−6 7/12 − 4/ 13 =
To subtract the given fractions, we need to have a common denominator.
To find the common denominator, we need to find the least common multiple (LCM) of 12 and 13.
The prime factorization of 12:
12 = 2 × 2 × 3
The prime factorization of 13:
13 = 13 × 1
So, the LCM of 12 and 13 is 2 × 2 × 3 × 13 = 156.
Now, let's convert the fractions to have a common denominator of 156:
−6 7/12 = −6 * 12/12 + 7/12 = -72/12 + 7/12 = -65/12
−4/13 = -4 * 12/13 * 12 = -48/156
Now, we can subtract the fractions:
-65/12 - 48/156 = -845/156
Therefore, −6 7/12 − 4/13 = -845/156.
reduce the fraction
To reduce the fraction -845/156, we need to find the greatest common divisor (GCD) of the numerator (-845) and the denominator (156).
The prime factorization of -845:
-845 = -1 × 5 × 13 × 13
The prime factorization of 156:
156 = 2 × 2 × 3 × 13
The only common prime factor they share is 13, raised to the power of one.
Therefore, the GCD of -845 and 156 is 13.
To reduce the fraction, we divide the numerator and denominator by the GCD:
-845 ÷ 13 = -65
156 ÷ 13 = 12
So, the reduced form of the fraction -845/156 is -65/12.
reduce it more pls
To further reduce the fraction -65/12, we need to find the greatest common divisor (GCD) of -65 and 12.
The prime factorization of -65:
-65 = -1 × 5 × 13
The prime factorization of 12:
12 = 2 × 2 × 3
There are no common prime factors between -65 and 12.
Therefore, the GCD of -65 and 12 is 1.
To reduce the fraction, we divide the numerator and denominator by the GCD:
-65 ÷ 1 = -65
12 ÷ 1 = 12
So, the reduced form of the fraction -65/12 is -65/12. Since there are no common factors other than 1, the fraction cannot be simplified any further.
wrong
Apologies for the incorrect response. Let's try reducing the fraction -845/156 further.
The prime factorization of -845:
-845 = -1 × 5 × 13 × 13
The prime factorization of 156:
156 = 2 × 2 × 3 × 13
The common prime factors between -845 and 156 are 13 and 13.
To reduce the fraction, we divide the numerator and denominator by the GCD (greatest common divisor), which is 13:
-845 ÷ 13 = -65
156 ÷ 13 = 12
So, the reduced form of the fraction -845/156 is -65/12. It cannot be simplified any further since there are no additional common factors between the numerator and denominator.