Answer :
To determine the correct representation of the division problem involving the numbers 175, 5, and 35, let's look at each option step-by-step:
1. Option 1: [tex]\(\frac{175}{5}=35\)[/tex]
- This expression states that 175 divided by 5 equals 35.
- Since 175 is the dividend, 5 is the divisor, and 35 is the quotient, this representation is correct.
2. Option 2: [tex]\(35 \div 5=175\)[/tex]
- This expression implies that 35 divided by 5 equals 175.
- This is incorrect because dividing a smaller number (35) by a larger number (5) cannot result in a larger number (175).
3. Option 3: [tex]\(5 \div 175=35\)[/tex]
- This expression indicates that 5 divided by 175 equals 35.
- This is incorrect as dividing a smaller number (5) by a larger number (175) should yield a fraction or smaller decimal, not a larger whole number like 35.
4. Option 4: [tex]\(\frac{175}{35}=5\)[/tex]
- This expression states that 175 divided by 35 equals 5.
- Since 175 divided by 35 gives us 5, this representation is also correct.
Therefore, the correct representations of this division problem are [tex]\(\frac{175}{5}=35\)[/tex] and [tex]\(\frac{175}{35}=5\)[/tex]. These two options accurately represent the relationships between the dividend, divisor, and quotient in this problem.
1. Option 1: [tex]\(\frac{175}{5}=35\)[/tex]
- This expression states that 175 divided by 5 equals 35.
- Since 175 is the dividend, 5 is the divisor, and 35 is the quotient, this representation is correct.
2. Option 2: [tex]\(35 \div 5=175\)[/tex]
- This expression implies that 35 divided by 5 equals 175.
- This is incorrect because dividing a smaller number (35) by a larger number (5) cannot result in a larger number (175).
3. Option 3: [tex]\(5 \div 175=35\)[/tex]
- This expression indicates that 5 divided by 175 equals 35.
- This is incorrect as dividing a smaller number (5) by a larger number (175) should yield a fraction or smaller decimal, not a larger whole number like 35.
4. Option 4: [tex]\(\frac{175}{35}=5\)[/tex]
- This expression states that 175 divided by 35 equals 5.
- Since 175 divided by 35 gives us 5, this representation is also correct.
Therefore, the correct representations of this division problem are [tex]\(\frac{175}{5}=35\)[/tex] and [tex]\(\frac{175}{35}=5\)[/tex]. These two options accurately represent the relationships between the dividend, divisor, and quotient in this problem.
