Reference / Curriculum / 3B / Chapter 10

3B · Chapter 10 · exam

Chapter practice examination

Original untimed practice examination. Not a secure or official placement test.

Original untimed practice examination. Not a secure or official placement test. Solutions are available as revealable feedback and in a separate complete answer key. No answer submissions or accounts are required.

Assessment · 24 questions

Questions

Show your thinking; use diagrams when they help. Do not open solutions during your first attempt.

  1. A1

    A student answers the following question with “<”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Compare 2/3 and 1/9. Write > or < and justify using equal parts. (3 points)

    Reveal explanation

    Answer: >

    The suggested answer is not correct. Rename as 6/9 and 1/9. Compare numerators: 2/3 > 1/9.

    Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.

    2/31/9
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. A2

    Complete the equivalent fraction: 2/10 = ?/40. (2 points)

    Reveal explanation

    Answer: 8

    Subdivide each of the 10 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 2/10 = 8/40.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    2/108/40
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. A3

    Calculate 3/8 − 1/8. Give the answer in simplest form. (2 points)

    Reveal explanation

    Answer: 1/4

    Both fractions use 8ths. 3 − 1 pieces make 1/4 of a whole after simplification.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    3/81/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. A4

    Simplify 3/9 fully. (2 points)

    Reveal explanation

    Answer: 1/3

    Divide numerator and denominator by their greatest common factor 3. The equivalent simplest fraction is 1/3.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    3/9
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. A5

    A student answers the following question with “9”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Complete the equivalent fraction: 2/8 = ?/32. (3 points)

    Reveal explanation

    Answer: 8

    The suggested answer is not correct. Subdivide each of the 8 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 2/8 = 8/32.

    Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.

    2/88/32
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  6. A6

    Calculate 7/8 − 1/8. Give the answer in simplest form. (2 points)

    Reveal explanation

    Answer: 3/4

    Both fractions use 8ths. 7 − 1 pieces make 3/4 of a whole after simplification.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    7/81/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  7. A7

    Compare 3/4 and 7/8. Write > or < and justify using equal parts. (2 points)

    Reveal explanation

    Answer: <

    Rename as 6/8 and 7/8. Compare numerators: 3/4 < 7/8.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    3/47/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  8. A8

    Compare 2/3 and 7/8. Write > or < and justify using equal parts. (2 points)

    Reveal explanation

    Answer: <

    Rename as 16/24 and 21/24. Compare numerators: 2/3 < 7/8.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    2/37/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  9. A9

    A student answers the following question with “6/8”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Simplify 10/16 fully. (3 points)

    Reveal explanation

    Answer: 5/8

    The suggested answer is not correct. Divide numerator and denominator by their greatest common factor 2. The equivalent simplest fraction is 5/8.

    Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.

    10/16
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  10. A10

    Draw or explain why 1/5 and 4/20 represent the same amount. (3 points)

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 5 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 1/5 = 4/20.

    Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.

    1/54/20
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  11. A11

    Complete the equivalent fraction: 7/10 = ?/30. (2 points)

    Reveal explanation

    Answer: 21

    Subdivide each of the 10 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 7/10 = 21/30.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    7/1021/30
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  12. A12

    Compare 4/6 and 4/5. Write > or < and justify using equal parts. (2 points)

    Reveal explanation

    Answer: <

    Rename as 20/30 and 24/30. Compare numerators: 4/6 < 4/5.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    4/64/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  13. A13

    A student answers the following question with “<”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Compare 5/8 and 3/8. Write > or < and justify using equal parts. (3 points)

    Reveal explanation

    Answer: >

    The suggested answer is not correct. Rename as 5/8 and 3/8. Compare numerators: 5/8 > 3/8.

    Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.

    5/83/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  14. A14

    Find 1/5 + 1/10; rename parts and simplify. (2 points)

    Reveal explanation

    Answer: 3/10

    First rename 1/5 as 2/10. Add 1/10 to get 3/10 = 3/10.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    1/51/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  15. A15

    Draw or explain why 8/12 and 16/24 represent the same amount. (3 points)

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 12 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 8/12 = 16/24.

    Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.

    8/1216/24
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  16. A16

    Complete the equivalent fraction: 5/8 = ?/32. (2 points)

    Reveal explanation

    Answer: 20

    Subdivide each of the 8 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 5/8 = 20/32.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    5/820/32
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  17. A17

    A student answers the following question with “12/10”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Find 3/5 + 5/10; rename parts and simplify. (3 points)

    Reveal explanation

    Answer: 11/10

    The suggested answer is not correct. First rename 3/5 as 6/10. Add 5/10 to get 11/10 = 11/10.

    Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.

    3/55/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  18. A18

    Calculate 3/5 + 2/5. Give the answer in simplest form. (2 points)

    Reveal explanation

    Answer: 1

    Both fractions use 5ths. 3 + 2 pieces make 1 of a whole after simplification.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    3/52/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  19. A19

    Simplify 6/12 fully. (2 points)

    Reveal explanation

    Answer: 1/2

    Divide numerator and denominator by their greatest common factor 6. The equivalent simplest fraction is 1/2.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    6/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  20. A20

    Draw or explain why 5/6 and 20/24 represent the same amount. (3 points)

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 6 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 5/6 = 20/24.

    Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.

    5/620/24
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  21. A21

    A student answers the following question with “5/5”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Simplify 24/30 fully. (3 points)

    Reveal explanation

    Answer: 4/5

    The suggested answer is not correct. Divide numerator and denominator by their greatest common factor 6. The equivalent simplest fraction is 4/5.

    Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.

    24/30
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  22. A22

    Compare 2/10 and 7/10. Write > or < and justify using equal parts. (2 points)

    Reveal explanation

    Answer: <

    Rename as 2/10 and 7/10. Compare numerators: 2/10 < 7/10.

    Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.

    2/107/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  23. A23

    Explain why reducing 6/12 by dividing numerator and denominator by 3 preserves the value. (3 points)

    Reveal explanation

    Answer: 2/4

    Grouping numerator and denominator into threes gives 2/4; both represent the same share of the same whole.

    Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.

  24. A24

    A student changes 2/9 to 4/9 and says the fractions are equivalent. Is this correct? Give the correct denominator if the numerator doubles. (3 points)

    Reveal explanation

    Answer: 4/18

    No. Both numerator and denominator must be multiplied by 2 to preserve the same portion: 2/9 = 4/18.

    Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.

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