To graph each fraction on a number line, we need to find a common denominator for each fraction. The fractions reported are:
Brad: 4/5
Alice: 1/2
Andre: 4/6
To find a common denominator, we can list the multiples of each denominator:
For 5: 5, 10, 15, 20, 25, ...
For 2: 2, 4, 6, 8, 10, ...
For 6: 6, 12, 18, 24, ...
From this list, we can see that the least common multiple (LCM) of 5, 2, and 6 is 30. So, we can rewrite the fractions as:
Brad: 24/30
Alice: 15/30
Andre: 20/30
Now, we can graph these fractions on a number line labeled from 0 to 1. We divide the line segment into 30 equal parts, and mark the points corresponding to each fraction:
0 1/30 2/30 3/30 4/30 5/30 6/30 7/30 8/30 9/30 10/30 11/30 12/30 13/30 14/30 15/30 16/30 17/30 18/30 19/30 20/30 21/30 22/30 23/30 24/30 25/30 26/30 27/30 28/30 29/30 1
Brad's fraction of 24/30 falls between the points 23/30 and 25/30.
Alice's fraction of 15/30 falls exactly on the point 15/30.
Andre's fraction of 20/30 falls exactly on the point 20/30.
From the number line, we can see that Brad made the greatest fraction of goals because his fraction is the greatest among the three.