7.EE.B.3
7th Grade
Expressions & Equations
Multi-Step Rational Problems
Solve multi-step real-life and mathematical problems with positive and negative rational numbers in any form, and assess the reasonableness of answers.
How to explain it
The anchor students hold onto: Set up each step in order. Use fractions, decimals, or integers in any form; convert as needed. Check that the answer is reasonable using estimation.
Multi-step rational number fluency supports 7.EE.B.4 equation solving, where both sides may involve fractions or decimals, and builds toward proportional reasoning in 8th grade.
Worked examples
Example 1
Multi-Step Fractions
Find: 3/4 + 2 × 1/3.
Step 1Order of operations: multiply first. 2 × 1/3 = 2/3.
Step 2Add: 3/4 + 2/3. LCD = 12: 9/12 + 8/12 = 17/12.
Answer17/12 = 1 5/12
Example 2
Decimals + Negatives
-3.5 + 2 × 1.25: what is it?
Step 1Multiply first: 2 × 1.25 = 2.5.
Step 2Add: -3.5 + 2.5 = -1.
Answer-1
Example 3
Reasonableness
Is 1/3 of 11.7 close to 4?
Step 1Estimate: 1/3 of 12 ≈ 4.
Step 2Exact: 11.7 ÷ 3 = 3.9.
AnswerYes, 3.9 ≈ 4 (reasonable)
Common mistakes
What students write
Adds instead of subtracts when a quantity is lost, dropped, or described as negative.
The fix
A loss of 4.7 means adding -4.7, not +4.7. Restate: the value decreases by 4.7.
Try this
Maya computes the net change: a temperature starts at -5.6 degrees, then gains 2.3 degrees, then loses 4.7 degrees. Maya’s work: -5.6 + 2.3 = -3.3 -3.3 + 4.7 = 1.4 degrees Identify Maya’s error and show the correct solution.
What students write
Subtracts mixed numbers without regrouping when the fraction part is smaller.
The fix
Regroup: 3 1/4 - 1 3/4 → rewrite 3 1/4 as 2 5/4, then subtract to get 1 2/4 = 1 1/2.
Try this
Liam subtracts: 3 1/4 - 1 3/4. Liam’s work: 3 1/4 - 1 3/4 Whole parts: 3 - 1 = 2 Fraction parts: 3/4 - 1/4 = 2/4 Answer: 2 2/4 = 2 1/2 Identify Liam’s error and show the correct solution.
Teacher tip
Head off the two predictable errors before they happen. First: A loss of 4.7 means adding -4.7, not +4.7. Restate: the value decreases by 4.7. Second: Regroup: 3 1/4 - 1 3/4 → rewrite 3 1/4 as 2 5/4, then subtract to get 1 2/4 = 1 1/2.