Question
Mark found the quotient of 2,105÷5%0D%0A2%0D%0A,%0D%0A105%0D%0A÷%0D%0A5%0D%0A using the standard algorithm. His work is shown. %0D%0A%0D%0A%0D%0A %0D%0A%0D%0AWhen dividing 2,105%0D%0A2%0D%0A,%0D%0A105%0D%0A by 5%0D%0A5%0D%0A , is there a remainder? Explain how you know using Mark's work. %0D%0AFree Response
Answers
Answered by
GPT-4o mini
To determine if there is a remainder when dividing 2,105 by 5 using Mark's work, we need to first carry out the division. The steps of the standard division algorithm can be summarized as follows:
1. **Convert the Percentage to a Decimal**: Since the problem involves 5%, convert it to decimal form. 5% is equivalent to 0.05.
2. **Set up the Division**: We are dividing 2,105 by 0.05.
3. **Adjust for Division**: Dividing by a decimal can be converted into a simpler problem by multiplying both the dividend and the divisor by 100 to eliminate the decimal. This gives:
\[
\frac{2,105 \times 100}{0.05 \times 100} = \frac{210,500}{5}
\]
4. **Perform the Division**: Now, we divide 210,500 by 5:
- 5 goes into 21 four times (5 x 4 = 20), leaving a remainder of 1.
- Bring down the next digit (0) making it 10; 5 goes into 10 two times (5 x 2 = 10), leaving no remainder.
- Bring down the next digit (5); 5 goes into 5 one time (5 x 1 = 5), leaving no remainder.
- Bring down the last digit (0); 5 goes into 0 zero times, leaving a remainder of 0.
Combining this information:
- After performing the entire division, we find that 210,500 divided by 5 equals 42,100 with a remainder of 0.
**Conclusion**: Since the final remainder is 0, we can conclude that there is no remainder when dividing 2,105 by 5. Mark's work shows that after dividing, every digit was accounted for, leading to a complete division with no leftover values. Thus, 2,105 is evenly divisible by 5.
1. **Convert the Percentage to a Decimal**: Since the problem involves 5%, convert it to decimal form. 5% is equivalent to 0.05.
2. **Set up the Division**: We are dividing 2,105 by 0.05.
3. **Adjust for Division**: Dividing by a decimal can be converted into a simpler problem by multiplying both the dividend and the divisor by 100 to eliminate the decimal. This gives:
\[
\frac{2,105 \times 100}{0.05 \times 100} = \frac{210,500}{5}
\]
4. **Perform the Division**: Now, we divide 210,500 by 5:
- 5 goes into 21 four times (5 x 4 = 20), leaving a remainder of 1.
- Bring down the next digit (0) making it 10; 5 goes into 10 two times (5 x 2 = 10), leaving no remainder.
- Bring down the next digit (5); 5 goes into 5 one time (5 x 1 = 5), leaving no remainder.
- Bring down the last digit (0); 5 goes into 0 zero times, leaving a remainder of 0.
Combining this information:
- After performing the entire division, we find that 210,500 divided by 5 equals 42,100 with a remainder of 0.
**Conclusion**: Since the final remainder is 0, we can conclude that there is no remainder when dividing 2,105 by 5. Mark's work shows that after dividing, every digit was accounted for, leading to a complete division with no leftover values. Thus, 2,105 is evenly divisible by 5.