Sometimes we don't realize how much knowing the origin or background of a word (etymology) will impact our basic understanding of what we are actually saying and doing. Let's look at the breakdown of the word Algebra.
"The word algebra comes from the Arabic الجبر (al-jabr lit. "the reunion of broken parts") from the title of the book Ilm al-jabr wa'l-muḳābala by the Persian mathematician and astronomer al-Khwarizmi (sounds like algorithm). The word entered the English language during the fifteenth century, from either Spanish, Italian, or Medieval Latin." Wikipedia
The broken parts are the two expressions joined by an equal sign (jabr). Then there's a filling in of holes/unknowns/variables in our equations by way of "qabala", balancing/opposing/opposite operation.
"In Arabic, al- is the definite article "the." The first noun in the title is jebr "reunion of broken parts," from the verb jabara "to reunite, to consolidate." The second noun is from the verb qabala, with meanings that include "to place in front of, to balance, to oppose, to set equal."
Together the two nouns describe some of the manipulations so common in algebra: combining like terms, transposing a term to the opposite side of an equation, setting two quantities equal, etc. Because the original Arabic title was so long, and because it was in Arabic, Europeans soon shortened it. The result was algeber or something phonetically similar, which then took on the meanings of both nouns and eventually acquired its modern sense."