A decade is 10 years. Which expression gives the number of years in d decades, 10+d, 10d, or d÷10. Explain your choice.

10d

10 times the number of decades

The expression that gives the number of years in d decades is 10d.

To explain why, let's break down each expression:

1. 10+d: This expression adds 10 and d. However, since a decade is 10 years, adding 10 to d would overestimate the total number of years. For example, if d is 2, then 10+d would give us 10+2 = 12 years, which is incorrect because 2 decades equal 20 years, not 12.

2. 10d: This expression multiplies 10 by d. Since a decade is 10 years, multiplying 10 by d gives us the correct result. For example, if d is 2, then 10d would give us 10*2 = 20 years, which is correct because 2 decades equal 20 years.

3. d÷10: This expression divides d by 10. Dividing d by 10 would underestimate the total number of years. For example, if d is 20, then d÷10 would give us 20/10 = 2 years, which is incorrect because 20 decades equal 200 years, not 2.

Therefore, the expression that correctly gives the number of years in d decades is 10d.