Simple Multiplication and Subtraction Word Problems

In a word or story problem, the words ... times as many (or, os few) as ... may indicate either the need for multiplication or division in the translation of the problem into mathematical language. Below we shall consider a few examples. As in other word problems, it is important to separate the essential information from the specific coating of a particular problem.

(Note: In the applet below, all underlied words and numbers can be clicked on. Please feel free to do just that.)

// foreground color // background color // information pieces start with '@', followed by // a single letter from {v,a,f,e}, followed by ": ". // v - variable - anything that may change on a click // variables must precede all other pieces // f - formulation - word problem with embedded variables. // Many formulations are possible for a single problem. // Only one is shown at a time // e - equation - equation is like a formulation with a // potential provision to, e.g., enclose negative numbers // into parentheses // a - answer - like an equation, but allowed to have a parsable // portion. Parsables are written in the reverse Polish notations // with variables and operations separated by a comma // d - directive // define color, skip line // // whatever it is, a variable can be of the three types: // i = integer - on click changes up (right of center) and down (left of center) // a = attribute - any clickable and changeable word // v = variable - like an attribute but without related attributes // all 'name's below are 1 letter from [A-Ba-b1-0] // i, name, initial value, min, max // v, name, list of symbols // formulations // equations

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?

(There are many more word problems discussed and solved at this site. The math tutorial continues with a similar approach over several additional examples.)

Word Problems

  1. Problems of class a + x = b
  2. Problems of class a · x = b
  3. From Word Problem to Equation
  4. Problems of class x / a = b / c
  5. Problems of class x = a + b
  6. Problems of class x = a + b (II)
  7. Problems of class x = a × b
  8. Solving Two Simultaneous Linear Equations

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