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Shapeshifting Fraction Format

The greatest reward for a student is not a good grade. It is the willingness of his teacher to listen to him.

- Nikolay Konstantinov

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1. Consider the following six numbers: 315, 1101, 7628, 13025, 110124, and 876. Which are divisible by 3?

315 and 110124
315, 1101, and 7628
315, 1101, and 110124
315, 1101, 110124, and 876

2. Consider the following six numbers: 315, 1101, 7628, 13025, 110124, and 876. Which are divisible by 4?

7628 and 876
7628 and 110124
7628, 110124, and 876
1101, 7628, 110124, and 876

3. How many factors does 126 have?

ten (2 × 63, 3 × 42, 6 × 21, 7 × 18, 9 × 14)
twelve (1 × 126, 2 × 63, 3 × 42, 6 × 21, 7 × 18, 9 × 14)
fourteen (1 × 126, 2 × 63, 3 × 42, 4 × 32, 6 × 21, 7 × 18, 9 × 14)

4. What is the prime factorization of 126?

12 × 6
3 × 4 × 2 × 3
2 × 3 × 4 × 7
2 × 3 × 3 × 7
2 × 2 × 2 × 3 × 3
2 × 2 × 3 × 3 × 7

5. Fully reduce the fraction 16⁄120

2⁄15 2⁄30 2⁄60 4⁄15 4⁄30 4⁄60

6. Change 0.45 to a fraction. Remember to simplify.

9⁄20 45⁄100 45⁄10

7. What is the decimal notation for four-twentieths?

0.04 0.4 0.16 0.2 5

8. Write this decimal, which is less than one: three hundred and eleven ten-thousandths.

3.11 0.311 0.0311 0.00311

9. Which decimal is greater, 0.040199 or 0.040201?

0.040199 is greater 0.040201 is greater

10. Little Bo Peep has a dozen sheep. She shears 1 pound of wool from the first, 1.5 pounds from the second, 2 pounds from the third, and so forth, increasing by 0.5 pounds each time until she shears 6.5 pounds of wool from the last sheep. What is the average amount of wool taken per sheep? How do you know how much to round this answer?

3.75 pounds. She probably owns a scale that is accurate to the hundredth of a pound.
3.75 pounds. We can use one more decimal place than number(s) from the original problem.
3.8 pounds. We can use the same number of decimal places as number(s) from the original problem.
4 pounds. I dislike rounding.