Tìm x .2 3/4 : x = 3 1/7 : 0,1. 2 2/3 : x = 2 1/12 : ( -0,06 )

To solve these proportions, we can cross-multiply and then solve for x.

a) 2 3/4 : x = 3 1/7 : 0.1

First, convert the mixed numbers to improper fractions:
2 3/4 = (2 * 4 + 3) / 4 = 11/4
3 1/7 = (3 * 7 + 1) / 7 = 22/7

Now we have:
(11/4) / x = (22/7) / 0.1

Cross-multiplying:
(11/4) * 0.1 = (22/7) * x

Simplifying:
11/40 = 22x/7

Cross-multiplying again:
11 * 7 = 40 * 22x
77 = 880x

Dividing both sides by 880:
x = 77/880

Therefore, the solution is x = 77/880.

b) 2 2/3 : x = 2 1/12 : (-0.06)

Again, convert the mixed numbers to improper fractions:
2 2/3 = (2 * 3 + 2) / 3 = 8/3
2 1/12 = (2 * 12 + 1) / 12 = 25/12

Now we have:
(8/3) / x = (25/12) / (-0.06)

Cross-multiplying:
(8/3) * (-0.06) = (25/12) * x

Simplifying:
-0.16 = (25/12) * x

Cross-multiplying again:
-0.16 * 12 = 25x
-1.92 = 25x

Dividing both sides by 25:
x = -1.92/25

Therefore, the solution is x = -1.92/25.