Solving proportions 2 exercise examples | Algebra Basics | Khan Academy

TL;DR

Learn how to solve proportions using algebraic techniques such as cross-multiplication and multiplying both sides by the denominators.

Transcript

• [Instructor] We have the proportion x minus nine over 12 is equal to two over three, and we wanna solve for the x that satisfies this proportion. Now, there's a bunch of ways that you could do it. A lot of people, as soon as they see a proportion like this, they wanna cross-multiply. They wanna say, hey, three times x minus nine is going to be eq... Read More

Key Insights

• ✖️ There are multiple ways to solve proportions, such as cross-multiplication and multiplying both sides by the denominators.
• ✖️ Cross-multiplication is equivalent to multiplying both sides by the denominators in terms of achieving the same end result.
• 🙃 Performing the same operation on both sides of the equation is necessary to maintain the equality of the equation.
• 👻 Algebraic manipulation allows for solving proportions and determining the value of the unknown variable.
• ❓ Proportions can involve variables in both the numerator and denominator.
• ❓ The process of solving proportions involves simplifying the equation by eliminating fractions.
• 😑 Distributing and simplifying algebraic expressions are essential steps in solving proportions.

Questions & Answers

Q: What are the two methods for solving proportions shown in the video?

The two methods for solving proportions demonstrated are cross-multiplication and multiplying both sides by the denominators.

Q: Why is it necessary to perform the same operation on both sides of the equation?

Performing the same operation on both sides of the equation ensures that the equation remains balanced and maintains equality.

Q: How does cross-multiplication help solve proportions?

Cross-multiplication eliminates the denominators by multiplying the numerator of one fraction with the denominator of the other fraction. This allows for solving the equation for the unknown variable.

Q: How does multiplying both sides by the denominators help solve proportions?

Multiplying both sides of the equation by the denominators eliminates the fractions, making it easier to isolate and solve for the unknown variable.

Summary & Key Takeaways

• The video demonstrates two methods of solving proportions: cross-multiplication and multiplying both sides by the denominators.

• By cross-multiplying, you can get rid of the denominators and solve for the unknown variable.

• Alternatively, by multiplying both sides by the denominators, you can eliminate the denominators and achieve the same result.