Choose a fraction between ½ and 1. Suppose you make 7 ½ jumps of that amount. On the number line, you START at ½ . Where do you end up?
So, if I choose 3/5, then I get
1/2 + (7 1/2)(3/5) = 1/2 + (15/2)(3/5) = 1/2 + 9/2 = 5
To determine where you end up after making 7 ½ jumps of a fraction between ½ and 1, we can divide the interval between ½ and 1 into equal parts.
Step 1: Calculate the size of each jump:
The interval between ½ and 1 can be determined by subtracting ½ from 1:
1 - ½ = ½
Step 2: Divide the interval into equal parts:
Since we want to make 7 ½ jumps, we need to divide the interval size (½) into 7 equal parts.
½ / 7 = 1/14
Step 3: Calculate the distance traveled with 7 whole jumps:
To calculate the distance covered by 7 whole jumps, we simply multiply the size of each jump by the total number of jumps:
(1/14) * 7 = 7/14
Step 4: Calculate the distance traveled with ½ jump:
To determine the distance covered by ½ jump, we multiply the size of each jump (1/14) by ½:
(1/14) * (1/2) = 1/28
Step 5: Determine the final destination:
To find the final position, we add the distances traveled with whole jumps and the distance traveled with the half jump:
7/14 + 1/28 = 14/28 + 1/28 = 15/28
Therefore, you will end up at 15/28 on the number line after making 7 ½ jumps of a fraction between ½ and 1, starting at ½.