Add −3 1/6+5 3/4. Write your answer as a reduced mixed number.
To add -3 1/6 and 5 3/4, we first need to find a common denominator. The denominators are 6 and 4. The least common multiple of 6 and 4 is 12.
Converting -3 1/6 to an improper fraction:
-3 1/6 = -3 * 6 / 6 + 1/6 = -18/6 + 1/6 = -17/6
Converting 5 3/4 to an improper fraction:
5 3/4 = 5 * 4 / 4 + 3/4 = 20/4 + 3/4 = 23/4
Now, we add the fractions:
-17/6 + 23/4
Since the denominators are different, we need to find a common denominator. The common denominator is 6*4 = 24.
Converting -17/6 to have a denominator of 24:
-17/6 = -17 * 4 / 6 = -68/24
Converting 23/4 to have a denominator of 24:
23/4 = 23 * 6 / 4 = 138/24
Now, we can add the fractions:
-68/24 + 138/24 = (138 - 68) / 24 = 70/24
Simplifying the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 2:
70/24 = 35/12
Therefore, -3 1/6 + 5 3/4 = 35/12 when written as an improper fraction.
To write the answer as a reduced mixed number, we divide the numerator (35) by the denominator (12):
35 ÷ 12 = 2 remainder 11
Thus, the answer as a reduced mixed number is 2 11/12.
To add the fractions −3 1/6 and 5 3/4, we first need to find a common denominator for the fractions. The common denominator for 6 and 4 is 12.
Next, we convert the mixed numbers to improper fractions:
-3 1/6 = -19/6
5 3/4 = 23/4
Now that both fractions have the same denominator, we can add them:
-19/6 + 23/4
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 12.
-19/6 * 2/2 = -38/12
23/4 * 3/3 = 69/12
Now, we can add the fractions:
-38/12 + 69/12 = 31/12
To convert the improper fraction 31/12 to a mixed number, we divide the numerator by the denominator:
31 ÷ 12 = 2 remainder 7
The quotient becomes the whole number, and the remainder becomes the numerator of the fractional part. Therefore, the answer is 2 7/12.