Answer :
To solve this problem, we need to understand the terms used in a division:
- Dividend: The number that is being divided.
- Divisor: The number by which we're dividing.
- Quotient: The result of the division.
In this case, Marci's division involved:
- Dividend: 175
- Divisor: 5
- Quotient: 35
The goal is to find which mathematical representation correctly matches this division scenario.
Let's evaluate each option:
1. [tex]$35 \div 5 = 175$[/tex]
- Here, 35 is the dividend and 5 is the divisor. If we divide 35 by 5, we do not get 175. This cannot be correct because it suggests the quotient is 175, which contradicts the given quotient of 35.
2. [tex]$\frac{175}{35} = 5$[/tex]
- This suggests dividing 175 by 35. The result should be 5. Verifying, if 175 divided by 35 equals 5, this is correct. However, the goal is to represent the original division setup, which involved 175 divided by 5, not 35.
3. [tex]$\frac{175}{5} = 35$[/tex]
- Here, 175 is the dividend, 5 is the divisor, and if we perform this division, the result is indeed 35. This correlation represents the situation described: dividing 175 by 5 yields a quotient of 35.
4. [tex]$5 \div 175 = 35$[/tex]
- This suggests 5 is divided by 175. If you divide 5 by 175, you do not get 35; rather, you get a much smaller number which does not match the conditions given.
Based on the evaluation, the correct representation of the division problem Marci performed is:
[tex]$$\frac{175}{5} = 35$$[/tex]
- Dividend: The number that is being divided.
- Divisor: The number by which we're dividing.
- Quotient: The result of the division.
In this case, Marci's division involved:
- Dividend: 175
- Divisor: 5
- Quotient: 35
The goal is to find which mathematical representation correctly matches this division scenario.
Let's evaluate each option:
1. [tex]$35 \div 5 = 175$[/tex]
- Here, 35 is the dividend and 5 is the divisor. If we divide 35 by 5, we do not get 175. This cannot be correct because it suggests the quotient is 175, which contradicts the given quotient of 35.
2. [tex]$\frac{175}{35} = 5$[/tex]
- This suggests dividing 175 by 35. The result should be 5. Verifying, if 175 divided by 35 equals 5, this is correct. However, the goal is to represent the original division setup, which involved 175 divided by 5, not 35.
3. [tex]$\frac{175}{5} = 35$[/tex]
- Here, 175 is the dividend, 5 is the divisor, and if we perform this division, the result is indeed 35. This correlation represents the situation described: dividing 175 by 5 yields a quotient of 35.
4. [tex]$5 \div 175 = 35$[/tex]
- This suggests 5 is divided by 175. If you divide 5 by 175, you do not get 35; rather, you get a much smaller number which does not match the conditions given.
Based on the evaluation, the correct representation of the division problem Marci performed is:
[tex]$$\frac{175}{5} = 35$$[/tex]
