Determine Whether a Decimal is a Solution of an Equation
Solving equations with decimals is important in our everyday lives because money is usually written with decimals. When applications involve money, such as shopping for yourself, making your family’s budget, or planning for the future of your business, you’ll be solving equations with decimals.
Now that we’ve worked with decimals, we are ready to find solutions to equations involving decimals. The steps we take to determine whether a number is a solution to an equation are the same whether the solution is a whole number, an integer, a fraction, or a decimal. We’ll list these steps here again for easy reference.
How To: Determine Whether a Number Is a Solution to an Equation
- Substitute the number for the variable in the equation.
- Simplify the expressions on both sides of the equation.
- Determine whether the resulting equation is true.
- If so, the number is a solution.
- If not, the number is not a solution.
Solve Equations with Decimals
In previous modules, we solved equations using the properties of equality. We will use these same properties to solve equations with decimals. Remember, when you add, subtract, multiply, or divide the same quantity from both sides of an equation, you still have equality.
properties of equality
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Subtraction Property of Equality For any numbers [latex]a,b,\text{and }c[/latex] If [latex]a=b[/latex], then [latex]a-c=b-c[/latex] |
Addition Property of Equality For any numbers [latex]a,b,\text{and }c[/latex] If [latex]a=b[/latex], then [latex]a+c=b+c[/latex] |
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The Division Property of Equality For any numbers [latex]a,b,\text{and }c,\text{and }c\ne 0[/latex] If [latex]a=b[/latex], then [latex]{\Large\frac{a}{c}}={\Large\frac{b}{c}}[/latex] |
The Multiplication Property of Equality For any numbers [latex]a,b,\text{and }c[/latex] If [latex]a=b[/latex], then [latex]ac=bc[/latex] |
Solving Equations By Clearing Decimals
Some equations have decimals in them. This kind of equation will occur when we solve problems dealing with money and percent. But, we know, decimals are really another way to represent fractions. For example, [latex]0.3=\Large\frac{3}{10}[/latex] and [latex]0.17=\Large\frac{17}{100}[/latex]. 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.
Solve the following: