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.
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
This is a 22-problem sheet — one page to work through, one page of answers to check against. Within that, nine of the twenty-two problems involve a negative quantity, so the answer is not always larger than what went in; the problems are written as situations, so a student has to translate before they can calculate. The whole sheet sits inside Common Core 7.NS.3, in the grade 7 The Number System strand.
Skills practiced
At this point in the sequence, work in word problems is really about percent, proportion, and algebraic modeling. To finish it, a student has to read a situation and choose an operation before computing, work in fractional units and simplify the result, and keep decimal points aligned rather than right-aligning digits out of habit. Watch how the answers are reached, not just whether they land — the method is what carries into grade 8.
How to use this worksheet
Work it without a calculator. Every problem on this sheet is designed to be done by hand, and reaching for a calculator at grade 7 skips exactly the reasoning being built. Print a second copy before writing on the first; a sheet worked twice a week apart tells you far more than a sheet worked once.
One mistake to watch for
Percent increase is computed against the wrong base: 20% off $50 then 20% back on returns to $50.
The percent is being applied to whichever number is nearest rather than to the stated base.
Name the base out loud before every percent computation. The second 20% is 20% of $40, not of $50 — which is why the price does not come back.
Related worksheets
More grade 7 word problems
The rest of the grade 7 word problems set, pitched at the same level as this one.
- Grade 7 Percent, Tax, Tip, and Discount Word Problems — grade 7, 14 problems
A step either side
Word problems either side of grade 7, for stepping the difficulty rather than repeating it.
- 6.RP.3 — Ratios & Rates in the Real World — grade 6, 22 problems
- Grade 8 Word Problems: Writing and Solving Linear Equations — grade 8, 14 problems
No sign-up and no paywall — download the word problems sheet, print it, and the answers for all twenty-two problems are on the page behind it.