Josiah skated for 4 1/3 hours last month and 5 5/12 hours this month. How many hours did Josiah skate in all?Write your answer as a fraction or as a whole or mixed number.
Question
Josiah skated for 4 1/3 hours last month and 5 5/12 hours this month. How many hours did Josiah skate in all?Write your answer as a fraction or as a whole or mixed number.
Solution
First, we need to convert the mixed numbers into improper fractions.
For 4 1/3 hours, the improper fraction is (4*3 + 1)/3 = 13/3 hours.
For 5 5/12 hours, the improper fraction is (5*12 + 5)/12 = 65/12 hours.
Next, we add these two fractions. But before we can add them, we need to find a common denominator. The least common multiple of 3 and 12 is 12.
So, we convert 13/3 to 52/12.
Now, we can add the two fractions: 52/12 + 65/12 = 117/12 hours.
Finally, we convert this improper fraction back into a mixed number.
117 divided by 12 is 9 with a remainder of 9.
So, Josiah skated for 9 9/12 hours in all.
But we can simplify 9/12 to 3/4.
So, the final answer is 9 3/4 hours.
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