Exploring Ratios and Unit Rates

The video tutorial covers the concepts of ratios and unit rates, explaining how to write and simplify ratios using fractions, colons, and the word 'to'. It emphasizes the importance of keeping ratios as improper fractions and simplifying them. The tutorial also introduces rates and unit rates, providing examples of calculating unit rates for various scenarios. Finally, it introduces dimensional analysis, demonstrating how to multiply quantities with different units and cancel out units to find the product.

Which of the following is NOT a correct way to write the ratio 2 to 1?

• 1/2

• 2/1

• 2:1

• 2 to 1

Why should ratios always be written as improper fractions?

• To make calculations easier

• To avoid confusion with mixed numbers

• To ensure they are simplified

• To make them easier to read

What is the simplified form of the ratio 28:63?

• 4/9

• 28/63

• 9/4

• 7/9

How should the ratio 36:12 be written in simplest form?

• 1/3

• 3/1

• 3

• 36/12

What is a unit rate?

• A rate with a numerator of 1

• A rate with different units

• A rate with a denominator of 1

• A rate with equal numerator and denominator

Which of the following is an example of a unit rate?

• 5 miles per 2 hours

• 10 dollars per 5 pounds

• 3 apples per 1 basket

• 60 miles per 1 hour

If 5 pounds of bananas cost $3.95, how much does 1 pound cost?

• $0.79

• $0.50

• $1.00

• $0.95

A package of 20 CDs costs $18, and a package of 35 CDs costs $22. Which package has the lower cost per CD?

• 35 CDs package

• Cannot be determined

• 20 CDs package

• Both have the same cost per CD

In dimensional analysis, what happens to the units when you multiply 12 gallons by 8 miles per gallon?

• The units remain the same

• The gallons cancel out

• The miles cancel out

• The units double

How do you handle different denominators in dimensional analysis?

• Ignore them

• Divide them

• Find a common denominator

• Multiply them directly