2- 26/27 : 39/45

To simplify the ratio \(2 - \frac{26}{27} : \frac{39}{45}\), let's break it down step by step.

First, simplify \(2 - \frac{26}{27}\):

1. Convert \(2\) to a fraction with a denominator of \(27\): \[ 2 = \frac{54}{27} \]

2. Now subtract: \[ \frac{54}{27} - \frac{26}{27} = \frac{54 - 26}{27} = \frac{28}{27} \]

Next, simplify \(\frac{39}{45}\):

1. Find the greatest common divisor (GCD) of \(39\) and \(45\). The GCD is \(3\).
2. Divide both the numerator and the denominator by \(3\): \[ \frac{39 \div 3}{45 \div 3} = \frac{13}{15} \]

Now we can rewrite the ratio:

\[ \frac{28}{27} : \frac{13}{15} \]

To express this ratio in a more usual form, we cross-multiply:

\[ 28 \times 15 : 27 \times 13 \]

Calculating each term:

1. \(28 \times 15 = 420\)
2. \(27 \times 13 = 351\)

Thus, the ratio simplifies to:

\[ 420 : 351 \]

To further simplify, find the GCD of \(420\) and \(351\). The GCD is \(3\).

Now divide both sides by \(3\):

\[ \frac{420 \div 3}{351 \div 3} = 140 : 117 \]

So, the final simplified ratio is:

\[ \mathbf{140 : 117} \]