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To solve a problem using algebra, we must first express the problem algebraically. To express a problem algebraically, we must scrutinize the wording of the problem to determine the variables and constants that are present and the relationships among them. Then we must translate the verbal phrases and statements to algebraic expressions and equations.
To help us translate verbal expressions to mathematics, we can use the following table as a mathematics dictionary.
Word or Phrase | Mathematical Operation |
Sum, sum of, added to, increased by, more than, plus, and | |
Difference, minus, subtracted from, decreased by, less, less than | |
Product, the product of, of, muitiplied by, times | |
Quotient, divided by, ratio | |
Equals, is equal to, is, the result is, becomes | |
A number, an unknown quantity, an unknown, a quantity | (or any symbol) |
Translate the following phrases or sentences into mathematical expressions or equations.
Translate the following phrases or sentences into mathematical expressions or equations.
Ten times a number is eight more than five times the same number.
Sometimes the structure of the sentence indicates the use of grouping symbols.
Translate the following phrases or sentences into mathematical expressions or equations.
A number plus one is divided by three times the number minus twelve and the result is four.
Notice that since the phrase "three times the number minus twelve" does not contain a comma, we get the expression
. If the phrase had appeared as "three times the number, minus twelve," the result would have been
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