Two Step Equations with Fractions

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.

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.

Solved Examples

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.

Example:
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.

Example:
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.

Example:
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.

Real-life Examples

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.

Financial Calculations:
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.

Proportional Relationships:
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.

FAQs

Grade 7 Science Worksheets

• Elements and Compounds
• Solar Energy
• Photosynthesis
• Electricity and Magnetism
• Law of conservation of energy
• Periodic table
• Properties of Matter
• Waves
• Energy Resources 
• Weather and Climate
• Immune, Circulatory and Digestive Systems
• Organs in Multi-cellular Organism
• Sedimentary, Igneous, and Metamorphic Rocks
• Structure of the Earth
• Law of Conservation of Mass
• Physical and Chemical Changes
• Scientific Method
• Human Digestive System
• Environmental Science
• Renewable and Non-renewable energy Resources
• Characteristics of Living Organisms
• Life Science
• Earth and Space Science
• Solar Eclipse
• Heat Technology
• Newton’s Laws of Motions
• Physical Science
• Tools, Measurement and SI Units
• Earth Atmosphere
• Interactions of Living things
• The Earth Ecosystem
• Organelles in Plant and Animal cells
• Layers of the Earth
• Cycles in Nature

Grade 7 Math Worksheets

• Fractions
• Linear equations word problems
• Statistics
• Properties of Parallel Line
• Finding slope from an equation
• Identifying Quadrilaterals
• Percent Change
• Properties of addition and multiplication
• Pythagorean Theorem
• Solving two step inequalities
• Symmetry
• Fractions to Decimals (New)
• Whole Number Exponents with Integer Bases (New)
• Adding and Subtracting Fractions (New)
• Integer Addition and Subtraction (New)
• Dividing Mixed Numbers (New)
• Basics of Coordinate Geometry (New)