Final answer:
To find the result of 7 1/2 divided by 2 5/8, convert the mixed numbers into improper fractions, multiply the first fraction by the reciprocal of the second, and simplify the result. The answer in simplest form is 20/7 or 2 6/7.
Step-by-step explanation:
To solve the division problem 7 1/2 divided by 2 5/8, we first need to convert each mixed number to an improper fraction. An improper fraction happens when the numerator is larger than the denominator. So, we convert 7 1/2 to 15/2, and 2 5/8 to 21/8.
Secondly, we rewrite the division problem as a multiplication problem by using the reciprocal (or the 'flip') of the second fraction. The reciprocal of 21/8 is 8/21. So the problem now looks like this: 15/2 * 8/21.
Then we multiply the numerators together to get a new numerator, and the denominators together to get a new denominator. So, we get 120/42.
Lastly, we simplify the fraction by dividing both the numerator and the denominator by the greatest common factor. For 120/42, the greatest common factor is 6. Our final answer, then, is 20/7 or 2 6/7 in mixed number form.
Learn more about Division of Fractions