common multiple (LCM) of 48 and 100, we take the highest power of each prime factor that appears in either number.
LCM(48, 100) = 2^4 * 3 * 5^2 = 2400.
Now that we have the common denominator, we can rewrite the fractions with this denominator:
26/48 = (26 * 50) / (48 * 50) = 1300/2400
19/100 = (19 * 24) / (100 * 24) = 456/2400
The expression now becomes:
1300/2400 - 456/2400
Now that the fractions have the same denominator, we can subtract the numerators while keeping the denominator unchanged:
(1300 - 456) / 2400
The numerator simplifies to 844, so the expression simplifies to:
844/2400
This fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator.
The GCD(844, 2400) = 4
Dividing both the numerator and denominator by 4, we get:
844/2400 = 211/600
Therefore, 26/48 - 19/100 simplifies to 211/600.