Question

​A cyclist rode her bicycle 10 1/2 miles on Monday, 12 7/8 miles on Tuesday, and 11 4/5 miles on Wednesday. Compute the total distance for the three days.

Answer 1

The total distance the cyclist rode over the three days is 35 7/40 miles, which is calculated by converting mixed numbers to improper fractions, finding a common denominator, and then adding the fractions together.

Step-by-step explanation:

To compute the total distance the cyclist rode over the three days, we would simply add the distances together. This involves adding mixed numbers, which is a part of mathematics dealing with basic arithmetic operations. First, we write down the distances:

• Monday: 10 1/2 miles
• Tuesday: 12 7/8 miles
• Wednesday: 11 4/5 miles

Now, let's perform the addition step by step:

1. Convert the mixed numbers to improper fractions:
   10 1/2 = (10*2+1)/2 = 21/2 miles
   12 7/8 = (12*8+7)/8 = 103/8 miles
   11 4/5 = (11*5+4)/5 = 59/5 miles
2. Add the improper fractions together:
   21/2 + 103/8 + 59/5 = (21*4)/8 + 103/8 + (59*8)/40 = 84/8 + 103/8 + 472/40
3. Since 84/8 and 103/8 already have a common denominator, add them first:
   84/8 + 103/8 = 187/8 miles
4. To add 187/8 and 472/40, find the common denominator (which is 40), and add:
   (187*5)/40 + 472/40 = 935/40 + 472/40
5. Add the numerators:
   935 + 472 = 1407
6. Thus, the total distance is 1407/40 miles. As the final step, convert this improper fraction back into a mixed number:
   1407/40 = 35 7/40 miles.

Therefore, the cyclist rode a total of 35 7/40 miles over the three days.

Learn more about Total Distance Calculation