Depth · one concept from first principles · step 2 of 4
A car travels in one hour. If the car uses of gasoline to travel , how many liters of gasoline does it need to travel for hours and minutes at the same speed?
An hour is 60 minutes, so 24 minutes is 24/60 = 0.4 and the time is 2.4 hours.
Changing the small unit (minutes) into the bigger unit (hours) lets us use the hourly speed directly, and a 5th grader can see 24/60 = 0.4 because 24 is four-tenths of 60.
5.MD.A.1Analyze The Units2 hours 24 minutes is 2.4 hours.
An hour is always the same fixed 60 minutes, so a stretch of minutes can be renamed as a part of an hour.
24 out of 60 equal minutes is the same share of the hour as 4 out of 10, and 4 out of 10 is what the decimal 0.4 records.
Since the car goes 83.5 km each hour, in 2.4 hours it covers 83.5 multiplied by 2.4 kilometers.
Distance is just the per-hour amount added up 2.4 times; multiplying decimals to hundredths is exactly the grade-5 skill of scaling a measurement by a decimal.
5.NBT.B.7Identify SubproblemsEach kilometer uses 0.08 L, so 200.4 km uses 200.4 multiplied by 0.08 liters.
Fuel is the per-km amount repeated for every kilometer; this last subproblem turns distance into liters, finishing the chain with one more decimal multiplication.
5.NBT.B.7Identify SubproblemsTurn the minutes into a decimal part of an hour first, then multiply step by step: hours to kilometers, kilometers to liters.
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The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Meeting Time with Piecewise Rates. Why the shapes repeat →