Problem
How many times the unit quantity
An airplane flies 864 km every hour at a steady speed. Find how far it travels in 4 hours and 30 minutes.
OperationsBase-ten numbers
Your answer
km
Watch out Don't turn 30 minutes into 4.3 hours by dropping it after the decimal point — 30 minutes is half an hour, so the time is 4.5 hours.
How to solve
Strategy Analyze the Units — Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 4 full hours plus a half hour.
1STEP 1
Distance in the 4 whole hours
Each hour adds 864 km, so 4 hours add 864 x 4 = 3456 km.
864 × 4 = 3456 km
Four equal hours is just multiplying the one-hour distance by 4.
4.NBT.B.5Identify SubproblemsDuring the 4 whole hours the plane covers 864 x 4 = 3456 km.
Why?
The speed never changes, so each of the 4 hours adds the very same 864 km, and joining 4 equal groups of 864 is exactly what 864 x 4 counts.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
To find 864 x 4 you split 864 into 800 + 60 + 4, take 4 of each part, and add the pieces to get 3200 + 240 + 16 = 3456.
Why?
Taking 4 of (800 + 60 + 4) is the same as 4 of 800 plus 4 of 60 plus 4 of 4, so the group may be split before multiplying.
🧱Distributive propertya groups of (b and c) is a groups of b plus a groups of c — you can split the group.
Why?
The 8, 6, and 4 in 864 are worth 800, 60, and 4 because each digit sits one place higher than the last, so adding 3200 + 240 + 16 rebuilds the whole number.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
2STEP 2
Distance in the extra 30 minutes
30 minutes is half an hour, so the plane covers half of 864 km, which is 864 / 2 = 432 km.
864 ÷ 2 = 432 km
Half an hour means half the hourly distance -- a simple halving.
4.OA.A.2Analyze The Units3STEP 3
Add the two parts
Total distance is the 4-hour part plus the half-hour part: 3456 + 432 = 3888 km.
3456 + 432 = 3888 km
Adding the whole-hour and half-hour distances gives the full trip.
4.OA.A.3Identify SubproblemsAnswer
3888 km
3456 + 432 = 3888
In 4.5 hours the distance should be a bit more than 4 x 864 = 3456 and less than 5 x 864 = 4320. The answer 3888 falls right between them, as expected for 4.5 hours. Units stay in km throughout.
Takeaway
This only needs Grade 4 multiplying and halving -- 4 full hours plus a half hour of the same speed!
- Distance in the 4 whole hours
- Distance in the extra 30 minutes
- Add the two parts
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