Exploring Ratios and Proportions

The video tutorial covers the concepts of ratios and proportions, starting with a review of ratios, their simplification, and different ways to express them. It then explains proportions, how to solve them using cross multiplication and scaling, and applies these concepts to practical problems like calculating the number of life jackets needed for a given number of goggles. The tutorial also includes a section on calculating total travel distance using speed and time, checks for proportion equivalency, and ends with a problem on university enrollment ratios.

What is a ratio?

• An addition of two different units

• A multiplicative comparison of two quantities describing different attributes

• A multiplicative comparison of two quantities describing the same attribute

• A division of two quantities

How can a ratio be expressed?

• Using subtraction

• As a fraction, in words, or using a colon

• Only as a fraction

• Only in words

What does it mean to simplify a ratio?

• To multiply the terms by the same number

• To add the same number to both terms

• To reduce the terms to their smallest form

• To increase the ratio size

What is a proportion?

• An equation that shows two unequal ratios

• A method to multiply ratios

• A type of fraction

• An equation that shows two equal ratios

How can proportions be solved?

• By addition

• By division only

• By cross multiplication and division

• By subtraction

If 40 pairs of goggles are ordered, how many life jackets should be ordered according to the ratio 8:5?

• 40 life jackets

• 64 life jackets

• 25 life jackets

• 32 life jackets

How many total miles did Christy travel by plane and car?

• 846 miles

• 71 miles

• 775 miles

• 925 miles

What is the ratio of in-state to out-of-state students?

• 9 to 2

• 7 to 2

• 7 to 9

• 2 to 7

How many in-state students were there in the freshman class?

• 7 students

• 189 students

• 243 students

• 54 students

What is the simplified form of the ratio 24 to 64?

• 3 to 8

• 8 to 3

• 24 to 64

• 6 to 16