Question

Harvey the hamster can run 3 and 1/6 km in 1/4 of an hour. What is his average speed in kilometers per hour?

Answer 1

Answer:  12 & 2/3 km per hour

In decimal form, this is approximately 12.667 km per hour.

As an improper fraction, 12 & 2/3 = 38/3

==================================================

Explanation:

Let's use this formula

a & b/c = (a*c+b)/c

to convert the given mixed number to an improper fraction.

3 & 1/6 = (3*6+1)/6

3 & 1/6 = 19/6

The mixed number 3 & 1/6 is the same as the improper fraction 19/6

The hamster runs 19/6 km in 1/4 of an hour.

We can express that as the ratio

19/6 km : 1/4 hr

Multiply both parts by 4 so that the "1/4 hr" turns into "1 hr"

19/6 km : 1/4 hr

4*19/6 km : 4*1/4 hr

76/6 km : 1 hr

38/3 km : 1 hr

Harvey runs 38/3 km in 1 hour

Let's convert that to a mixed number

38/3 leads to a decimal, but 36/3 leads to a whole number

So,

38/3 = (36+2)/3

38/3 = 36/3 + 2/3

38/3 = 12 + 2/3

38/3 = 12 & 2/3

You can use your calculator to note that 38/3 = 12.667 approximately, which is also the value of 12 & 2/3, since 2/3 = 0.667 approximately. This helps confirm we did the conversion correctly.