Multi-Step Real-Life and Mathematical Problems with Rational Numbers

In this assignment, you will solve various real-life and mathematical problems using positive and negative rational numbers in different forms, such as whole numbers, fractions, and decimals. You will apply properties of operations and convert between forms as needed to find solutions. Remember to use estimation and mental computation to assess the reasonableness of your answers.

Solve the following problems using the appropriate mathematical operations and conversions. Show your work for each problem and check your answers using estimation strategies.

A store is having a sale where all items are 15% off. If a jacket originally costs $80, what is the sale price?

A recipe calls for 2 1/2 cups of flour. If you want to make 1/2 of the recipe, how much flour do you need?

If a car travels 150 miles using 5 gallons of gas, what is the car's fuel efficiency in miles per gallon?

You have $45.75 and you want to buy 3 books that cost $12.50 each. Do you have enough money? If not, how much more do you need?

A rectangular garden is 12 1/3 feet long and 9 1/4 feet wide. What is the area of the garden in square feet?

A runner completes a race in 1.5 hours. If the race is 13.1 miles long, what is the runner's average speed in miles per hour?

A movie theater sells adult tickets for $8.75 and child tickets for $5.50. If a family buys 2 adult tickets and 3 child tickets, what is the total cost?

If a student scores 85% on a test with 40 questions, how many questions did the student answer correctly?

A piece of ribbon is 4 2/5 meters long. If you cut it into pieces that are each 2/5 meter long, how many pieces do you get?

A cyclist rides 7.5 miles in 0.5 hours. What is the cyclist's speed in miles per hour?