Solving Equations with Fractions

The video tutorial explains how to solve the equation four-ninths x equals five-thirds using two methods. The first method involves using reciprocals to isolate x, while the second method clears fractions by multiplying both sides by the least common denominator. Both methods yield the same solution, x equals fifteen-fourths. The solution is verified by substituting back into the original equation, confirming its correctness.

What is the first step in solving the equation four-ninths x equals five-thirds?

• Multiply both sides by five-thirds

• Subtract five-thirds from both sides

• Add four-ninths to both sides

• Isolate x on one side

What operation is used to isolate x in the first method?

• Multiplication by the reciprocal

• Subtraction

• Division by the reciprocal

• Addition

What is the reciprocal of four-ninths?

• Nine-fourths

• Four-ninths

• Nine-thirds

• Three-fourths

What is the solution to the equation using the first method?

• x equals five-thirds

• x equals nine-fourths

• x equals four-fifths

• x equals fifteen-fourths

What is the least common multiple of three and nine?

• Six

• Nine

• Three

• Twelve

What is the purpose of multiplying both sides by the least common denominator in the second method?

• To add fractions

• To clear fractions

• To divide fractions

• To subtract fractions

What is the final step in solving the equation using the second method?

• Add four

• Multiply by four

• Subtract four

• Divide by four

What is the solution to the equation using the second method?

• x equals fifteen-fourths

• x equals four-fifths

• x equals five-thirds

• x equals nine-fourths

How do you verify the solution to the equation?

• By dividing the solution by the original equation

• By multiplying the solution by the original equation

• By substituting the solution back into the original equation

• By adding the solution to both sides

What does the verification process confirm?

• The solution needs adjustment

• The solution is correct

• The solution is an approximation

• The solution is incorrect