Reference / Curriculum / 3B / Chapter 10

3B · Chapter 10 · consolidation

Practice A

Original cumulative chapter practice to consolidate taught ideas.

Original cumulative chapter practice to consolidate taught ideas. Solutions are available as revealable feedback and in a separate complete answer key. No answer submissions or accounts are required.

Assessment · 18 questions

Questions

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

  1. A1

    Draw or explain why 3/10 and 9/30 represent the same amount.

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 10 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 3/10 = 9/30.

    3/109/30
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. A2

    Complete the equivalent fraction: 3/4 = ?/16.

    Reveal explanation

    Answer: 12

    Subdivide each of the 4 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 3/4 = 12/16.

    3/412/16
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. A3

    Simplify 4/32 fully.

    Reveal explanation

    Answer: 1/8

    Divide numerator and denominator by their greatest common factor 4. The equivalent simplest fraction is 1/8.

    4/32
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. A4

    Compare 3/6 and 4/10. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 15/30 and 12/30. Compare numerators: 3/6 > 4/10.

    3/64/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. A5

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

    Reveal explanation

    Answer: >

    Rename as 21/28 and 8/28. Compare numerators: 3/4 > 2/7.

    3/42/7
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  6. A6

    Draw or explain why 2/6 and 4/12 represent the same amount.

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 6 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 2/6 = 4/12.

    2/64/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  7. A7

    Complete the equivalent fraction: 2/4 = ?/12.

    Reveal explanation

    Answer: 6

    Subdivide each of the 4 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 2/4 = 6/12.

    2/46/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  8. A8

    Simplify 8/20 fully.

    Reveal explanation

    Answer: 2/5

    Divide numerator and denominator by their greatest common factor 4. The equivalent simplest fraction is 2/5.

    8/20
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  9. A9

    Compare 6/8 and 1/10. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 30/40 and 4/40. Compare numerators: 6/8 > 1/10.

    6/81/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  10. A10

    Compare 5/10 and 3/9. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 45/90 and 30/90. Compare numerators: 5/10 > 3/9.

    5/103/9
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  11. A11

    Draw or explain why 5/6 and 10/12 represent the same amount.

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 6 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 5/6 = 10/12.

    5/610/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  12. A12

    Complete the equivalent fraction: 2/5 = ?/20.

    Reveal explanation

    Answer: 8

    Subdivide each of the 5 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 2/5 = 8/20.

    2/58/20
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  13. A13

    Simplify 27/36 fully.

    Reveal explanation

    Answer: 3/4

    Divide numerator and denominator by their greatest common factor 9. The equivalent simplest fraction is 3/4.

    27/36
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  14. A14

    Compare 2/5 and 8/10. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: <

    Rename as 4/10 and 8/10. Compare numerators: 2/5 < 8/10.

    2/58/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  15. A15

    Compare 4/5 and 8/9. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: <

    Rename as 36/45 and 40/45. Compare numerators: 4/5 < 8/9.

    4/58/9
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  16. A16

    Draw or explain why 1/10 and 4/40 represent the same amount.

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 10 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 1/10 = 4/40.

    1/104/40
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  17. A17

    Explain why reducing 6/21 by dividing numerator and denominator by 3 preserves the value.

    Reveal explanation

    Answer: 2/7

    Grouping numerator and denominator into threes gives 2/7; both represent the same share of the same whole.

  18. A18

    A student changes 2/7 to 4/7 and says the fractions are equivalent. Is this correct? Give the correct denominator if the numerator doubles.

    Reveal explanation

    Answer: 4/14

    No. Both numerator and denominator must be multiplied by 2 to preserve the same portion: 2/7 = 4/14.

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