7.EE.3: Multi-Step Problems with Rational Numbers
Also written as 7.EE.B.3 and CCSS.MATH.CONTENT.7.EE.B.3 · Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
The Official Wording
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Common Core State Standards, Grade 7, Expressions & Equations · Read it at the source · Checked October 14, 2026
What 7.EE.3 Means in Plain English
Seventh graders work long problems where the numbers arrive as fractions, decimals, percents and negatives, and they switch forms whenever it helps. Scaling a 12-cookie recipe with 1 3/4 cups of flour to 30 cookies is 1.75 × 2.5 = 4.375, or 4 3/8 cups.
Then they judge the answer by estimating: about 2 cups for 12 cookies means about 5 cups for 30, so 4 3/8 is believable and 43.75 is not. In 8th grade the same habits carry into equations with several steps (8.EE.7).
7.EE.3 I Can Statements
- I can solve problems that mix fractions, decimals and negative numbers.
- I can choose the easiest form of a number for each step.
- I can estimate to check that my exact answer is reasonable.
7.EE.3 Worked Example
Negative depths, a fraction of a distance and a decimal dive in one problem, with an estimate made before the exact answer is trusted.
A submarine at -1,200 feet rises 3/8 of the distance to the surface, then dives 145.5 feet. What is its depth now? Check that the answer is reasonable.
- Find the rise first. The distance to the surface is 1,200 feet, and 3/8 of it is easier as a fraction: 1,200 ÷ 8 = 150, then times 3.3/8 × 1,200 = 450 feet
- Rising moves up toward 0, so add 450 to the starting depth.-1,200 + 450 = -750
- Diving moves down, so add -145.5. The decimal can stay a decimal.-750 + (-145.5) = -895.5
- Estimate before trusting it: 3/8 is close to 0.4, and 0.4 × 1,200 = 480, so the rise ends near -720 and a dive of about 150 lands near -870.Estimate about -870, exact -895.5
Check it: Work backward: -895.5 + 145.5 = -750, and -750 - 450 = -1,200, the starting depth.
Common Mistakes with 7.EE.3
Converting a fraction that was easier left alone
3/8 × 1,200 ≈ 0.38 × 1,200 = 456
Try this: Choose the form that fits the numbers: 1,200 ÷ 8 = 150 and 150 × 3 = 450, exact and quicker than rounding 3/8.
Reporting the discount as the price
15% off a $38.40 jacket: 38.40 × 0.15 = 5.76, so it costs $5.76
Try this: Estimate first: 15% off should leave most of the price, about $33, so $5.76 is the discount, not the cost.
Reading the fraction’s digits as a decimal
2 1/4 + 0.6 = 2.14 + 0.6 = 2.74
Try this: Convert by dividing, not by copying digits: 1/4 = 1 ÷ 4 = 0.25, so the sum is 2.25 + 0.6 = 2.85.
Where 7.EE.3 Fits
Practice 7.EE.3
Quick Check
- A worker earning $18.40 an hour gets a 5% raise. What is the new hourly wage?
- A board 8 1/2 feet long is cut into pieces 0.75 foot long. How many whole pieces can be cut?
- At 5 a.m. it was -4.5 °F. The temperature rose 2 1/4 degrees an hour for 4 hours. What was it at 9 a.m.?