Overview:
Writing equations in algebra is a process of translating words into mathematical symbols and operations. The difference between expressions in arithmetic and those in algebra is that variables are used to express unknown quantities, but the process is similar. That way, equations can be derived to express everyday relationships between numbers and unknown quantities.
How Do Letters Represent Variables?
When translating a statement in words to an algebraic equation, clearly state what the variable represents. Suppose that the starting quarterback for one high school team rushes y yards for the season. His yardage is represented by the variable y. Similarly, the class president can have gotten v more votes than her challenger in the class election.
What Expressions Represent Addition and Subtraction?
Terms such as “more than”, “sum”, “increase”, or “total” represent addition. Conversely, terms such as “less than”, “minus”, “decrease”, and “difference” represent subtraction. The starting quarterback’s yardage, y, is 30 yards more than the previous school record. In that case, y-30 equals the old school record.
What Expressions Represent Multiplication and Division?
Multiplication terms include “times”, “product”, and such words as “twice” or “triple”. Division terms include “quotient”, and “divided by”. If there are 120 students in either the band or choir and there are twice as many in the band as in the choir, how many are in each group? Let x equal the number of students in choir. Then 2x will equal the number of students in the band. If the total cost of taxes is represented by z, then z/12 will be the cost per month.
How Are the Symbols Put Together?
Putting the variables, numbers, and symbols for the operations together in an equation goes a long way towards solving it. For example, if x is the number of students in choir and 2x is the number of students in band, an equation for the number in each group is x + 2x = 120, or 3x = 120, or x = 40. There are 40 students in choir and 80 in band, 120 all together
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