Two Step Equations with Fractions
Grade 7 Math Worksheets
Equations are like puzzles that allow us to find the missing pieces of mathematical expressions. In this article, we embark on a journey into the realm of two-step equations with fractions, designed specifically for Grade 7 students.
As we delve into this fascinating topic, we will unravel the complexity of solving equations that involve fractions through systematic and logical steps. Two-step equations require multiple operations to isolate the variable, while fractions introduce an additional layer of intricacy.
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Two Step Equations with Fractions - Grade 7 Math Worksheet PDF
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Clearing the Fraction:
The first step in solving a two-step equation with fractions is to eliminate the fraction. This can be accomplished by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. By doing so, the fractions are eliminated, and the equation becomes more manageable.
Isolating the Variable:
Once the fractions are cleared, the equation is simplified to a two-step equation with integers. The goal is to isolate the variable on one side of the equation. This is achieved by performing inverse operations, such as addition or subtraction, and multiplication or division, to both sides of the equation in a systematic manner.
Checking the Solution:
After finding a solution to the equation, it is essential to check the validity of the solution. This involves substituting the value of the variable back into the original equation and ensuring that both sides of the equation are equal. Checking the solution helps to verify its accuracy and reinforces the understanding of the equation.
Formula 1: Clearing the Fraction
To clear the fraction in an equation, multiply both sides of the equation by the least common multiple (LCM) of the denominators.
Solve the equation: 3/4x + 1/2 = 5
Step 1: Clearing the Fraction
The denominators in this equation are 4 and 2, and their LCM is 4. Multiply both sides of the equation by 4 to eliminate the fractions:
4 * (3/4x + 1/2) = 4 * 5
3x + 2 = 20
Formula 2: Isolating the Variable
To isolate the variable term in a two-step equation, apply inverse operations to both sides of the equation.
Using the equation from the previous example: 3x + 2 = 20
Step 2: Isolating the Variable
To isolate the variable term, subtract 2 from both sides of the equation:
3x + 2 – 2 = 20 – 2
3x = 18
Next, divide both sides of the equation by the coefficient of x (which is 3) to solve for x:
(3x)/3 = 18/3
x = 6
So, the solution to the equation is x = 6.
Formula 3: Checking the Solution
After obtaining a value for the variable, it is important to check the solution’s validity by substituting it back into the original equation.
Using the original equation: 3/4x + 1/2 = 5
Step 3: Checking the Solution
Substitute the value x = 6 back into the original equation:
3/4(6) + 1/2 = 5
18/4 + 2/4 = 5
20/4 = 5
5 = 5
Since both sides of the equation are equal, the solution x = 6 is valid.
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Cooking and Baking:
In cooking and baking, recipes often require adjusting ingredient quantities based on the desired number of servings. Two-step equations with fractions can be used to determine the amount of each ingredient needed. For instance, if a recipe serves 4 people but you need to adjust it to serve 6 people, you can set up an equation with fractions to find the new ingredient quantities.
Managing finances often involves calculations that require solving two-step equations with fractions. For instance, determining the total cost of an item after applying a discount and sales tax involves setting up an equation with fractions and solving for the final price.
Dilution and Mixing Solutions:
In science or chemistry experiments, diluting or mixing solutions requires accurate calculations. Two-step equations with fractions can be utilized to determine the ratio of different solutions needed to achieve a desired concentration.
Scaling Maps or Blueprints:
When working with maps or blueprints, scaling is important for accurate measurements. Two-step equations with fractions can be employed to determine the scaled dimensions or distances. For example, if you need to scale a blueprint down to 1/4 of its original size, you can set up an equation with fractions to calculate the new measurements.
Two-step equations with fractions are also useful in scenarios involving proportional relationships. For instance, if you want to convert measurements between different units, such as converting pounds to kilograms or inches to centimeters, you can set up a proportion using a two-step equation with fractions.
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What are two-step equations with fractions?
Two-step equations with fractions are algebraic equations that involve two operations and include fractions. These equations require multiple steps to isolate the variable and find its value. They often involve addition, subtraction, multiplication, or division, combined with fractions. Solving two-step equations with fractions requires applying inverse operations to eliminate the fractions and isolate the variable.
How do I solve two-step equations with fractions?
To solve a two-step equation with fractions, follow these steps:
Clear the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.
Simplify the resulting equation by performing the necessary operations to isolate the variable on one side.
Solve for the variable by applying inverse operations, such as addition or subtraction, multiplication or division, to both sides of the equation.
Check the solution by substituting the found value back into the original equation and verifying that both sides are equal.
How can I simplify fractions in two-step equations?
To simplify fractions in two-step equations, you can apply basic fraction operations:
Find the common denominator if the fractions have different denominators.
Add or subtract the fractions by combining the numerators over the common denominator.
Multiply or divide the fractions by multiplying the numerators together and the denominators together, or by using the reciprocal of the divisor.
What if the two-step equation with fractions has variables on both sides?
If the two-step equation with fractions has variables on both sides, start by clearing the fractions using the steps mentioned earlier. Once the fractions are eliminated, collect like terms on each side of the equation and move the variables to one side by applying inverse operations. Finally, solve for the variable by simplifying the equation and performing the necessary operations.
Can I check my solution in two-step equations with fractions?
Yes, it is important to check the solution in two-step equations with fractions. After obtaining the value for the variable, substitute it back into the original equation and evaluate both sides. If both sides of the equation are equal, the solution is valid. Checking the solution helps ensure accuracy and confirms that the equation has been solved correctly.
By understanding these frequently asked questions and practicing solving two-step equations with fractions, Grade 7 students can develop their algebraic skills and confidently handle equations involving fractions in a variety of contexts.
Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn
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