Writing Algebraic Expressions
CONVENTION
We generally write the variable before the number in an addition problem. [ x + 8 ]
We generally write the number before the variable in a multiplication problem. [ 8x ]
ADDITION (see convention above)
Total [A board is cut into two pieces. One piece has a length of 67 inches. If the other piece has a length of
z inches, what was the total length of the board, in inches, before it was cut?  z + 67]
Sum [The sum of 8 and w  w + 8]
Altogether [ Jolene has w computers upstairs and eight computers downstairs. How many computers does
she have altogether?  w + 8]
More than*– not the same as IS MORE THAN [8 more than w  w + 8]
Added to [8 added to w  w + 8]
Increased by [w increased by 8  w + 8]
Plus [8 plus w  w + 8]
SUBTRACTION (careful with order)
Less than*– not the same as IS LESS THAN [18 less than y  y – 18]
Difference [the difference of r and 4  r – 4]
Other [If a 53-inch board is cut into two pieces and one piece is x inches, how long is the other piece? 
53 - x]
Left or left over [In a given month, Jolene earns d dollars and owes $987 in expenses. How much, in
dollars, does she have left after paying for expenses?  d – 987]
Decreased by [z decreased by 72  z – 72]
Subtracted from* [8 subtracted from m  m – 8]
Minus [7 minus n  n – 7]
MULTIPLICATION (see convention above)
Product [the product of m and 7  7m]
Twice [twice z  2z]
Of [one-half of x  ½x]
Times [three times z  3z]
Multiplied by [g multiplied by 4  4g]
At/each [y DVDs at $12 each  12y ]
DIVISION (careful with order)
Quotient [the quotient of m and 3  m/3 ]
Each—careful with “at” and “total” and other addition or multiplication words. (If 6 DVDs cost x dollars
total, how much does each DVD cost?  x/6)
Per [If Jolene earns y dollars in a year, how much is that per week?  y/52]
Ratio [The ratio of n and 7  n/7]
Divided by [n divided by 8  n/8]
“percent” means “Divided by 100” [ z percent  z/100 ]
PROPORTIONS
How many _______ are in _____ [How many minutes are there in h hours?  60h]
If one ________, how many are _____ [If one notebook costs n dollars, what is the cost, in dollars, of 15
notebooks?  15n]
*CAREFUL WITH ORDER—these words indicate switch the order
From
Than