Fractions Decimals Percents Worksheets - Free Printable

Problem Analysis:

The task involves solving two challenges by identifying the correct fraction from a list of 8 possibilities based on given clues. Let's break down each challenge step by step.

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Challenge A:

#### Clues:
1. I am more than two-tenths.
2. I am not a percentage.
3. Written as a decimal, I have more than one decimal place.
4. If you round me to the nearest whole, I would round down.

#### Possible Answers:
- A: 0.43
- B: 58%
- C: \( \frac{13}{25} \)
- D: 0.89
- E: \( \frac{17}{100} \)
- F: 14%
- G: \( \frac{37}{50} \)
- H: 0.3

#### Step-by-Step Solution:
1. Clue 1: I am more than two-tenths.
- Two-tenths is \( 0.2 \).
- Eliminate any values less than or equal to \( 0.2 \):
- \( \frac{17}{100} = 0.17 \) (eliminated).
- \( 0.3 \) (eliminated).

2. Clue 2: I am not a percentage.
- Eliminate percentages:
- \( 58\% \) (eliminated).
- \( 14\% \) (eliminated).

3. Clue 3: Written as a decimal, I have more than one decimal place.
- Check the remaining options:
- \( 0.43 \): Has two decimal places.
- \( \frac{13}{25} = 0.52 \): Has two decimal places.
- \( 0.89 \): Has two decimal places.
- \( \frac{37}{50} = 0.74 \): Has two decimal places.

4. Clue 4: If you round me to the nearest whole, I would round down.
- Round each remaining option to the nearest whole number:
- \( 0.43 \): Rounds to 0 (rounds down).
- \( 0.52 \): Rounds to 1 (rounds up).
- \( 0.89 \): Rounds to 1 (rounds up).
- \( 0.74 \): Rounds to 1 (rounds up).

- The only value that rounds down is \( 0.43 \).

#### Final Answer for Challenge A:
\[ \boxed{A} \]

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Challenge B:

#### Clues:
1. I am less than \( \frac{3}{4} \).
2. I am not a decimal.
3. If you round me to the nearest whole, I would round up.
4. I am more than six-tenths.

#### Possible Answers:
- A: 0.43
- B: 58%
- C: \( \frac{13}{25} \)
- D: 0.89
- E: \( \frac{17}{100} \)
- F: 14%
- G: \( \frac{37}{50} \)
- H: 0.3

#### Step-by-Step Solution:
1. Clue 1: I am less than \( \frac{3}{4} \).
- \( \frac{3}{4} = 0.75 \).
- Eliminate any values greater than or equal to \( 0.75 \):
- \( 0.89 \) (eliminated).
- \( \frac{37}{50} = 0.74 \) (kept).
- \( 0.43 \) (kept).
- \( \frac{13}{25} = 0.52 \) (kept).
- \( 0.3 \) (kept).

2. Clue 2: I am not a decimal.
- Eliminate decimals:
- \( 0.43 \) (eliminated).
- \( 0.3 \) (eliminated).

3. Clue 3: If you round me to the nearest whole, I would round up.
- Check the remaining options:
- \( \frac{13}{25} = 0.52 \): Rounds to 1 (rounds up).
- \( \frac{37}{50} = 0.74 \): Rounds to 1 (rounds up).

4. Clue 4: I am more than six-tenths.
- Six-tenths is \( 0.6 \).
- Check the remaining options:
- \( \frac{13}{25} = 0.52 \): Less than \( 0.6 \) (eliminated).
- \( \frac{37}{50} = 0.74 \): Greater than \( 0.6 \) (kept).

#### Final Answer for Challenge B:
\[ \boxed{G} \]

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Final Answers:

- Challenge A: \( \boxed{A} \)
- Challenge B: \( \boxed{G} \)