Final answer:
Mr. Díaz can make 6 badges with the 3/4 yard of ribbon he has by using 1/8 yard of ribbon for each badge.
Step-by-step explanation:
Mr. Díaz has 3/4 yard of ribbon to make badges for the science fair, and he uses 1/8 yard of ribbon for each badge. To find out how many badges he can make, we need to determine how many times 1/8 yard can fit into 3/4 yard.
To calculate this, we divide 3/4 by 1/8, which is equivalent to multiplying 3/4 by the reciprocal of 1/8:
(3/4) × (8/1) = (3 × 8) / (4 × 1) = 24/4 = 6
Therefore, Mr. Díaz can make 6 badges with the ribbon he has.