Proportions and Word Problems

This video tutorial covers the concept of proportions, starting with a historical context involving Pythagoras and musical intervals. It explains how to solve proportion word problems using equivalent ratios and cross-multiplication. Two example problems are solved: calculating sales tax and determining the amount of juice for a given price. Alternative methods for solving proportions are also discussed. The video concludes with a mention of additional resources available for further learning.

Who is credited with discovering the relationship between string length and musical intervals?

• Pythagoras

• Aristotle

• Euclid

• Archimedes

What is the musical interval called when one string is twice the length of another?

• Octave

• Fourth

• Third

• Fifth

What is a proportion in mathematical terms?

• A single ratio

• A difference of ratios

• Two equivalent ratios

• A sum of ratios

What is the first step in solving a proportion word problem?

• Guess the answer

• Subtract all numbers

• Write a proportional equation

• Add all numbers

What is the first step in solving a proportion word problem?

• Write a proportional equation

• Add all numbers

• Guess the answer

• Subtract all numbers

In the sales tax problem, what is the initial price of the hat?

• $20

• $10

• $16

• $25

What is the sales tax on a $120 coat if the tax on a $16 hat is $1.32?

• $12.56

• $11.56

• $10.56

• $9.56

What is the result of cross-multiplying in a proportion?

• A sum of ratios

• A different proportion

• An equivalent equation

• A new ratio

What is the final step in solving the sales tax problem?

• Multiply by the coefficient

• Subtract the numbers

• Add the numbers

• Divide by the coefficient

What is the purpose of rounding in the sales tax problem?

• To make the number larger

• To adjust for currency format

• To change the equation

• To make the number smaller