Answer:
-9 1/4
Step-by-step explanation:
-5 3/4 - 3 1/2
Get a common denominator
-5 3/4 - 3 1/2 *2/2
-5 3/4 - 3 2/4
-8 5/4
Rewritng
-8 4/4 - 1/4
-9 1/4
The answer to this question is 23
6/11 = 0.54_54 . . . . . the digits 54 are repeated indefinitely
You can arrive at the digits 54 by multiplying the numerator (6) by 9. This will be the case for any proper fraction with 11 as a denominator.
The idea is to find a linear combination a_1(5, -6) + a_2(-2, -2) = (-6, 2)
It boils down to a system of equations:
Take the augmented matrix:
<span>[<span><span>5<span>−6</span></span><span><span>−2</span><span>−2</span></span><span><span>−6</span>2</span></span>]</span>
Reduced form:
<span>[<span><span>10</span><span>01</span><span><span>−<span>811</span></span><span>1311</span></span></span>]</span>
-(8/11)*(5, -6) + (13/11)*(-2, -2) = (-6, 2)