How Do You Use Fractions to Solve Two-Step Equations?

How Do You Use Fractions to Solve Two-Step Equations?

A two-step problem is an algebra problem in which you have to solve for at least one other unknown before you can calculate the actual answer to the problem. Some word problems deal with fractions or percentages of an unknown whole.

  1. Determine the information you have

    Read through the problem. Write down all of the numbers you find in the problem, converting words like "half" into "1/2." Label each number for what it represents in the problem. Then determine any relationships you already know between these terms. Write these relationships in terms of equations. One of the equations will probably show variables that when added together make up the whole.

  2. Figure out how many parts there are in the whole

    If you think of the unknown whole as equal to 1, then the component variables can be rewritten as simple fractions of the whole. You can then write equations that relate the individual terms to the whole. For example, if the word problem expressed a particular value of money as 1/6 of a person's total allowance, then you know that the value (v) can be expressed in terms of 6v=A or the total amount.

  3. Isolate and cancel the fractions

    To isolate a variable with a fractional coefficient, move over terms to the other side of the equation. To cancel, multiply both sides by the reciprocal of that coefficient.

  4. Use substitution to solve the problem

    With isolated fractions and equations to show their relationship, you can use substitution to change all of the variables in an equation to the same variable. Solve for the variable by isolating it and simplifying the numbers on the other side. Then use that solved variables value to find the answer to the problem.