7.NS.3 — Rational Numbers in the Real World
Practice solving multi-step real-world problems using addition, subtraction, multiplication, and division with integers, fractions, and decimals, including negatives.
Download
Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
Read each problem carefully, show your work, and write your answer with its unit.
- 1.The temperature in Anchorage was -14.5°F in the morning. By noon it had risen 8.75°F, and by evening it dropped 12.25°F. What was the temperature in the evening?
- 2.Maria owes her friend $23.50. She earns $15.75 babysitting and uses all of it to pay back part of her debt. How much does she still owe?
- 3.A submarine was at -240 feet. It rose 3/4 of that distance toward the surface. What is the submarine's new depth?
- 4.Jake's bank account balance was -$45.20. He deposited $120.00 and then spent $67.89 on groceries. What is his new balance?
- 5.A recipe calls for 2 1/4 cups of flour per batch. If Sofia wants to make 3 1/2 batches, how many cups of flour does she need?
- 6.The temperature changed by -3.6°F each hour for 5.5 hours. What was the total change in temperature?
- 7.A football team gained 6 1/2 yards on the first play, lost 3 3/4 yards on the second play, and gained 2 1/4 yards on the third play. What was the total yardage change after three plays?
- 8.Carlos drove from his home to the city, which is 84.6 miles away. He drove 1/3 of the distance before stopping for gas. How many miles does he still need to drive?
- 9.A scientist recorded the following temperature readings (in °C) over four days: -6.2, 4.8, -3.5, and 1.1. What was the average daily temperature?
- 10.Lena had $52.40 in her account. She made three equal withdrawals of $18.75 each. What is her account balance after the withdrawals?
- 11.A deep-sea fish swam from -320 feet to -185 feet. How many feet did the fish rise?
- 12.A store marked down all prices by 1/5. If a jacket originally cost $87.50, how much does the jacket cost after the markdown?
- 13.Ethan hiked up a mountain gaining 2,150 feet in elevation over 6.5 hours. What was his average elevation gain per hour? Round to the nearest hundredth.
- 14.The water level in a reservoir dropped 0.75 feet per day for 8 days and then rose 1.25 feet per day for 3 days. What was the total change in water level?
- 15.Priya scored -3 1/2 points on a penalty in a trivia game, then earned 7 3/4 points on the next question, and lost 2 1/4 points on a penalty. What is her total score for those three rounds?
- 16.A scuba diver descended at a rate of -4.5 meters per minute. After 6.4 minutes, how deep is the diver?
- 17.Alex borrowed $120 from his parents. He paid back 3/8 of the debt in the first month and 1/4 of the debt in the second month. How much does he still owe?
- 18.A stock lost $2.35 per share on Monday, gained $1.80 per share on Tuesday, and lost $0.95 per share on Wednesday. If Mia owns 40 shares, what is the total change in the value of her investment?
- 19.A chef has 15 3/4 pounds of ground beef. He uses 2 1/8 pounds for each meatloaf. How many complete meatloaves can he make, and how much beef is left over?
- 20.On a winter night, the temperature was -8.4°F. The next morning it was -22.9°F. How many degrees did the temperature drop overnight?
- 21.A city's budget had a surplus of $4,500,000. The city spent $6,750,000 on road repairs and received a state grant of $1,250,000. What is the new budget balance?
- 22.Rosa swam 3/4 of a mile each session for 5 sessions, and then 1 1/2 miles each session for 3 sessions. How many total miles did she swim?
What this worksheet covers
22 story problems fill this word problems page; problem 8 asks "Carlos drove from his home to the city, which is 84.6 miles…", and the sheet stays at that level throughout. What makes this set particular: thirteen of the 22 problems involve a negative quantity and the problems are written as situations that have to be translated before they can be calculated. Further down, problem 15 asks "Priya scored -3 1/2 points on a penalty in a trivia game,…". The sheet sits inside Common Core 7.NS.3, in the grade 7 The Number System strand.
Skills practised
At grade 7, integers is about adding, subtracting, multiplying and dividing integers, and order of operations with signed numbers, and this sheet takes one slice of that. Specifically, the problems practise rational Numbers in the Real World. To finish it, a student has to read a situation and choose an operation before computing, work in fractional units and give the answer in lowest terms, and keep the decimal points aligned.
About the word problems format
Story problems are set one to a line with room to work underneath, problem 8, "Carlos drove from his home to the city, which is 84.6 miles…" among them, and the key gives each of the 22 answers with its unit. Temperatures, depths, floors and balances give negative numbers a meaning that makes the direction of an answer checkable.
Set A, Set B and Set C
Set A is the original MathSheetLab worksheet; Sets B and C keep its structure and redraw the numbers, with each answer recomputed rather than copied. Where Set A's problem 12 is "A store marked down all prices by 1/5. If a jacket…", Set B's is "On a winter night, the temperature was -4.1°F. The next…".
22 story problem(s) drawn from the 7.NS.3 context family (rational-number stories (temperature, money, depth)) — parameters inferred from the standard and grade
How to use this worksheet
Work it without a calculator. Every one of the 22 integers problems is designed to be done by hand, and reaching for a calculator at grade 7 skips exactly the reasoning being built. If more than a third of the 22 problems come back wrong, stop and step back a grade in integers rather than assigning Set B.
One mistake to watch for
The sign rule for multiplication is applied to addition: -3 + (-4) is answered 7. On this grade 7 word problems, problem 15 ("Priya scored -3 1/2 points on a penalty in a trivia game,…") is the kind of item where it shows.
One rule — "two negatives make a positive" — is being used for every operation.
Separate the two rules explicitly: adding moves along the line, multiplying flips or keeps direction.
Other grade 7 integers formats
The same skill in the other formats available at this grade.
- Drill — Grade 7 Adding Rational Numbers, 20 problems
- Timed Drill — Grade 7 Integers Timed Drill, 60 problems
- Missing Number — Grade 7 Integers Missing Number, 24 problems
- Mixed Review — Grade 7 Subtracting Rational Numbers, 20 problems
A step either side
The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.
- Grade 6 Integers Word Problems — grade 6, 10 problems
- Grade 8 Integers Word Problems — grade 8, 10 problems
Word Problems sheets in other grade 7 topics
Six PDFs, no sign-up: three versions of this grade 7 integers word problems and three answer keys, each 22 problems long.