Solving Problems with Rational Numbers

Warmup

Explain why you chose that equation.

Activity #1

Locate Fractions on a Number Line.

• Locate the given fractions on the number line.
• When you finish, click . You may use the check boxes on the right to insert tick marks for accuracy. If you get them all correct, you’ll get a remark.
• Click for another set of fractions.
• Practice as much as you can to better understand the number line.

Activity #2

Complete a Table.

A tank of water is being drained. Due to a problem, the sensor does not start working until some time into the draining process. The sensor starts its recording at time zero when there are 770 liters in the tank.

• Study the trend in the applets below and enter the missing information.

(1.) Given that the drain empties the tank at a constant rate of 14 liters per minute, complete the table:

(2.) Later, someone wants to use the data to find out how long the tank had been draining before the sensor started. Complete this table:

Activity #3

Find Sum and Difference of Numbers(Application).

The table shows transactions in a checking account.

• Use the data to answer the questions that follow.

Challenge #1

A utility company charges $0.12 per kilowatt-hour for energy a customer uses. They give a credit of $0.025 for every kilowatt-hour of electricity a customer with a solar panel generates that they don’t use themselves. A customer has a charge of $82.04 and a credit of -$4.10 on this month’s bill.

(1.) What is the amount due this month?

(2.) How many kilowatt-hours did they use?

(3.) How many kilowatt-hours did they generate that they didn’t use themselves?

Challenge #2

A large aquarium of water is being filled with a hose. Due to a problem, the sensor does not start working until some time into the filling process. The sensor starts its recording at the time zero minutes. The sensor initially detects the tank has 225 liters of water in it.

(1.) The hose fills the aquarium at a constant rate of 15 liters per minute. What will the sensor read at the time 5 minutes?

(2.) Later, someone wants to use the data for the large aquarium above to find the amount of water at times before the sensor started. What should the sensor have read at the time -7 minutes?

Challenge #3

(1.) Find the value of the expression below without a calculator.

(2)(-30) + (-3)(-20) + (-6)(-10) – (2)(3)(10)

(2.) Write an expression that uses addition, subtraction, multiplication, and division and only negative numbers that has the same value as your answer above.

Quiz Time

https://www.ixl.com/math/grade-7/multi-step-word-problems-with-positive-rational-numbers