Arithmetic Operations and Word Problems

This video tutorial covers various mathematical problems involving rational numbers, ratios, and expressions. It includes solving real-world problems like calculating coffee-to-water ratios, determining a runner's pace, and finding sales tax rates. The video also explores expressions with negative numbers, comparing quantities, and ordering expressions. Finally, it demonstrates creating expressions using different operations.

If a coffee maker's instructions say to use 2 tablespoons of coffee for every 6 ounces of water, how many tablespoons are needed for 18 ounces?

• 4 tablespoons

• 6 tablespoons

• 8 tablespoons

• 10 tablespoons

A runner takes 17.5 minutes to run 2.5 kilometers. How long will it take her to run 5 kilometers at the same pace?

• 30 minutes

• 40 minutes

• 35 minutes

• 25 minutes

If an ice cream cone costs $3.25 and the total cost with tax is $3.51, what is the sales tax rate?

• 10%

• 8%

• 12%

• 6%

What is the result of the expression: negative 22 plus 5?

• 27

• 17

• -27

• -17

Calculate the result of negative 22 minus negative 5.

• -17

• -27

• 17

• 27

What is the product of negative 22 times negative 5?

• -110

• 100

• 110

• -100

If x is negative one-fourth, what is the value of 1 minus x?

• 1.25

• 0.75

• -1.25

• -0.75

Order the following expressions from least to greatest if x is negative one-fourth: x, x-1, 1-x, -1/x.

• x, x-1, 1-x, -1/x

• x-1, x, 1-x, -1/x

• 1-x, x, x-1, -1/x

• -1/x, x-1, x, 1-x

Which of the following expressions equals negative three-fourths using a sum?

• -1 - 1/4

• 1 - 1/4

• 1 + 1/4

• -1 + 1/4

Which expression involving division and subtraction results in negative three-fourths?

• -1 - 1/4

• -1/4 - 1

• 1 - 1/4

• 1/4 - 1