GMAT: Math 18 | Problem solving | GMAT | Khan Academy

TL;DR

The video covers order of operations with fractions, finding the mass of oxygen in water, and solving equations using substitution.

Transcript

We're on problem 96. It says 1/2 plus, open brackets, 2/3 times 3/8 divided by 4 minus 9/16. Do you know order of operations, and can you deal with fractions? 2/3 times 3/8, the 3's cancel out, and the 2 and the 8 become 1/4. 1/4 divided by 4, let me write this, 1/2 plus 1/4 divided by 4, that's the same thing as times 1/4, minus 9 over 16. So that... Read More

Key Insights

• 🤝 Understanding the order of operations is essential when dealing with fractions and complex calculations.
• 🥳 Mass ratios allow us to determine the amount of a constituent element in a compound based on a relative mass comparison.
• 😑 Substitution can be an effective method for solving equations by expressing one variable in terms of another.

Questions & Answers

Q: How do you apply the order of operations when dealing with fractions?

When dealing with fractions, it is important to follow the order of operations (PEMDAS/BODMAS) just like with whole numbers. Simplify any operations within the fractions first, then perform multiplication and division from left to right, and finally, addition and subtraction from left to right.

Q: How can you calculate the mass of oxygen in a given amount of water?

To calculate the mass of oxygen in a given amount of water, you need to know the mass ratio of hydrogen to oxygen. Set up an equation using this ratio, substituting the mass of hydrogen with the given mass of water. Solve for the mass of oxygen by multiplying the mass of water by the ratio of oxygen to hydrogen.

Q: How can you solve an equation using substitution?

To solve an equation using substitution, isolate one variable in terms of another in one equation. Then, substitute this expression for the isolated variable in the other equation. Simplify the resulting equation and solve for the remaining variable.

Q: What is the significance of the scale in the final problem?

The scale in the final problem represents the intensity of a phenomenon. Each reading on the scale corresponds to a specific intensity value. The problem asks how many times greater the intensity is for a reading of 8 compared to a reading of 3.

Summary & Key Takeaways

• The video starts by explaining how to solve a math problem involving fractions and the order of operations.

• It then moves on to calculating the mass of oxygen in a given amount of water based on the mass ratio of hydrogen to oxygen.

• Finally, the video demonstrates how to solve an equation by substituting one variable in terms of another.