Flashcard 3.2

Front

What is the process to clear a fraction in an equation?

Back

To clear a fraction in an equation, multiply every term by the least common denominator (LCD) of all the fractions present in the equation.

Front

What is the least common denominator (LCD) of the fractions 24 and 3?

Back

The least common denominator (LCD) of 24 and 3 is 24.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation \( \frac{5}{24} + c = \frac{1}{3} \)?

Back

The first step is to clear the fractions by multiplying the entire equation by the least common denominator, which is 24.

Front

What is the result of multiplying \( \frac{5}{24} \) by 24?

Back

The result is 5.

Front

What is the result of multiplying \( \frac{1}{3} \) by 24?

Back

The result is 8.

Front

If you have the equation \( 5 + 24c = 8 \), how do you solve for c?

Back

Subtract 5 from both sides to get \( 24c = 3 \), then divide both sides by 24 to find \( c = \frac{1}{8} \).

Front

What is the importance of checking your solution in an equation?

Back

Checking your solution ensures that the value satisfies the original equation, confirming that no errors were made during the solving process.

Front

What does it mean to combine like terms in an equation?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power to simplify the equation.

Front

What is the definition of a variable in algebra?

Back

A variable is a symbol, often a letter, that represents an unknown value in mathematical expressions and equations.