|  Algebraic Expressions: Unlike equations, algebraic expressions do not contain an equal sign. |  | The word "terms" refers to values that are added or subtracted. 7n + 2 has two terms.
The word "factors" refers to values that are multiplied. The term 7n has two factors: 7 and n.
| The skill of translating between verbal statements and algebraic expressions requires an agreement of the words that are commonly used to stand for mathematical operations. A sampling of words used to represent mathematical operations: | ADD | SUBTRACT | MULTIPLY | Split | | add
sum
increased by
more than
exceeds
total
plus
in all
gain
deposit | subtract
deviation
decreased by
fewer
less than *
diminished past
minus
take away
withdraw
reduced by
| multiply
product
of
times
double
triple
twice
| carve up
quotient
per
divided equally
split into
fraction
ratio of
| * Remember that " less than " reverses the order of what you read. [ 6 less than ten, becomes x - 6 ] |  | Always look for the placement of commas in the exact statements. They will assistance you make up one's mind how to properly group terms in your algebraic expression.
For example: the verbal statement "v times, a number increased past 6" translates to v(n + vi) and is not fiven + six. |
 | (Think that variables tin be represented by any letter or symbol, unless otherwise directed.) | | Verbal Statement | Algebraic Expression | | ane. | 5 increased by four times a number | 5 + 4n | | two. | Eight less than twice a number | iinorthward - 8 | | 3. | Three times a number, increased by nine | 3due north + nine | | four. | The product of iv, and a number decreased by 7 | 4(north - 7) | | 5. | The number of feet in 10 yards. | 3x | | 6. | Express the width of a rectangle which is seven less than its length, 50. | l - 7 | | seven. | A number repeated as a factor 3 times. | n • due north • north = n three | Terms used to refer to specific expressions: | TERM | DESCRIPTION | EXAMPLES | | monomial | The product of non-negative integer powers of variables. It has ONE term. (mono implies ane) | 12, -3x , 2x 2, -7ab , 4t 3 due south 4 | | binomial | The sum of two monomials. It has Two unlike terms. (bi implies two) | viiten + 4, x 2 +1, 3a - 2b | | trinomial | The sum of three monomials. It has 3 unllike terms. (tri implies three) | x ii + 410 + 4, fourp ii - threeq 3 - 1 | | polynomial | A generic term for the sum of one or more than monomials. (poly implies many) | 4x, due south + 2,a 2 + b2 + c |
Algebraic Equations: Dissimilar expressions, algebraic equations incorporate an equal sign.
EQUA tion  EQUA l sign
Yous volition still come across the "words" used to represent mathematical operations, as shown in the chart at the pinnacle of the folio. To that list, we tin can now add a sampling of words that imply "an equal sign".
| EQUAL | is, are, was, were, equivalent to, aforementioned equally, yields, gives | As well, continue to look for commas, to assistance you group your terms. | | When trying to create equations, y'all may find information technology difficult to quickly make it at an answer. When this happens, it is oftentimes helpful to make upward a numerical case from the state of affairs so you can see how the numbers are related to one another. In addition, a numerical case is useful for checking to see if the equation you lot wrote is accurate. |
| | | | Exact Argument | Algebraic Equation | | i. | Three times a number, divided by ten equals fifteen. |  | | two. | X less than the quotient of a number and two is zero. |  | | 3. | Twelve more than the product of a number and ii is xxx-six. | iin + 12 = 36 | | 4. | Represent the toll of access to a movie web site which charges a $5 fee for the first month, and then $28 a month for continued access after the offset month.
Numerical Example: For 4 months the cost would be: Toll = $5 + $28•(4-1). Supersede 4 with thousand for number of months. | c = cost, m = months
c = 5 + 28(m - ane) | | v. | If chocolate doughnuts cost $one.x and chocolate flake muffins cost $2.25, how many of each can you lot purchase for $twenty?
Numerical Example: The cost of 3 doughnuts and 2 muffins will exist: Price = $1.50•3 + $2.25• two. Replace 3 with d for doughnuts, 2 with one thousand for muffins, and Cost with $20.
| d =doughnuts, m = muffins
20 = i.50d + 2.25k | | half-dozen. | Express the surface area of a rectangle whose length is twice its width decreased past 6.
Numerical Case: If the width is 10, the length is 14, then the area, A = 10 • fourteen. Just supercede 10 with westward for width, and fourteen with 2westward - half dozen for the length. | A = surface area, w = width
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