Problem
Solve multi-step decimal problems in order
Nami walks 1.9 km in an hour. Evan's hourly distance is 0.7 of Nami's minus 0.2 km, and Jacob's is 1.8 times Evan's. Find who walked the farthest in one hour.
Base-ten numbers
Your answer
How to solve
Strategy Identify Subproblems — Each distance is built from the one before it, so we break the question into a chain of small steps: first Evan (from Nami), then Jacob (from Evan), then compare. Tracking the kilometer unit keeps every multiplication and subtraction lined up correctly.
1STEP 1
Find Evan's distance
Evan walked 0.2 km less than 0.7 times Nami's 1.9 km. First multiply 0.7 by 1.9, then subtract 0.2.
0.7 × 1.9 = 1.33, 1.33 - 0.2 = 1.13
Breaking a hard sentence into 'multiply, then subtract' is exactly the order words like 'less than 0.7 times' tell us to use.
5.NBT.B.7Identify SubproblemsEvan's distance is seven tenths of Nami's, with 0.2 km taken off that amount.
Why?
Taking 0.7 of Nami's 1.9 km means cutting that distance into ten equal parts and keeping seven of them.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
The 0.2 km is said to be how much less Evan walked than that amount, so it comes off the seven-tenths share and not off Nami's distance.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
2STEP 2
Find Jacob's distance
Jacob walked 1.8 times Evan's 1.13 km, so multiply 1.8 by 1.13.
1.8 × 1.13 = 2.034
Now that Evan's distance is a known number, Jacob's becomes a plain decimal multiplication.
5.NBT.B.7Identify Subproblems3STEP 3
Compare all three distances
Line up the three distances in kilometers and compare: Nami 1.9, Evan 1.13, Jacob 2.034. The largest is Jacob's.
2.034 ＞ 1.9 ＞ 1.13
Since every distance is in the same unit (km), I can compare the numbers directly to see who went farthest.
5.NBT.B.7Analyze The UnitsAnswer
Jacob (2.034 km)
All answers are in kilometers. Evan (1.13) is less than Nami (1.9), which fits 'less than 0.7 times'. Jacob is 1.8 times Evan, almost double, so Jacob being the biggest at about 2 km makes sense.
Takeaway
When each answer depends on the one before it, solve the steps in order, one at a time.
- Find Evan's distance
- Find Jacob's distance
- Compare all three distances
Where next?
Another one like thissuggested
Step back and solidifysuggested