About Lesson
Solving Equations with Decimal Coefficients
Some equations have decimals in them. This kind of equation will occur when we solve problems dealing with money and percent. But decimals are really another way to represent fractions. For example,
and
So, when we have an equation with decimals, we can use the same process we used to clear fractions—multiply both sides of the equation by the least common denominator.
Key Concepts
- Solve equations with fraction coefficients by clearing the fractions.
- Find the least common denominator of all the fractions in the equation.
- Multiply both sides of the equation by that LCD. This clears the fractions.
- Solve using the General Strategy for Solving Linear Equations.
Examples
Solve
Solution:
Look at the decimals and think of the equivalent fractions.
Notice, the LCD is
By multiplying by the LCD we will clear the decimals.
![]() |
|
Multiply both sides by 100. | ![]() |
Distribute. | ![]() |
Multiply, and now no more decimals. | ![]() |
Collect the variables to the right. | ![]() |
Simplify. | ![]() |
Collect the constants to the left. | ![]() |
Simplify. | ![]() |
Divide by 19. | ![]() |
Simplify. | ![]() |
Check: Let | |
![]() |
Solve:
Solution:
![]() |
|
Distribute first. | ![]() |
Combine like terms. | ![]() |
To clear decimals, multiply by 100. | ![]() |
Distribute. | ![]() |
Subtract 15 from both sides. | ![]() |
Simplify. | ![]() |
Divide by 30. | ![]() |
Simplify. | ![]() |
Check: Let | |
![]() |