Expressions and Word Problems in Mathematics

This video tutorial covers various mathematical problems involving rational numbers, percentages, and expressions. It includes practical examples such as calculating coffee ratios, determining race times, and finding sales tax rates. The tutorial also explores expressions with negative numbers and ordering expressions by value, providing a comprehensive understanding of these concepts for seventh-grade students.

If a coffee maker uses 2 tablespoons of coffee for every 6 ounces of water, how many tablespoons are needed for 33 ounces?

• 9 tablespoons

• 10 tablespoons

• 11 tablespoons

• 12 tablespoons

A runner takes 17.5 minutes to run 2.5 kilometers. How long will it take her to complete a 10-kilometer race at the same pace?

• 60 minutes

• 65 minutes

• 70 minutes

• 75 minutes

An ice cream cone costs $3.25, and with tax, it costs $3.51. What is the sales tax rate?

• 8%

• 7%

• 9%

• 6%

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

• -15

• -17

• -20

• -18

Calculate the result of negative 22 minus negative 5.

• -17

• -15

• -20

• -18

If a new box of laundry soap holds 2 kg and is 25% more than the old box, how much did the old box hold?

• 1.5 kg

• 1.6 kg

• 1.8 kg

• 1.7 kg

Given x = -1/4, order the expressions from least to greatest: x - 1, x, 1 - x, -1/x.

• x, 1 - x, x - 1, -1/x

• x - 1, x, 1 - x, -1/x

• x - 1, x, -1/x, 1 - x

• x, x - 1, 1 - x, -1/x

Which expression equals negative three-fourths using a sum?

• -1 + 3/4

• -1 + 1/4

• -3/4 + 1/4

• -1 - 1/4

Which expression equals negative three-fourths using a product?

• -1 * 3/4

• -3/4 * 2

• -1/2 * 3/2

• -3/4 * 1

Which expression equals negative three-fourths using a quotient?

• -1 / 4/3

• -3/4 / 2

• -3/4 / 1

• -1 / 3/4