Conversion a mixed number -2 2/
7
to a improper fraction: -2 2/7 = -2 2/
7
= -2 · 7 + (-2)/
7
= -14 + (-2)/
7
= -16/
7
To find a new numerator:
a) Multiply the whole number -2 by the denominator 7. Whole number -2 equally -2 * 7/
7
= -14/
7
b) Add the answer from previous step -14 to the numerator 2. New numerator is -14 + 2 = -12
c) Write a previous answer (new numerator -12) over the denominator 7.
Minus two and two sevenths is minus twelve sevenths
Add: -16/
7
+ 3/
2
= -16 · 2/
7 · 2
+ 3 · 7/
2 · 7
= -32/
14
+ 21/
14
= -32 + 21/
14
= -11/
14
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 2) = 14. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 2 = 14. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - minus sixteen sevenths plus three halfs is minus eleven fourteenths.