Final answer:
To find the product of three and one half times one and two thirds, convert both to improper fractions (7/2 and 5/3), multiply them to get 35/6, and convert back to a mixed number to get five and five sixths.
Step-by-step explanation:
Solving Fraction Multiplication
To solve the problem three and one half times one and two thirds, you first need to convert the mixed numbers to improper fractions. Three and one half is equal to 7/2 (since 3 × 2 + 1 = 7), and one and two thirds is equal to 5/3 (since 1 × 3 + 2 = 5).
Next, multiply these two improper fractions: (7/2) × (5/3). Multiply the numerators together and the denominators together: (7 × 5) / (2 × 3), which gives us 35/6.
Now, convert the improper fraction 35/6 back to a mixed number. To do this, divide 35 by 6, which gives us 5 with a remainder of 5. Therefore, the mixed number is 5 and 5/6. So, three and one half times one and two thirds equals five and five sixths (choice b).