A supply bin starts with 3 1/2 kg. 1/2 kg is used, then 6 kg is added. How much is in the bin now?
Write a signed equation first; keep the unit attached to the result.
CCSS 7.NS.A.3 · real-world four-operation problems
Grade 7 Rational Number Word Problem Worksheets
Apply signed rational-number operations in contexts where the direction and units matter. Problems cover temperature, elevation, account changes, signed rates, equal sharing of a change, and multistep quantities.
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Rational Number Word Problems
Rational-number word problems · Grade 7 standard · Seed 271701
1.
2.
A supply bin starts with 3 1/2 kg. 1 1/2 kg is used, then 2 kg is added. How much is in the bin now?
Write a signed equation first; keep the unit attached to the result.
3.
A quantity changes by 8 units evenly over 2 hours. What is the change per hour?
Write a signed equation first; keep the unit attached to the result.
4.
A drone's altitude changes at -1/2 meters per second for 6 seconds. What is the total altitude change?
Write a signed equation first; keep the unit attached to the result.
5.
A quantity changes by -13 1/2 units evenly over 3 hours. What is the change per hour?
Write a signed equation first; keep the unit attached to the result.
6.
A supply bin starts with 5 1/2 kg. 1 1/2 kg is used, then 3 1/2 kg is added. How much is in the bin now?
Write a signed equation first; keep the unit attached to the result.
7.
A diver is at -5 1/2 meters relative to sea level. The diver's elevation changes by 1 1/4 meters. What is the new elevation?
Write a signed equation first; keep the unit attached to the result.
8.
An account balance is $17.73. A transaction changes the balance by $41.26. What is the new balance?
Write a signed equation first; keep the unit attached to the result.
9.
A diver is at -5 1/2 meters relative to sea level. The diver's elevation changes by 1 3/4 meters. What is the new elevation?
Write a signed equation first; keep the unit attached to the result.
10.
A drone's altitude changes at -2 meters per second for 5 seconds. What is the total altitude change?
Write a signed equation first; keep the unit attached to the result.
Exact-construction rule: operations use normalized integer numerator/denominator pairs, number-line positions use exact ticks, repeating decimals come from remainder cycles, and money contexts use exact cents. No answer depends on binary floating-point rounding.
Solving word problems with positive and negative numbers
Translate the story into a signed operation before calculating. A negative number can show a debt, a drop in temperature, or a position below sea level, and the sign must keep its meaning. After calculating, check that the sign and the units make sense in the original situation.
Worked examples
- A diver at −18 m rises 7 m twice. −18 + 2 × 7 = −18 + 14 = −4, so the diver is at −4 m.
- The temperature is −5° and falls 8°. −5 − 8 = −13, so it is −13°.
- An account is at −$12.50 and gets a $20 deposit. −12.50 + 20 = 7.50, so the balance is $7.50.
Common slips
- Treating a drop as a positive change. A fall of 8° means subtracting 8.
- Dropping the sign, so a debt of $12.50 is read as a balance.
- Leaving off the units, so the answer does not say meters, degrees, or dollars.
How to use this worksheet
Ask students to write the operation with signs before computing and to describe the answer in a sentence. The answer key gives the signed result with units.
Common Core connection
- 7.NS.A.3 · Solve real-world problems involving all four operations with rational numbers.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Note 1
Translate the context into a signed operation before calculating.
Note 2
A negative quantity may represent direction, debt, depth, or decrease; keep the meaning attached to the sign.
Note 3
Example: a diver at -18 m ascends 7 m twice, so -18 + 2 times 7 = -4 m.
Note 4
Check whether the final sign and unit make sense in the original situation.
Continue the 7.NS progression
Move to another Grade 7 rational-number skill
Quick answers
Are the contexts only about money?
No. The generator rotates through temperature, elevation, balances, rates, equal changes, and inventory-style multistep situations.
Do the word problems use exact values?
Yes. Money uses exact cents and fractional quantities remain rational throughout the calculation.
Which standard does this practice?
CCSS 7.NS.A.3: solve real-world and mathematical problems involving the four operations with rational numbers.
How is this different from the Grade 7 equation word problems?
This route stays numerical and focuses on choosing the right signed operation. The expressions-and-equations word problems add writing a variable equation and an explicit reasonableness check.