'To reduce an equation' definitions:

Definition of 'To reduce an equation'

From: GCIDE

Reduce \Re*duce"\ (r[-e]*d[=u]s"), v. t. [imp. & p. p. Reduced (-d[=u]st"),; p. pr. & vb. n. Reducing (-d[=u]"s[i^]ng).] [L. reducere, reductum; pref. red-. re-, re- + ducere to lead. See Duke, and cf. Redoubt, n.]
1. To bring or lead back to any former place or condition. [Obs.] [1913 Webster]
And to his brother's house reduced his wife. --Chapman. [1913 Webster]
The sheep must of necessity be scattered, unless the great Shephered of souls oppose, or some of his delegates reduce and direct us. --Evelyn. [1913 Webster]
2. To bring to any inferior state, with respect to rank, size, quantity, quality, value, etc.; to diminish; to lower; to degrade; to impair; as, to reduce a sergeant to the ranks; to reduce a drawing; to reduce expenses; to reduce the intensity of heat. "An ancient but reduced family." --Sir W. Scott. [1913 Webster]
Nothing so excellent but a man may fasten upon something belonging to it, to reduce it. --Tillotson. [1913 Webster]
Having reduced Their foe to misery beneath their fears. --Milton. [1913 Webster]
Hester Prynne was shocked at the condition to which she found the clergyman reduced. --Hawthorne. [1913 Webster]
3. To bring to terms; to humble; to conquer; to subdue; to capture; as, to reduce a province or a fort. [1913 Webster]
4. To bring to a certain state or condition by grinding, pounding, kneading, rubbing, etc.; as, to reduce a substance to powder, or to a pasty mass; to reduce fruit, wood, or paper rags, to pulp. [1913 Webster]
It were but right And equal to reduce me to my dust. --Milton. [1913 Webster]
5. To bring into a certain order, arrangement, classification, etc.; to bring under rules or within certain limits of descriptions and terms adapted to use in computation; as, to reduce animals or vegetables to a class or classes; to reduce a series of observations in astronomy; to reduce language to rules. [1913 Webster]
6. (Arith.) (a) To change, as numbers, from one denomination into another without altering their value, or from one denomination into others of the same value; as, to reduce pounds, shillings, and pence to pence, or to reduce pence to pounds; to reduce days and hours to minutes, or minutes to days and hours. (b) To change the form of a quantity or expression without altering its value; as, to reduce fractions to their lowest terms, to a common denominator, etc. [1913 Webster]
7. (Chem.) To add an electron to an atom or ion. Specifically: To remove oxygen from; to deoxidize. (Metallurgy) To bring to the metallic state by separating from combined oxygen and impurities; as, metals are reduced from their ores. (Chem.) To combine with, or to subject to the action of, hydrogen or any other reducing agent; as, ferric iron is reduced to ferrous iron; aldehydes can be reduced to alcohols by lithium hydride; -- opposed to oxidize. [1913 Webster +PJC]
8. (Med.) To restore to its proper place or condition, as a displaced organ or part; as, to reduce a dislocation, a fracture, or a hernia. [1913 Webster]
Reduced iron (Chem.), metallic iron obtained through deoxidation of an oxide of iron by exposure to a current of hydrogen or other reducing agent. When hydrogen is used the product is called also iron by hydrogen.
To reduce an equation (Alg.), to bring the unknown quantity by itself on one side, and all the known quantities on the other side, without destroying the equation.
To reduce an expression (Alg.), to obtain an equivalent expression of simpler form.
To reduce a square (Mil.), to reform the line or column from the square. [1913 Webster]
Syn: To diminish; lessen; decrease; abate; shorten; curtail; impair; lower; subject; subdue; subjugate; conquer. [1913 Webster]