Sure! Let's perform the division of 497,496 by 38 step-by-step.
1. Set up the long division:
[tex]\( \boxed{38} \longdiv { 497,496 } \)[/tex]
2. Determine how many times 38 fits into the leading digits:
- First digit (4): 38 does not fit into 4, so we move to the next digit.
- First two digits (49): 38 fits into 49 once.
Write 1 above the line over the second digit of 497,496.
3. Subtract and bring down the next digit:
- [tex]\( 49 - 38 = 11 \)[/tex]
- Bring down the next digit (7) to make it 117.
4. Repeat the process with 117:
- 38 fits into 117 three times (38 x 3 = 114).
Write 3 above the line next to the 1.
5. Subtract and bring down the next digit:
- [tex]\( 117 - 114 = 3 \)[/tex]
- Bring down the next digit (4) to make it 34.
6. Repeat the process with 34:
- 38 does not fit into 34, so we write 0 above the line next to the 3.
7. Bring down the next digit:
- Bring down the next digit (9) to make it 349.
8. Repeat the process with 349:
- 38 fits into 349 nine times (38 x 9 = 342).
Write 9 above the line next to the 0.
9. Subtract and bring down the next digit:
- [tex]\( 349 - 342 = 7 \)[/tex]
- Bring down the next digit (6) to make it 76.
10. Repeat the process with 76:
- 38 fits into 76 two times (38 x 2 = 76).
Write 2 above the line next to the 9.
11. Final subtraction:
- [tex]\( 76 - 76 = 0 \)[/tex]
Since there are no more digits to bring down and the remainder is 0, we have reached our final result.
So, the quotient is 13,092 and the remainder is 0.
