Multiplying and Reciprocals of Numbers

The video tutorial explains how to solve equations with rational coefficients, focusing on equations that include fractions. It demonstrates three examples, each involving multiplying by the reciprocal to isolate the variable. The tutorial emphasizes handling negative numbers and simplifying fractions to solve for the variable. The process is consistent across different equation setups, ensuring students understand the method to clear fractions and solve for the variable.

What is the first step in solving an equation with a fraction as a coefficient?

• Divide by the fraction

• Subtract the fraction from both sides

• Multiply by the reciprocal of the fraction

• Add the fraction to both sides

In the first example, what is the reciprocal of -1/3?

• -3

• 3

• -1/3

• 1/3

What happens when you multiply two negative numbers?

• The result is undefined

• The result is zero

• The result is positive

• The result is negative

In the second example, what is the purpose of writing a 1 under the 6?

• To make it a whole number

• To change the sign

• To convert it into a fraction

• To simplify the equation

What is the result of multiplying 6 by -7 in the second example?

• -42

• 42

• -21

• 21

In the third example, where is the variable located?

• On the right side

• On the left side

• Above the fraction

• In the middle

What is the reciprocal of -1/6 in the third example?

• -6

• 6

• -1/6

• 1/6

What is the result of multiplying -6 by -5 in the third example?

• -30

• 30

• 1

• -1

What is the final value of X in the third example?

• -30

• 30

• 5

• -5

What is the key takeaway from solving equations with negative rational coefficients?

• Always add fractions

• Divide by the reciprocal to isolate the variable

• Always subtract fractions

• Multiply by the reciprocal to isolate the variable