Solving Equations with Fractions

The video tutorial explains how to solve a quadratic equation using two methods: clearing fractions and working with fractions. It begins with an introduction to quadratic equations and the zero product property. The first method involves clearing fractions by multiplying both sides by the least common denominator. The second method keeps the fractions in the equation. Both methods lead to the same solutions, demonstrating the flexibility in solving quadratic equations.

What is the degree of the given equation, and what does it signify?

• Degree one, linear equation

• Degree four, quartic equation

• Degree two, quadratic equation

• Degree three, cubic equation

What is the first step in clearing fractions from the equation?

• Subtract fractions from both sides

• Add fractions to both sides

• Multiply both sides by the least common denominator

• Divide both sides by the least common denominator

After clearing fractions, what is the next step in solving the equation?

• Add terms to both sides

• Factor the equation

• Divide terms by a constant

• Multiply terms by a constant

What is the greatest common factor in the equation y^2 - 7y?

• y

• 7

• y^2

• 1

What property is used to find solutions after factoring the equation?

• Commutative property

• Distributive property

• Associative property

• Zero product property

When solving with fractions intact, what is the least common denominator used?

• Two

• Three

• Four

• Five

How is negative 2y expressed to combine with 1/3y?

• As -2/3y

• As -6/3y

• As -3/3y

• As -1/3y

What is the factored form of 1/3y^2 - 7/3y?

• y^2 - 7y

• 1/3y(y - 7)

• y(y - 7)

• 1/3(y - 7)

What are the solutions to the equation after factoring with fractions?

• y = 0 and y = 7

• y = 1 and y = -7

• y = 1 and y = 7

• y = 0 and y = -7

What is the outcome of using different methods to solve the equation?

• Infinite solutions

• Same solutions

• No solutions

• Different solutions