Clearing Fractions

Definition

Clearing fractions is the process of removing or eliminating fractions from an equation in order to solve for the unknown variable. This technique is particularly important when solving equations that contain fractional coefficients or terms.

5 Must Know Facts For Your Next Test

1. Clearing fractions is a crucial step in solving equations with fractional coefficients or terms, as it allows you to eliminate the fractions and work with whole numbers.
2. The process of clearing fractions typically involves finding the least common denominator (LCD) of all the fractions in the equation and then converting the fractions to equivalent fractions with the LCD.
3. Cross-multiplication is a common technique used to clear fractions, where you multiply the numerator of one fraction by the denominator of the other fraction, and vice versa, to eliminate the fractions.
4. The distributive property can also be used to clear fractions by distributing the variable or constant to the numerator and denominator of the fraction.
5. Clearing fractions is an essential skill for solving a wide range of algebraic equations, including linear, quadratic, and rational equations.

Review Questions

• Explain the purpose of clearing fractions when solving equations.
  • The purpose of clearing fractions when solving equations is to eliminate the fractional coefficients or terms, allowing you to work with whole numbers and simplify the equation. This is an important step because it makes the equation easier to manipulate and solve for the unknown variable. By clearing the fractions, you can apply standard algebraic techniques, such as combining like terms, factoring, or using the quadratic formula, to find the solution.
• Describe the process of finding the least common denominator (LCD) and using it to clear fractions.
  • To clear fractions, you first need to find the least common denominator (LCD) of all the fractions in the equation. The LCD is the smallest positive integer that is divisible by all the denominators of the fractions. Once you have the LCD, you can convert each fraction to an equivalent fraction with the LCD as the denominator. This is done by multiplying the numerator and denominator of the fraction by the appropriate factor to make the denominator the LCD. After converting all the fractions, you can then perform operations, such as adding or subtracting the fractions, to clear them from the equation.
• Analyze how the distributive property can be used to clear fractions in an equation.
  • The distributive property can be a useful tool for clearing fractions in an equation. By distributing the variable or constant term outside the fraction to the numerator and denominator, you can effectively eliminate the fraction. For example, in the equation $\frac{2x}{3} = 4$, you can distribute the $2x$ to the numerator and denominator, resulting in $\frac{2x}{3} = \frac{2x}{3}$, which can then be simplified to $x = 6$. This approach allows you to clear the fraction without the need for finding a common denominator or using cross-multiplication, making the equation easier to solve.

Related terms

Least Common Denominator (LCD): The smallest positive integer that is divisible by all the denominators of the fractions in an equation, used to convert the fractions to equivalent fractions with a common denominator.

Cross-Multiplication: A method for solving proportions or equations with fractions by multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa, to eliminate the fractions.

Distributive Property: The property that allows you to multiply a term outside of a fraction by each term inside the fraction, used to clear fractions by distributing the variable or constant to the numerator and denominator.