Ms. Johnson has 138 jump ropes. She buys 312 more. Ms. Johnson gives out the total number of jump ropes equally to 7 gym teachers. What is the GREATEST number of jump ropes each gym teacher can receive?

To find the greatest number of jump ropes each gym teacher can receive, we need to divide the total number of jump ropes by the number of gym teachers.

The total number of jump ropes Ms. Johnson has is 138 + 312 = <<138+312=450>>450.

Therefore, each gym teacher can receive 450 / 7 = <<450/7=64.28571428571429>>64 jump ropes.

However, since we are looking for the greatest number of jump ropes each gym teacher can receive, we need to round down to the nearest whole number.

Therefore, the greatest number of jump ropes each gym teacher can receive is 64.

To find the greatest number of jump ropes each gym teacher can receive, we need to divide the total number of jump ropes by the number of gym teachers.

First, let's calculate the total number of jump ropes Ms. Johnson has after buying more:

Total Number of jump ropes = Initial Number of jump ropes + Number of jump ropes bought
Total Number of jump ropes = 138 + 312
Total Number of jump ropes = 450

Now, let's divide the total number of jump ropes by the number of gym teachers to find the greatest number of jump ropes each can receive:

Number of jump ropes per gym teacher = Total Number of jump ropes ÷ Number of gym teachers
Number of jump ropes per gym teacher = 450 ÷ 7
Number of jump ropes per gym teacher ≈ 64.29

Since we cannot have a fraction of a jump rope, we need to round down to the nearest whole number. Therefore, the greatest number of jump ropes each gym teacher can receive is 64.

45 jump ropes.