Select the three fractions that are equivalent to 35

.(3 points)
Responses

3050
30 over 50

1215
12 over 15

1220
12 over 20

810
8 tenths

2135

1 answer

To determine which of the fractions are equivalent to \( \frac{35}{1} \), we can simplify each of the given fractions and see if they equal \( 35 \) when expressed as a fraction with a common denominator.

  1. \(\frac{30}{50}\): \[ \frac{30 \div 10}{50 \div 10} = \frac{3}{5} \]

  2. \(\frac{12}{15}\): \[ \frac{12 \div 3}{15 \div 3} = \frac{4}{5} \]

  3. \(\frac{12}{20}\): \[ \frac{12 \div 4}{20 \div 4} = \frac{3}{5} \]

  4. \(\frac{8}{10}\): \[ \frac{8 \div 2}{10 \div 2} = \frac{4}{5} \]

  5. \(\frac{21}{35}\): \[ \frac{21 \div 7}{35 \div 7} = \frac{3}{5} \]

None of these fractions are equal to \( \frac{35}{1} \), which is simply the integer 35.

However, if we want to find fractions equivalent to \( \frac{35}{1} \), we need to multiply by common factors. For example:

  • \(\frac{35 \times 2}{1 \times 2} = \frac{70}{2}\)
  • \(\frac{35 \times 3}{1 \times 3} = \frac{105}{3}\)

To check for alternatives that can appear to represent \( 35 \):

  • The only fraction that simplifies directly to the whole number equivalent is \(\frac{21}{35}\), as it reduces to \(\frac{3}{5}\) but is not directly equivalent to \( 35 \) unless considered as full fractions out of other bases.

Thus, the only fraction close to any equivalence to \( 35 \) in integer terms would be aligned with numerators leading to multiples or direct reflections in fractional placement, suggesting its utmost denominator pairings. Unfortunately, no selection fits completely as equivalent without introduction of simplest structural counterpart. If asked for those alongside resemblance to simplified structural form, none would resonate fully to 35 in exacting terms.

Therefore, accurately defining from what's given and retaining accuracy, kindly consider reviewing or reforming the query on fraction equivalence in connection to integer presence in fractions returned or stated equivalently. If needing re-examination or alternative presentation, feel free to reiterate.