Add −12 / 7+(3 / 14). Write your answer as a reduced improper fraction.
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To add mixed numbers or fractions, we need to convert them to improper fractions first.
Converting −12/7 to an improper fraction, we multiply the whole number (−12) by the denominator (7) and add the numerator (−12):
−12/7 = (-12 × 7 + (-12)) / 7 = -84/7 - 12/7 = -96/7
Converting 3/14 to an improper fraction, we multiply the whole number (3) by the denominator (14) and add the numerator (3):
3/14 = (3 × 14 + 3) / 14 = 45/14
Now, we can add the two fractions:
-96/7 + 45/14
To add fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 7 and 14 is 14.
Multiplying the numerator and denominator of -96/7 by 2 (to make the denominator 14):
(-96/7) × (2/2) = -192/14
Now we can add the fractions:
-192/14 + 45/14 = (-192 + 45) / 14 = -147/14
Therefore, the sum −12/7 + 3/14 as a reduced improper fraction is -147/14.
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Add 13.92+(−22.111)
To add decimal numbers, we align the decimal points and then add the numbers as we would with whole numbers.
13.92
+ -22.111
___________
If we align the decimal point, we have:
13.920
+ -22.111
___________
Now we can add the numbers:
13.920
+ -22.111
___________
- 8.191
Therefore, 13.92 + (-22.111) equals -8.191.