The worksheets below will help you feel more confident when you are working with equations that contain some type of decimal value whether the decimal value is a constant or coefficient within the equation. These problems will show you a wide array of different types of equations. Some of them will be in word form from the start. Your first step in that case should be to get everything in number form. From there, just apply the process that we described above. The lessons will also provide you with different approaches to these problems that you may have not considered before. Just remember math is awesome because there are countless methods that can be used to solve the same problems. Use these worksheets to show your students how to write out and solve equations with unknown variables that include numbers with decimals.
Print Solving Equations With Decimals Worksheets
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Equations with Decimals Lesson
Learn how to write equations with decimals and solve them. Example: The sum of two-tenths and a number y is -0.45. This lesson will walk you through all 5 steps that are needed to solve it.
Practice Worksheet 1
You are provided with a that is explained for you. You then will solve 2 problems on your own that have decimals found on both sides of the equation.
Sentence to Equations
Write out the following 10 equations and solve them. Example: The difference of 15 hundredths and a secret number is 10 thousandths. As you see, you will be creating decimal values in the process.
Complex Equation Practice
Do not let the title fool you, these are just the next level of difficulty with these types of problems. Solve the following 10 equations. Example: 89.7x = -296.2
Show the Skill
This sheet has 8 problems to help you gain more experience with this skill. Example: 5 - (-7 - 11x) = 81
Solving Equations w/Decimals Warm Up
Write out these 3 equations and then solve them. Example: The product of a mystery number and 26 thousandths is 8.5.
How to Solve Equations with Decimals
Decimals are an important part of our lives. Not every number in your life is a whole number; there will be times you have to deal with decimals. A decimal is defined as a fraction where the denominator is a power of ten, while the numerator is shown by an amount placed on the right side of the decimal point.
Many of us are aware of how decimals work and what the rules are around them. For instance, every number with a decimal point can be converted to a fraction, e.g., 0.5 can also be written as ½. Another important part of mathematics is the usage of equations. We are now going to combine the two and explain how we solve equations with decimals with them.
When solving a mathematical equation, you want to make sure that it is simplified as far as possible in order to find a solution. With decimals, you must change them into fractions in order to simplify calculations. To convert a decimal into a fraction, you need to see how many points after the decimal the next integer is and then multiply that amount with 10, 100, 1000, and so on.
For example, if the decimal is 0.4, you will multiply it by 10 so that it may be converted into a whole number. To calculate this, let us demonstrate how this would work in an equation.
First, you take your equation.
0.4x + 4 = 12
Next, you multiply the entire equation by 10 because that is what converts 0.4 into a whole number.
10(0.4x + 4 = 12)
4x + 40 = 120
4x = 120 - 40
4x = 80
x= 80/4
x= 20
Let's look at a more complex equation,
0.3x + 2.5= 6.91
Next, we will multiply the entire equation by 100 to bring all decimal values up to whole numbers.
100(0.3x + 2.5= 6.91)
30x + 250 = 691
30x = 691 - 250
30x = 440
x = 441/30
x = 14.7
This is the simplest way to solve an equation with a decimal in it. Count the number of spaces after the decimal point, add the same number of zeros, i.e. 10, 100, 1000 and multiply it with the entire equation. This will remove all decimals and make it easier for you to solve the equations.
This is a method to solve simple equations, and in mathematics, equations will often be a lot more complex than this. Keep in mind that this same method is to be followed where you simplify the equation and try to remove them and convert it to whole numbers for added ease. There will be many instances when you aren't able to use a whole number for calculations due to a value not being presented as such. In such an event, a decimal value will be used, which works similar to two whole numbers but by considering the number after the decimal. For example, 1 and 1.1 might look similar, but they have different values.
Decimals often confuse students when they are first introduced to their use in equation form. A very effective way to go at these problems is to just get rid of the decimals, if you can. For example, if you were given the problem: 0.48x - 0.26 = 0.62. We could easily multiply every by 100 to make it much more recognizable for ourselves. If we were to do that: (100) 0.48x - (100)0.26 = (100)0.62. This would concert the values to 48x - 26 = 62. This is a much more manageable way to approach these problems. It also does not at all change the final value of the variable. Mix up those variables in different algebraic expressions that contain decimals and fractions. Students will also learn how to convert word problems into their proper algebraic equations. The set contains all introductory material, practice questions, and quizzes. This is where algebra starts to really expect you to understand the nature of both decimals and fractions. There is no slowing down here. Please note that some of the problems will include the use and calculations needed for fractions.
In a mathematical equation, using 1 and 1.1 means two different things. For example, in the equation x + y + 2 = 4 where (x = 1, 1.1) the value for Y is going to be different for both. This is the power of decimal, and so it must not be neglected or taken lightly. In the practical world, many figures exist in decimals because there are often many variances that exist out there that don't allow data to exist as whole numbers.