Flashcard 3.2

Front

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

Back

To clear a fraction, multiply both sides of the equation by the least common denominator (LCD) of all 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

Solve for \( c \) in the equation \( \frac{5}{24} + c = \frac{1}{3} \).

Back

First, clear the fraction by multiplying the entire equation by 24: \( 5 + 24c = 8 \). Then, isolate \( c \): \( 24c = 8 - 5 \) leads to \( 24c = 3 \) and \( c = \frac{3}{24} = \frac{1}{8} \).

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the first step in solving the equation \( 15 + 72c = 24 \)?

Back

Subtract 15 from both sides to isolate the term with \( c \): \( 72c = 24 - 15 \).

Front

How do you solve for \( c \) in the equation \( 72c = 9 \)?

Back

Divide both sides by 72: \( c = \frac{9}{72} = \frac{1}{8} \).

Front

What is the definition of a variable in mathematics?

Back

A variable is a symbol used to represent an unknown value in mathematical expressions or equations.

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

What does it mean to balance an equation?

Back

Balancing an equation means ensuring that both sides of the equation have the same value by performing the same operation on both sides.

Front

What is the purpose of using the least common denominator (LCD) in equations?

Back

The purpose of using the least common denominator (LCD) is to eliminate fractions, making the equation easier to solve.