Back to Algebra for
Adults.
Algebra for Adults:
Part 6, Operations and Expressions:
January 6, 2003:
Here are the problems from part 5.
Give the equivalent algebra statement for this verbal statement.
Six times any number plus two times the same number is equal to eight times the number.
Let n represent the number. Then 6n + 2n = 8n
The volume of a cylinder is given as 3.14 times the radius of the cylinder squared times the length of the cylinder. Let v represent the volume, r represent the radius, and l represent the length. Write the equivalent algebra statement for this verbal statement.
As you can see, this is much shorter than the equivalent verbal
statement.
We call this statement an equation.
From Microsoft's Bookshelf we get this:
Equation
Mathematics: A statement asserting the equality of two expressions,
usually written as a linear array of symbols that are separated
into left and right sides and joined by an equal sign.
As we said, this shorthand (equation) way of representing mathematical relationships is the big difference between basic mathematics and algebra. We will find that everything else will follow the old familiar operations, rules, and laws we discovered in basic math. To recall these things refer to the Algebra Archives and find the listings of Rules and Laws, Symbols and Operators , and Terms.
It is important to notice that algebraic expressions need not
be complete equations.
For example:
7z is an algebraic expression that means 7 times z.
6y is an algebraic expression that means 6 times y.
15/a is an algebraic expression that means 15 divided by a.
Now remember that division by zero is undefined or impossible in math. This is still true in algebra. Let's look at this expression.
15/a
Can you see that this division would be impossible in the case where a = 0?
In that case, the expression would be 15/0 which is undefined
or impossible.
All of the math rules still apply.
The thing we want to notice now is, we can express any mathematical
operation as an algebraic expression.
Here are some more examples:
z + 5 means z added to 5.
n + 12 means n added to 12.
7 – y means y subtracted from 7.
All of this becomes very handy when we want to express real
life situations as resolvable problems. Most of the mathematical
challenges which confront us in life do not come neatly packaged
as mathematical expressions. Instead, they are usually expressed
in some verbal form that we must change into algebraic expressions.
For example:
Express a weight that is ten times larger than another weight
(w).
The answer is 10w.
Express a distance that is 3 feet longer that the distance
(d).
The answer is d + 3 or, by the commutative law, 3 + d.
Express a height that is 2 feet shorter than a height x.
The answer is x - 2.
Express a volume that is 1/2 of a volume (v).
The answer is v/2.
These are simple expressions, but we can deal in the same way
with more complex situations.
For example:
Five times the sum of x and y is 5(x + y).
A weight (w) added to 3 times another weight (x) is w + 3x.
That is enough for now. Here are some verbal statements. Express each one of these algebraically.
75 subtracted from the quotient of b divided by c.
The sum of a and b divided by the product of c and d.
A length (x) added to three times a length (y) divided by 2.
A speed of twice x diminished by a speed of y divided by c.
The product of x and y and z added to the quotient of c divided by 2.
Half of z increased by a times 35.
Back to Algebra for Adults.
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