Match each fraction to a reasonable estimate
(-3/13)
(-1/4)
(-6/11)
(-3/4)
00
(-7/9)
(-1/2)
イ) Intro
!
Done
コロロロロロロロロロロロロロロロロロロ
10f17

Step-by-step explanation:

We'll drop all the minus signs, since they don't contribute anything but distraction.

When numerators or denominators are relatively large, changing their value by 1 unit will have a relatively small effect on the value of the fraction. For example, ...

  3/13 ≈ 3/12 = 1/4

If we compare the decimal values of these fractions, we see that ...

  3/13 ≈ 0.230769... (6-digit repeating decimal)

The closest of the offered "reasonable estimate" fractions is 1/4 = 0.25.

__

Likewise, 6/11 ≈ 6/12 = 1/2. In decimal, these fractions are ...

  6/11 = 0.54... (2-digit repeat)

  1/2 = 0.5

__

We can also increase or decrease both numerator and denominator by the same amount to get a fraction with nearly the same value. This works best when the numbers are larger.

  7/9 ≈ 6/8 = 3/4 . . . . . . both numerator and denominator decreased by 1

In decimal, these are ...

  7/9 = 0.7... (1-digit repeat)

  3/4 = 0.75

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

the solution is 12x-6y