Suppose a candy bar costs 45 cents. Then 45 × 2 is the cost of 2 candy bars, 45 × 3 is the cost of 3 candy bars, and so on. Generally, the cost of any number of candy bars is 45 cents times the number of bars. We can represent this situation with an algebraic expression.
The letter n stands for an unknown number, in this case,
candy bars. The unknown n is
called a variable
because its value varies. An algebraic expression contains at least one variable and at least one
mathematical operation, as shown
in the examples below.
h ÷ 3 5n + 1 
xy 4 × a
A numerical
expression contains only numbers and mathematical operations. For example, 6 + 2 ÷ 1 is a numerical expression.
In an expression involving multiplication, the quantities
being multiplied are
called factors,
and the result is the product.
To write a multiplication expression such as 4 × a, a raised dot or parentheses can be used. A fraction bar can be used to
represent division.
The result of a divison
expression is called a quotient.
To solve verbal problems in
mathematics, you may have to translate words into algebraic expressions. The
chart below shows some of the words and phrases used to indicate mathematical
operations.
|
Addition |
Subtraction |
Multiplication |
Division |
|
plus the sum of increased by more than added to the total of |
minus the difference of decreased by less than fewer than subtracted from |
times the product of multiplied by at of |
times the product of multiplied by at of |
Examples
Write an algebraic expression for
each verbal expression.
1.
the sum of m and 18
m+ 18
2.
g divided by y
g ÷ y
3. Write a numerical expression to represent
the distance a kangaroo can travel if it leaps 4 times.
30 · 4 or 30(4)
4. Write an algebraic expression to represent
the distance a kangaroo can travel if it leaps x times.
30 · x or 30x
You can also translate algebraic
expressions into verbal expressions.
Examples
Write a verbal expression for
each algebraic expression.
1.
32 – b
32 less b
b less than 32
the difference of 32 and b
b subtracted from 32
32 decreased by b
2.
(y ÷ 4) + 9
y divided by 4, plus 9
the quotient of y and 4, increased by 9
9 added to the ratio of y and 4
An equation is a mathematical sentence that
contains an equals sign (=). Some words used to indicate the equals sign are in
the chart at the right. An equation may contain numbers, variables, or
algebraic expressions.
|
Equality |
|
|
equals is is equivalent to |
is equal to is the same as is as much as is identical to |
Examples
Write an equation for each sentence.
1.
Three times g equals 21.
3g = 21
2.
Five more than twice n is 15.
2n + 5 = 15
Sumber
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