Skate and Climb: Balances and Reach

Use opposites to subtract and absolute value to measure distance.

Membership Records

At a skate and climbing gym, positive membership balances represent credit and negative balances represent money owed. Keep the order of each subtraction.

A staff member compares two membership balances using −8 − (−13). Which addition expression is equivalent?

A. 8 + 13B. −8 + 13C. −8 + (−13)D. 8 + (−13)

Complete the addition-of-the-opposite calculation for two balances.

6 − (−9) = 6 + =

Sofia's membership balance is −$4.50. A $2.25 equipment charge is subtracted from her balance.

Her new signed balance is dollars.

A staff member subtracts a saved balance from −$7 and gets −$2. Find the missing signed balance.

−7 − () = −2

Select every equation that correctly rewrites subtraction as addition of the opposite.

Climbing-Route Distances

Route positions are measured horizontally from a wall seam. Negative positions are left of the seam; positive positions are right of it. Distance is the absolute value of a difference.

The marked points show the starting positions of two climbing routes.

How far apart are the starting positions? meters

A route setter stands at position −0.5 meter. Select every hold that is no more than 2 meters horizontally from that position.

Hold Positions
Hold	Position (m)
Copper	−2.5
Slate	−3
Teal	1.25
Gold	2

Two footholds are at positions −7/8 meter and 3/8 meter. Find their horizontal distance. Write a fraction or mixed number.

Distance: meters

A hold is at position −0.25 meter. Two possible new holds are each exactly 1.5 meters horizontally from it. Find both positions.

Position to the left: meters
Position to the right: meters

10.

Two route markers have a horizontal distance of 0 meters. One is at −3 meters. Which equation gives the other marker's position, x?

A. |−3 − x| = 0, so x = −3.B. |−3 − x| = 0, so x = 0.C. |−3 − x| = 0, so x = 3.D. |−3 − x| = 0, so x = −6.

Check the Gym's Decisions

Apply subtraction and distance to each situation. Explain your reasoning in the final question.

11.

Malik's membership balance is −$11. It includes an incorrect charge recorded as −$6. The gym removes that entry by subtracting −6 from his balance.

Corrected signed balance: dollars

12.

Two route markers are at −1 meter and 5 meters relative to the original seam. A new reference seam is 4 meters to the right of the original seam. Subtract 4 from each position to use the new reference.

New position of the first marker: meters
Distance between the markers using the new positions: meters

13.

A membership account has a balance of −$14. A second account has a positive balance. The distance between the two balances on a number line is $23. What is the second balance?

A. The second balance is −$9.B. The second balance is +$23.C. The second balance is +$9.D. The second balance is +$37.

14.

An account balance is −$18. The gym removes an incorrect charge of −$7 by calculating −18 − (−7). Priya says, “Subtraction always makes a number smaller, so the corrected balance must be less than −18.” Explain why her claim fails here. Rewrite the subtraction as addition and find the corrected balance.