In this video lesson, we will learn strategies for solving equations with division. We will also discuss ways to handle negative signs and fractions to make the problem simpler to solve.
Handling Fractions and Equations with Division
Keep these tips in mind as you encounter equations with fractions:
Recognizing Division: In algebra, equations involving division are often represented with a fraction line. It's important to understand that when dealing with equations containing fractions, you can treat the fraction as division.
Handling Negative Fractions: When dealing with negative fractions, it is important to understand that the negative sign can be placed in different parts of the fraction. It can be placed in the front of the whole fraction, in the numerator, or in the denominator. In this example, we can simplify the problem by placing the negative sign in the denominator.
Lesson Notes
Let's look at the steps for solving equations with division.
Example 1: Solving x/2 = 15
Identifying the Operation: The expression x/2 can be read as x divided by 2, indicating division. This division is the key operation that needs to be addressed in order to solve the equation.
Undo: To isolate x, we need to undo the division by multiplying both sides of the equation by 2. By doing so, we ensure that the multiplication is correctly represented as placing the 2 next to the numerator to indicate multiplication.
Simplify: After multiplying both sides by 2, the left side of the equation simplifies to x, while the right side simplifies to 30. Therefore, the solution to the equation is x = 30.
Check: It is important to verify the solution by substituting x = 30 back into the original equation. By doing this, we can confirm whether the solution is correct or not. In this case, substituting x = 30 results in a true equation, indicating that the solution is correct.
Example 2: Solving -a/5 = 14
Undo: To isolate the variable a, we need to undo the division by multiplying both sides of the equation by -5. Note that in this example it makes sense to place the negative sign in the denominator so that we can undo the negative sign and the number 5 simultaneously.
Simplify: After multiplying both sides by -5, the left side of the equation simplifies to a, while the right side simplifies to -70. Therefore, the solution to the equation is a = -70.
Check: As with the previous example, it is important to check the solution by substituting a with -70 in the original equation. By doing this, we can confirm whether the solution is correct or not. In this case, substituting a = -70 results in a true equation, confirming that the solution is correct.
Summary and Practice
Understanding how to handle equations involving division, especially when represented as fractions, is crucial in solving algebra problems. By recognizing the division operation, handling negative signs strategically, and properly isolating the variable, you can confidently find the solutions to these equations.
Try this practice activity to see what you learned. Complete the steps of this equation by dragging each element on the right to its correct place.
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