Add −3 1/6+5 3/4. Write your answer as a reduced mixed number.

Answer 1

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.