To solve the division of two mixed numbers, first, convert them into improper fractions, then multiply by the reciprocal of the divisor. The solution to the student's question is 2.
Understanding Fractions and Division
To solve the expression 5 and 1 over 2 divided by 2 and 6 over 8, we need to perform a division between two mixed numbers. First, we convert both mixed numbers to improper fractions. The first mixed number 5 and 1 over 2 becomes 11/2. The second mixed number 2 and 6 over 8 simplifies to 22/8, which further simplifies to 11/4 after dividing both numerator and denominator by 2.
Next, we divide the two fractions, which is the same as multiplying by the reciprocal of the second fraction. So, 11/2 divided by 11/4 is equivalent to multiplying 11/2 by 4/11. Performing this multiplication gives us:
11/2 * 4/11
=(11 * 4) / (2 * 11)
=(44) / (22)
= 2
The result of the division is 2, meaning 5 and 1 over 2 divided by 2 and 6 over 8 equals 2.