How to properly convert a balanced (line level) audio signal to unbalanced?
The "proper" way to do this, as you asked, is to use an audio transformer per channel. Pricey though.

The way we've got round this on a PA installation I operate is to use unbalanced auxiliary outputs to drive the power amp. The main outputs on our mixer (a Yamaha MX12/4) are balanced XLRs so we use two of the unbalanced 1/4" group outputs to drive the (stereo) power amp, along with some careful selection of signal routing to get the correct signal out. 

Edit: I see you have a Yamaha mg12xu mixer. The manuals can be found 
here.

The 
technical specifications(PDF) show 
that the Stereo Out connections are balanced (and available on both XLR and 1/4" TRS jacks).

The Monitor Out, Group Out and Aux Send outputs (all pairs) are described, in the Analog Output 
Characteristics section,  as "Impedance Balanced" jacks. These are all unbalanced outputs with the single-ended signal applied to the tip of the jack. The sleeve is grounded. The ring is connected to ground via a resistor equal to the source impedance of the output amplifier (stated to be 150 Ω).

The arrangement is shown in the block diagram on page 2 of the technical specification and enlarged in the 
owner's manual(PDF) e.g. page 26.

This produces an unbalanced output that can be used to feed an unbalanced input via either a TS or TRS plug. It can also be used to feed a balanced cable and input via a TRS plug. The impedance balancing means that the balanced interference rejection on that circuit is retained. (However, as the return line isn't driven you lose 6 dB of signal and the circuit could cause more cross-talk to adjacent circuits as we are not sending equal magnitude but opposite polarity signals on the cable pair.)

The Aux Send outputs bypass the main group and stereo faders so it is probably more useful for you to use either the 
Monitor Out or Group Out outlets to drive your amplifier.

Which you use will affect how you setup and use the mixer. I suggest you study the overall block diagram in the technical specifications, and the more detailed sections in the owner's manual, to see which switches to set and to work out which outlets will better suit your needs.  (I find it useful to keep a copy of the overall block diagram 
by my mixer to sort out those awkward "where did the signal go" moments during bouts of finger trouble or when
visitors have used the mixer and changed the settings.)