Solving Equations with Fractions
Solving Equations with Fractions is a skill on Pengi from Lesson 5: Equations with Fractions in Yoshiwara Intermediate Algebra.
Key Concepts
Property To solve an equation with fractions, we multiply each side of the equation by the denominator of the fraction. This will clear the fraction and give us an equivalent equation without fractions. If the equation contains more than one fraction, we can clear all the denominators at once by multiplying both sides by the LCD of the fractions. We must multiply each term of an equation by the LCD, whether or not the term is a fraction.
Examples To solve $\frac{50}{10 x} = 5$, we multiply both sides by $10 x$ to get $50 = 5(10 x)$. Distributing gives $50 = 50 5x$, which simplifies to $5x=0$, so $x=0$.
Solve $\frac{5}{x} 2 = \frac{7}{2x + 1}$. The LCD is $x(2x+1)$. Multiplying each term gives $x(2x+1)(\frac{5}{x}) x(2x+1)(2) = x(2x+1)(\frac{7}{2x+1})$. This simplifies to $5(2x+1) 2x(2x+1) = 7x$, which becomes a quadratic equation to solve.
Common Questions
What is Solving Equations with Fractions?
Solving Equations with Fractions is a skill on Pengi from Lesson 5: Equations with Fractions in Yoshiwara Intermediate Algebra.
What grade level is Solving Equations with Fractions for?
Solving Equations with Fractions is part of the Grade 7 Math curriculum, covered in Yoshiwara Intermediate Algebra. It is designed for students studying Math at the Grade 7 level.
How can I learn Solving Equations with Fractions?
Pengi offers an AI-guided lesson for Solving Equations with Fractions that walks you through the key concepts step by step. The lesson is aligned to Yoshiwara Intermediate Algebra so the content matches what you see in class.
How do I practice Solving Equations with Fractions?
After learning the concept, use the Practice mode to work through targeted exercises on Solving Equations with Fractions. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Solving Equations with Fractions?
Solving Equations with Fractions is covered in Yoshiwara Intermediate Algebra, specifically in Chapter 8: Polynomial and Rational Functions under Lesson 5: Equations with Fractions. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Solving Equations with Fractions free to study on Pengi?
Yes, the core Learn and Practice modes for Solving Equations with Fractions are available for free on Pengi. No credit card is required to start studying.