Flashcard 3.2

Front

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

Back

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

Front

What is the least common denominator (LCD) of the fractions \( \frac{5}{24} \) and \( \frac{1}{3} \)?

Back

The least common denominator (LCD) of \( \frac{5}{24} \) and \( \frac{1}{3} \) 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 fraction by multiplying the entire equation by the least common denominator, which is 24.

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.

Front

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

Back

The result of multiplying \( \frac{5}{24} \) by 24 is 5.

Front

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

Back

The result of multiplying \( \frac{1}{3} \) by 24 is 8.

Front

If \( 5 + 24c = 8 \), 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 is an application-based question in mathematics?

Back

An application-based question requires the use of mathematical concepts to solve real-world problems or scenarios.