Explain why it is necessary to rename 4 1/4 if you subtract 3/4 from it

1/4 is less than 3/4, so 3/4 cannot be subtracted from it.

If you were paying for a 75 cent item with 4 1-dollar bills and a quarter, you would find that one of the bills would need to be changed to quarters. The same idea applies to this problem.

4 1/4 - 3/4

= 3 5/4 - 3/4 (4 1/4 gets renamed to 3 5/4)

= 3 2/4

= 3 1/2

4 1/4 - 3/4

= 4 1/4 - (1/4 + 1/2)

= (4 1/4 - 1/4) - 1/2

= 4 - 1/2

= 3 1/2 (we have implicitly renamed 4 to 3 2/2 so we can subtract 1/2)

If you were paying for a 75 cent item with 4 1-dollar bills and a quarter, you would find that one of the bills would need to be changed to quarters. The same idea applies to this problem.

4 1/4 - 3/4

= 3 5/4 - 3/4 (4 1/4 gets renamed to 3 5/4)

= 3 2/4

= 3 1/2

4 1/4 - 3/4

= 4 1/4 - (1/4 + 1/2)

= (4 1/4 - 1/4) - 1/2

= 4 - 1/2

= 3 1/2 (we have implicitly renamed 4 to 3 2/2 so we can subtract 1/2)

Because the answer reduces ,4 1/4-3/4 =7/2,