Ratio and Proportion

TL;DR

The content explains how to solve ratio problems and word problems involving ratios with step-by-step examples.

Transcript

Let's start with a warm up ratio problem. Then we can tackle some harder word problems. So I have the ratio 13/6 is equal to 5/x. I don't like having this x in the denominator, so let's multiply both sides of this equation by x. So if I multiply both sides by x, what's going to happen? On the right hand side, this x cancels out with that x. And the... Read More

Key Insights

• 🙃 Solving ratio problems involves multiplying both sides of the equation to eliminate the denominator and simplify.
• 😵 Cross multiplication is a shortcut method for solving ratio problems by setting the products of the numerators and denominators equal to each other.
• 💦 In word problems, working backwards involves solving for the variables in between the given information to find the desired variable.

Questions & Answers

Q: How can we solve ratio problems involving unknown variables?

In ratio problems, multiply both sides of the equation by the denominator to cancel it out, leaving the unknown variable on one side. Then solve for the variable by multiplying both sides by the inverse of the coefficient or using cross multiplication.

Q: How can we solve word problems involving ratios?

In word problems, identify the given information and variables. Use the ratios provided to set up equations. Solve for one variable at a time by multiplying both sides of the equation by the inverse of the coefficient. Substitute the solved variables into other equations to find the desired variable.

Q: What is cross multiplication?

Cross multiplication is a shortcut method in solving ratio problems. It involves multiplying the numerator on one side by the denominator on the other side, setting the products equal to each other. This step eliminates the need for writing out the ratio as a fraction and simplifying.

Q: How do we work backwards in word problems involving ratios?

To work backwards, start with the given information and solve for the variables in between. Substitute the solved variables into other equations until reaching the desired variable. Use multiplication and division to simplify and compute the final answer.

Summary & Key Takeaways

• The video starts with a warm-up ratio problem, demonstrating the process of solving for an unknown variable using cross multiplication and simplification.

• The video then proceeds to solve word problems involving ratios, using given information and equations to find the unknown variables.

• The examples show how to work backwards from given information to find the desired variable, using multiplication and division.