Answer :
To solve this problem, we need to determine which representation correctly shows the division that Marci performed using the given numbers: 175 as the dividend, 5 as the divisor, and 35 as the quotient.
Let's break down what each part means:
1. Dividend (175): The number that is being divided.
2. Divisor (5): The number by which the dividend is divided.
3. Quotient (35): The result of the division.
We need to check each given representation to see which one matches the correct division process:
1. [tex]\(35 \div 5 = 175\)[/tex]: This statement suggests dividing 35 by 5. However, since 175 is the dividend, this is incorrect because it shows a multiplication outcome.
2. [tex]\(\frac{175}{5} = 35\)[/tex]: This statement suggests dividing 175 by 5 and obtaining 35, which matches the information given (dividend 175, divisor 5, quotient 35). This is correct.
3. [tex]\(\frac{175}{35} = 5\)[/tex]: This statement suggests dividing 175 by 35 to get 5. This division flips the roles but still uses the same numbers to generate a true statement. The divisor and quotient are swapped, but it remains mathematically sound.
4. [tex]\(5 \div 175 = 35\)[/tex]: This statement suggests dividing 5 by 175, which would not give a quotient of 35. Therefore, this is incorrect.
Based on our analysis, options 2 and 3 are correct representations of Marci's division problem:
- [tex]\(\frac{175}{5} = 35\)[/tex]
- [tex]\(\frac{175}{35} = 5\)[/tex]
Let's break down what each part means:
1. Dividend (175): The number that is being divided.
2. Divisor (5): The number by which the dividend is divided.
3. Quotient (35): The result of the division.
We need to check each given representation to see which one matches the correct division process:
1. [tex]\(35 \div 5 = 175\)[/tex]: This statement suggests dividing 35 by 5. However, since 175 is the dividend, this is incorrect because it shows a multiplication outcome.
2. [tex]\(\frac{175}{5} = 35\)[/tex]: This statement suggests dividing 175 by 5 and obtaining 35, which matches the information given (dividend 175, divisor 5, quotient 35). This is correct.
3. [tex]\(\frac{175}{35} = 5\)[/tex]: This statement suggests dividing 175 by 35 to get 5. This division flips the roles but still uses the same numbers to generate a true statement. The divisor and quotient are swapped, but it remains mathematically sound.
4. [tex]\(5 \div 175 = 35\)[/tex]: This statement suggests dividing 5 by 175, which would not give a quotient of 35. Therefore, this is incorrect.
Based on our analysis, options 2 and 3 are correct representations of Marci's division problem:
- [tex]\(\frac{175}{5} = 35\)[/tex]
- [tex]\(\frac{175}{35} = 5\)[/tex]
