Edit in JSFiddle

var dragFix, startFix, stopFix;

window.myApp = {
  layout: {
    zoomScale: 0.8
  },
  draggable: {
    _uiHash: function() {
      return {
        helper: this.helper,
        position: this.position,
        originalPosition: this.originalPosition,
        offset: this.positionAbs,
        containment: this.containment
      };
    }
  },
  resizable: {
    _change: {
      e: function(event, dx) {
        return {
          width: this.originalSize.width + dx / myApp.layout.zoomScale
        };
      },
      w: function(event, dx) {
        var cs, sp;
        cs = this.originalSize;
        sp = this.originalPosition;
        return {
          left: sp.left + dx,
          width: cs.width - dx / myApp.layout.zoomScale
        };
      },
      n: function(event, dx, dy) {
        var cs, sp;
        cs = this.originalSize;
        sp = this.originalPosition;
        return {
          top: sp.top + dy,
          height: cs.height - dy / myApp.layout.zoomScale
        };
      },
      s: function(event, dx, dy) {
        return {
          height: this.originalSize.height + dy / myApp.layout.zoomScale
        };
      }
    },
    plugins: {
      containment: {
        resize: function(event) {
          var ce, co, continueResize, cop, cp, hoset, isOffsetRelative, isParent, o, pRatio, that, woset;
          woset = void 0;
          hoset = void 0;
          isParent = void 0;
          isOffsetRelative = void 0;
          that = $(this).resizable("instance");
          o = that.options;
          co = that.containerOffset;
          cp = that.position;
          pRatio = that._aspectRatio || event.shiftKey;
          cop = {
            top: 0,
            left: 0
          };
          ce = that.containerElement;
          continueResize = true;
          if (ce[0] !== document && /static/.test(ce.css("position"))) {
            cop = co;
          }
          if (cp.left < (that._helper ? co.left : 0)) {
            that.size.width = that.size.width + (that._helper ? that.position.left - co.left : that.position.left - cop.left);
            if (pRatio) {
              that.size.height = that.size.width / that.aspectRatio;
              continueResize = false;
            }
            that.position.left = (o.helper ? co.left : 0);
          }
          if (cp.top < (that._helper ? co.top : 0)) {
            that.size.height = that.size.height + (that._helper ? that.position.top - co.top : that.position.top);
            if (pRatio) {
              that.size.width = that.size.height * that.aspectRatio;
              continueResize = false;
            }
            that.position.top = (that._helper ? co.top : 0);
          }
          isParent = that.containerElement.get(0) === that.element.parent().get(0);
          isOffsetRelative = /relative|absolute/.test(that.containerElement.css("position"));
          if (isParent && isOffsetRelative) {
            that.offset.left = that.parentData.left + that.position.left;
            that.offset.top = that.parentData.top + that.position.top;
          } else {
            that.offset.left = that.element.offset().left;
            that.offset.top = that.element.offset().top;
          }
          woset = Math.round(Math.abs(that.sizeDiff.width + (that._helper ? that.offset.left - cop.left : (that.offset.left - co.left) / myApp.layout.zoomScale)));
          hoset = Math.round(Math.abs(that.sizeDiff.height + (that._helper ? that.offset.top - cop.top : (that.offset.top - co.top) / myApp.layout.zoomScale)));
          if (woset + that.size.width >= that.parentData.width) {
            that.size.width = that.parentData.width - woset;
            if (pRatio) {
              that.size.height = that.size.width / that.aspectRatio;
              continueResize = false;
            }
          }
          if (hoset + that.size.height >= that.parentData.height) {
            that.size.height = that.parentData.height - hoset;
            if (pRatio) {
              that.size.width = that.size.height * that.aspectRatio;
              continueResize = false;
            }
          }
          if (!continueResize) {
            that.position.left = that.prevPosition.left;
            that.position.top = that.prevPosition.top;
            that.size.width = that.prevSize.width;
            that.size.height = that.prevSize.height;
          }
        }
      }
    }
  }
};

$.ui.draggable.prototype._uiHash = myApp.draggable._uiHash;
$.extend($.ui.resizable.prototype._change, myApp.resizable._change);

startFix = function(event, ui) {
  ui.containment[2] *= myApp.layout.zoomScale;
  return ui.containment[3] *= myApp.layout.zoomScale;
};

stopFix = function(event, ui) {
  ui.containment[2] /= myApp.layout.zoomScale;
  return ui.containment[3] /= myApp.layout.zoomScale;
};

dragFix = function(event, ui) {
  var deltaX, deltaY;
  deltaX = ui.position.left - ui.originalPosition.left;
  deltaY = ui.position.top - ui.originalPosition.top;
  ui.position.left = ui.originalPosition.left + deltaX / myApp.layout.zoomScale;
  return ui.position.top = ui.originalPosition.top + deltaY / myApp.layout.zoomScale;
};

$("#draggable").resizable({containment: '#parent'}).draggable(
    {
        containment: '#parent',
        start: startFix,
        drag: dragFix,
        stop: stopFix
    }
);

var plugin, r_inst, _i, _len, _ref;

r_inst = $('#draggable').resizable('instance');

_ref = r_inst.plugins.resize;
for (_i = 0, _len = _ref.length; _i < _len; _i++) {
  plugin = _ref[_i];
  if (plugin[0] === 'containment') {
    plugin[1] = myApp.resizable.plugins.containment.resize;
  }
}

<body>
    <div id="parent">
        <div id="draggable">
            Hello!
        </div>
    </div>
</body>

#parent {
    background-color: blue;
    width: 400px;
    height: 400px;
    transform: scale(0.8);
    -moz-transform: scale(0.8);
    -webkit-transform: scale(0.8);
    transform-origin: center top 0px;
    -moz-transform-origin: center top 0px;
    -webkit-transform-origin: center top 0px;
}

#draggable {
    background-color: rgba(0,0,0,0.5);
    border: 1px solid black;
    width: 50px;
    height: 50px;
    color: white;
}