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3B · Chapter 10 · consolidation

Practice B

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 4/5 and 16/20 represent the same amount.

    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 4/5 = 16/20.

    4/516/20
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. A2

    Complete the equivalent fraction: 4/12 = ?/48.

    Reveal explanation

    Answer: 16

    Subdivide each of the 12 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 4/12 = 16/48.

    4/1216/48
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. A3

    Simplify 8/12 fully.

    Reveal explanation

    Answer: 2/3

    Divide numerator and denominator by their greatest common factor 4. The equivalent simplest fraction is 2/3.

    8/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. A4

    Compare 2/6 and 1/10. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 10/30 and 3/30. Compare numerators: 2/6 > 1/10.

    2/61/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. A5

    Compare 7/10 and 2/5. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 7/10 and 4/10. Compare numerators: 7/10 > 2/5.

    7/102/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  6. A6

    Calculate 2/6 + 2/6. Give the answer in simplest form.

    Reveal explanation

    Answer: 2/3

    Both fractions use 6ths. 2 + 2 pieces make 2/3 of a whole after simplification.

    2/62/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  7. A7

    Find 1/3 + 3/6; rename parts and simplify.

    Reveal explanation

    Answer: 5/6

    First rename 1/3 as 2/6. Add 3/6 to get 5/6 = 5/6.

    1/33/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  8. A8

    Draw or explain why 7/8 and 14/16 represent the same amount.

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 8 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 7/8 = 14/16.

    7/814/16
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  9. A9

    Complete the equivalent fraction: 4/5 = ?/15.

    Reveal explanation

    Answer: 12

    Subdivide each of the 5 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 4/5 = 12/15.

    4/512/15
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  10. A10

    Simplify 3/15 fully.

    Reveal explanation

    Answer: 1/5

    Divide numerator and denominator by their greatest common factor 3. The equivalent simplest fraction is 1/5.

    3/15
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  11. A11

    Compare 2/4 and 6/8. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: <

    Rename as 4/8 and 6/8. Compare numerators: 2/4 < 6/8.

    2/46/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  12. A12

    Compare 2/6 and 6/9. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: <

    Rename as 6/18 and 12/18. Compare numerators: 2/6 < 6/9.

    2/66/9
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  13. A13

    Calculate 3/5 − 1/5. Give the answer in simplest form.

    Reveal explanation

    Answer: 2/5

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

    3/51/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  14. A14

    Find 1/2 + 2/4; rename parts and simplify.

    Reveal explanation

    Answer: 1

    First rename 1/2 as 2/4. Add 2/4 to get 4/4 = 1.

    1/22/4
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  15. A15

    Draw or explain why 2/4 and 8/16 represent the same amount.

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 4 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 2/4 = 8/16.

    2/48/16
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  16. A16

    Complete the equivalent fraction: 5/6 = ?/12.

    Reveal explanation

    Answer: 10

    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.
  17. A17

    Explain why reducing 6/15 by dividing numerator and denominator by 3 preserves the value.

    Reveal explanation

    Answer: 2/5

    Grouping numerator and denominator into threes gives 2/5; both represent the same share of the same whole.

  18. A18

    A student changes 2/5 to 4/5 and says the fractions are equivalent. Is this correct? Give the correct denominator if the numerator doubles.

    Reveal explanation

    Answer: 4/10

    No. Both numerator and denominator must be multiplied by 2 to preserve the same portion: 2/5 = 4/10.

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