Write your answer as a reduced improper fraction -12/7+(3/14)
To solve the expression -12/7 + 3/14 as a reduced improper fraction, we need to find a common denominator for the fractions and then add them.
The common denominator for 7 and 14 is 14.
-12/7 can be converted to an equivalent fraction with a denominator of 14: (-12/7) x (2/2) = -24/14.
Now we can add the fractions: -24/14 + 3/14 = (-24 + 3) / 14 = -21/14.
Therefore, the answer as a reduced improper fraction is -21/14.
To reduce the improper fraction -12/7, we can divide both the numerator and denominator by their greatest common divisor, which is 1.
Dividing -12 by 1 gives us -12, and dividing 7 by 1 gives us 7.
So the reduced improper fraction -12/7 remains the same.
Now, adding -12/7 to 3/14 requires finding a common denominator.
To find the least common multiple (LCM) of 7 and 14, we can list the multiples of each number:
Multiples of 7: 7, 14, 21, 28, 35, 42, ...
Multiples of 14: 14, 28, 42, 56, 70, 84, ...
From the lists, we can see that 14 is the least common multiple of 7 and 14.
To rewrite the fractions with the common denominator of 14, we need to multiply the numerator and denominator of -12/7 by 2, and multiply the numerator and denominator of 3/14 by 1:
((-12 × 2)/(7 × 2)) + ((3 × 1)/(14 × 1))
(-24/14) + (3/14)
Now that the fractions have the same denominator, we can combine the numerators:
-24/14 + 3/14
(-24 + 3)/14
-21/14
Finally, we can further reduce the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 7:
(-21/7) ÷ (14/7)
-21/7 = -3
Therefore, the answer as a reduced improper fraction is -3.