Worksheet

Skate and Climb: Balances and Reach

Practice subtracting rational numbers and finding distances using membership balances and climbing-route positions.

Grade 7MathInteractive · Printable

Aligned to7.NS.A.1.c

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What’s included

Single worksheet
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1 Common Core standard
Printable answer key
14 questions
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Details

Format: Interactive · Printable
Grade: Grade 7
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students rewrite subtraction of rational numbers as addition of the opposite.
Students find distances between rational numbers using the absolute value of their difference.
Students apply signed subtraction to membership balances and climbing-route positions.

How to use

Have students complete the balance calculations before working with route distances. Use the final explanation to check their understanding of subtracting a negative.

Curriculum

Common Core standard covered

7.NS.A.1.c

Understand subtracting as adding the opposite, and see the distance between two numbers as the absolute value of their difference.

Preview

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Name Date

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 + 13
B. −8 + 13
C. −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.

−12 − 5 = −12 + (−5)4 − (−7) = −4 + 7−3 − (−10) = −3 + 109 − 6 = 9 + 6

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

CopperSlateTealGold

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.