Flashcard Sec 3.6 A&B

Front

What does it mean to 'clear the equation' when solving for a variable?

Back

Clearing the equation involves isolating the variable on one side of the equation by eliminating constants and coefficients through addition, subtraction, multiplication, or division.

Front

How do you clear fractions from an equation?

Back

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

Front

What is the purpose of multiplying by a specific number to clear decimals in an equation?

Back

Multiplying by a specific number, such as 100, helps to eliminate decimal points, making the equation easier to solve.

Front

What is the least common denominator (LCD) and how is it used in solving equations?

Back

The least common denominator is the smallest multiple that can be used to eliminate fractions in an equation, allowing for easier manipulation and solving.

Front

How do you identify the number to multiply by to clear fractions in an equation?

Back

Identify the denominators in the equation, find their least common multiple, and use that number to multiply each term.

Front

What steps should be taken to solve an equation with both fractions and decimals?

Back

First, clear the decimals by multiplying by an appropriate power of 10, then clear the fractions by multiplying by the least common denominator.

Front

What is the process of isolating a variable in an equation?

Back

Isolating a variable involves rearranging the equation to get the variable on one side and all other terms on the opposite side, often using inverse operations.

Front

Why is it important to clear fractions and decimals before solving an equation?

Back

Clearing fractions and decimals simplifies the equation, making it easier to perform calculations and reducing the likelihood of errors.

Front

What is an example of an equation that requires clearing fractions?

Back

An example is 4w + 2/7 = -4/5, where you would multiply by 35 to eliminate the fractions.

Front

How can you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.