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Find each answer mentally.
A train is traveling at a constant speed and goes kilometers in 6 minutes. At that rate:
How far does the train go in 1 minute?
Lin ran miles in of an hour. Noah ran miles in of an hour.
Who ran faster, Noah or Lin? Explain or show your reasoning.
In real life, the Mona Lisa measures feet by feet. A company that makes office supplies wants to print a scaled copy of the Mona Lisa on the cover of a notebook that measures 11 inches by 9 inches.
What size should they use for the scaled copy of the Mona Lisa on the notebook cover?
What is the scale factor from the real painting to its copy on the notebook cover?
Discuss your thinking with your partner. Did you use the same scale factor? If not, is one more reasonable than the other?
There are 12 inches in 1 foot, so we can say that for every 1 foot, there are 12 inches, or the ratio of feet to inches is . We can find the unit rates by dividing the numbers in the ratio:
,
so there is foot per inch.
,
so there are 12 inches per foot.
When the numbers in a ratio are fractions, we calculate the unit rates the same way: by dividing the numbers. For example, if someone runs mile in minutes, the ratio of minutes to miles is .
, so the person’s
pace is minutes per mile.
, so the person’s
speed is mile per minute.
A unit rate is a rate per 1.
For example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because . The other unit rate is of a pie per person, because .