Step 1 :Given the votes for Republican and Democratic candidates in 2010 and 2012, we need to find the percentage of votes cast for each party in both years.
Step 2 :In 2010, the total votes cast were 2089 thousand for Republicans and 1637 thousand for Democrats, making a total of 3726 thousand votes.
Step 3 :In 2012, the total votes cast were 2664 thousand for Republicans and 2403 thousand for Democrats, making a total of 5067 thousand votes.
Step 4 :To find the percentage of votes for each party, we divide the votes for that party by the total votes and multiply by 100.
Step 5 :For 2010, the percentage of votes for Republicans is \((2089 / 3726) \times 100 = 56.1\% \) and for Democrats is \((1637 / 3726) \times 100 = 43.9\%\).
Step 6 :For 2012, the percentage of votes for Republicans is \((2664 / 5067) \times 100 = 52.6\% \) and for Democrats is \((2403 / 5067) \times 100 = 47.4\%\).
Step 7 :So, the percentages of votes cast for Republican and Democratic House candidates in 2010 and 2012 are: 2010: Republican \(\boxed{56.1\%}\), Democrat \(\boxed{43.9\%}\) and 2012: Republican \(\boxed{52.6\%}\), Democrat \(\boxed{47.4\%}\). These values are rounded to one decimal place as needed.