Adding and Subtracting Rational Numbers

1/9/25 Adding and Subtracting Rational Numbers to Solve Problems
Lesson 5.1.7

I can...

compare and contrast subtraction expressions that have the same numbers in the opposite order

recognize that the difference of two numbers can be positive or negative, depending on the order they are listed, while the distance between two numbers is always positive

add and subtract signed numbers to solve problems in an unfamiliar context

interpret signed numbers used to present gains or losses in an unfamiliar context

Match

Solve these equations mentally. Match each equation with the current solution for "c."

• 247 + c = 458

• c + 43.87 = 58.92

• $$\frac{15}{8}\ +\ c\ =\ \frac{51}{8}$$

c = 211

c = 15.05

• c = 211

• c = 15.05

• $$c\ =\ \frac{36}{8}$$

Draw

Choose the subtraction equation that represents each addition equation.

​Explore - Page 1

The benefits of solar energy.

Multiple Choice

The month before installing solar panels, a family spent $206 on electricity. The next month, the family used the same amount of electricity, but their electric bill was $53. How much did the solar panels save them this month?

Which expression will correctly calculate the solution to this problem?

• $53 - $206

• $206 - $53

• $206 + $53

• $53 + $206

​Trying to find a missing number in an equation?

Think of algebra.

Do the opposite of the equation is saying

x + 5 = 8 (subtract 5 from both sides)

x - 7 = 12 (add 7 to both sides)

​Working with Subtraction

Subtracting a negative is the same as adding a positive

8 - (-4) is the same as 8 + 4

Negative minus a positive can be rewritten as negative plus negative using Keep Change Flip

-12 - 8

K C F

-12 + (-8) = -20

Match

Match each subtraction expression with its corresponding value.

• 50 - 400

• -120 - 400

• 610 - (-200)

• -50 - (-200)

• -500 - (-200)

-350

-520

810

150

-300

• -350

• -520

• 810

• 150

• -300

Match

Match each subtraction expression with its corresponding value.

• -9 - 5

• 2 - (-11)

• -3 - (-6)

• -3.6 - (-1.2)

• $$-3\ \frac{1}{2}\ -\ \left(-2\ \frac{1}{2}\right)$$

-14

13

3

-2.4

-1

• -14

• 13

• 3

• -2.4

• -1

Multiple Choice

Based on the information in the table, what do you think the inventory will be on Saturday morning?

• 18

• -18

• 22

• -22

Paying a Bill

Amount that needs to be paid would be a positive, but any credits that a person earned would be negative because it would be taken off a bill.

Example:
Water bill is $38.47, but you have a credit of $6.12. It would be -$6.12 because that amount would be taken off the bill and not need to be paid.

Multiple Choice

In July, Han's family used $19.24 of electricity. Their solar panels made $22.75 worth of electricity. What was the amount of the bill?

• -$41.99

• -$3.51

• $3.51

• $41.99

​Explore Pages 8 and 9

Geogebra activity involving plotting points on a coordinate plane with a Math Notebook page. You may complete that on your own time.

Multiple Choice

Assuming there are 0 coffee cups at the start of the week, how many cups are there at the end of the week?

• 5,109

• 2,329

• 0

• -1,109