Emily cycled 20.25 miles over 4 days last week. She cycled the same amount each day. How many miles did Emily cycle each day, to the nearest hundredth?

1 Answer
Tony B
Jun 18, 2016

#5.06" miles per day"#

Explanation:

Most people would use the shortcut and say "divide 4 into 20.25".
Once you know why the shortcut works you can use it with confidence.

#color(blue)("This is why the shortcut works")#
Treat the given information as a ratio giving

#("distance")/("time in days")" "->" "(20.25)/4#

But we need #("distance")/("1 day")#

So we need a way to change the 4 into 1. We know that #4-:4=1# so we can use that.

#color(brown)("What you do to the bottom you do to the top")#

#("distance")/("1 day") -=(20.25-:4)/(4-:4) = (5.0625)/1#

#color(green)("Notice we divided 20.25 by 4 which is the shortcut")#

So the full number of miles is #5.0625#

But we need the answer to the nearest # 1/100 th# which is the second decimal place. So what we are interested in is the red part.
The number after the 6 is less than 5 so we do not change the 6.

#color(red)(5.06)25#

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