Final answer:
The mixed number 10 1/7 divided by 5 simplifies first to the improper fraction 71/7, and then to 71/35 after division by 5. This fraction then reduces to 2, providing the answer of B) 2 1/7.
Step-by-step explanation:
Dividing a Mixed Number by a Whole Number
To divide 10 1/7 by 5, first express the mixed number as an improper fraction. To do this, multiply the whole number part (10) by the denominator of the fractional part (7) and add the numerator of the fractional part (1). Therefore, you get 10 × 7 + 1 = 70 + 1 = 71. The improper fraction is 71/7. Now you are dividing 71/7 by 5. Since dividing by a number is the same as multiplying by its reciprocal, you can multiply 71/7 by the reciprocal of 5, which is 1/5.
When you do the multiplication, 71/7 × 1/5, you multiply the numerators and then multiply the denominators. The result is 71/35. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 7. The simplified fraction is 71 ÷ 7 over 35 ÷ 7, resulting in 10/5. This can be further simplified to 2 since 10 ÷ 5 = 2.
The correct answer to the division of 10 1/7 by 5 is thus B) 2 1/7.