Solving Equations with Fractions

This video tutorial demonstrates solving two-step equations with fractions by first clearing the fractions. It explains how to find the least common denominator (LCD) using prime factorization and then solve the resulting equation. An alternative method is also shown, where the LCD is quickly identified and used to solve the equation. The tutorial concludes with the final solution and encourages viewers to explore another example where fractions are left in the equation.

What is the first step in solving two-step equations with fractions by clearing the fractions?

• Multiply each term by the variable

• Find the least common denominator

• Subtract fractions directly

• Add fractions directly

How can you determine the least common denominator (LCD) of fractions?

• By adding the denominators

• By subtracting the denominators

• By dividing the denominators

• By finding the least common multiple of the denominators

Why might you choose to build the LCD using prime factorization?

• To add more steps to the process

• To avoid using the LCD

• To ensure all denominators have the same prime factors

• To make the equation more complex

What is the purpose of multiplying each fraction by the LCD?

• To change the variable

• To increase the value of the fractions

• To clear the fractions from the equation

• To add more fractions to the equation

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CCSS.HSA.REI.A.2

What happens to the equation when you multiply each term by the LCD?

• The equation becomes more complex

• The variable is eliminated

• The fractions are cleared from the equation

• The equation remains unchanged

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CCSS.8.EE.C.7B

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

• Add or subtract to isolate the variable term

• Divide the entire equation by the variable

• Multiply the entire equation by zero

• Add fractions back into the equation

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CCSS.6.EE.B.7

What is the final step in solving the equation after isolating the variable term?

• Multiply both sides by the variable

• Divide both sides by the coefficient of the variable

• Add fractions to both sides

• Subtract the variable from both sides

How can you express an improper fraction as a mixed number?

• By adding the numerator and denominator

• By multiplying the numerator by the denominator

• By dividing the numerator by the denominator

• By subtracting the denominator from the numerator

What is an alternative method to solve equations with fractions?

• Divide each term by the LCD

• Directly multiply each term by the LCD

• Subtract all fractions from the equation

• Add all fractions together

What is the result of simplifying 13/8 as a mixed number?

• 2 and 5/8

• 1 and 3/8

• 2 and 1/8

• 1 and 5/8