Add −12/7+(3/14). Write your answer as a reduced improper fraction.(1 point)
−1/27+(3/14)=
To add -12/7 and 3/14, we need to find a common denominator.
The common denominator is 14.
-12/7 is equivalent to (-12/7) * (2/2) = -24/14
So, -12/7 = -24/14.
Now, we can add -24/14 and 3/14:
-24/14 + 3/14 = -21/14
Therefore, -12/7 + 3/14 = -21/14.
To add the fractions -12/7 and 3/14, we need to find a common denominator. The least common multiple of 7 and 14 is 14.
Now, let's convert -12/7 and 3/14 to fractions with a denominator of 14:
-12/7 = -24/14
3/14 stays the same
Now, we can add the fractions:
-24/14 + 3/14 = -21/14
The resulting fraction is -21/14. However, we can simplify this improper fraction by reducing it. The greatest common divisor of 21 and 14 is 7, so we divide both the numerator and denominator by 7:
-21/14 = -3/2
Therefore, the answer as a reduced improper fraction is -3/2.
To add the fractions −12/7 and 3/14, we need to find a common denominator and then add the fractions together.
Step 1: Find a common denominator
The denominators of the given fractions are 7 and 14. The least common multiple (LCM) of 7 and 14 is 14. Therefore, we need to express the fractions with a denominator of 14.
Step 2: Convert the fractions to have the common denominator
To convert the fractions, we need to multiply the numerator and denominator of each fraction by the same number so that the denominator becomes 14.
For the fraction −12/7:
Multiply the numerator and denominator by 2 (14 divided by 7):
−12/7 multiplied by 2/2 = −24/14
For the fraction 3/14:
No conversion is needed since the denominator is already 14.
Step 3: Add the fractions
Now that both fractions have a common denominator, we can add them:
−24/14 + 3/14 = (−24 + 3)/14 = −21/14
Step 4: Simplify the fraction (reduced improper fraction)
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 7 in this case:
−21 ÷ 7 / 14 ÷ 7 = −3/2
Therefore, the sum of −12/7 + 3/14 is −3/2.