Juan rode his bike 10 miles on sunday. on monday he rode 3 1/4 times as far on Sunday. How many miles did he ride on Monday?

3 1/4 * 10 = 30 10/4 = 32 1/2

To find the total distance Juan rode on Monday, we need to calculate 3 1/4 times the distance he rode on Sunday.

Step 1: Calculate 3 1/4 times the distance rode on Sunday
To calculate 3 1/4 times, we first need to convert the mixed number to a fraction. 3 1/4 can be expressed as the improper fraction 13/4.
Now we can multiply the distance rode on Sunday (10 miles) by 13/4.

10 miles * 13/4 = (10 * 13) / 4 = 130 / 4

Step 2: Simplify the fraction (130 / 4)
The fraction 130/4 can be reduced to its simplest form. Both the numerator (130) and the denominator (4) are divisible by 2.
Dividing both the numerator and denominator by 2 gives us:

130 / 2 = 65
4 / 2 = 2

The simplified fraction becomes 65/2.

Step 3: Convert the improper fraction to a mixed number
To convert the improper fraction 65/2 to a mixed number, we divide the numerator by the denominator:

65 ÷ 2 = 32 remainder 1

Thus, the mixed number is 32 1/2.

Conclusion:
Juan rode 32 1/2 miles on Monday.