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3B · Chapter 10 · review

Chapter review

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 · 26 questions

Questions

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

  1. A1

    Draw or explain why 3/6 and 6/12 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 3/6 = 6/12.

    3/66/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  2. A2

    Complete the equivalent fraction: 4/10 = ?/30.

    Reveal explanation

    Answer: 12

    Subdivide each of the 10 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 4/10 = 12/30.

    4/1012/30
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  3. A3

    Simplify 14/24 fully.

    Reveal explanation

    Answer: 7/12

    Divide numerator and denominator by their greatest common factor 2. The equivalent simplest fraction is 7/12.

    14/24
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  4. A4

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

    Reveal explanation

    Answer: >

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

    7/83/4
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  5. A5

    Compare 2/8 and 7/12. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: <

    Rename as 6/24 and 14/24. Compare numerators: 2/8 < 7/12.

    2/87/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  6. A6

    Calculate 1/6 + 3/6. Give the answer in simplest form.

    Reveal explanation

    Answer: 2/3

    Both fractions use 6ths. 1 + 3 pieces make 2/3 of a whole after simplification.

    1/63/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  7. A7

    Find 1/2 + 3/4; rename parts and simplify.

    Reveal explanation

    Answer: 5/4

    First rename 1/2 as 2/4. Add 3/4 to get 5/4 = 5/4.

    1/23/4
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  8. A8

    Draw or explain why 3/5 and 9/15 represent the same amount.

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 5 equal parts into 3 pieces. That multiplies shaded parts and total parts by 3, so 3/5 = 9/15.

    3/59/15
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  9. A9

    Complete the equivalent fraction: 1/3 = ?/12.

    Reveal explanation

    Answer: 4

    Subdivide each of the 3 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 1/3 = 4/12.

    1/34/12
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  10. A10

    Simplify 6/8 fully.

    Reveal explanation

    Answer: 3/4

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

    6/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  11. A11

    Compare 2/3 and 2/6. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 4/6 and 2/6. Compare numerators: 2/3 > 2/6.

    2/32/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  12. A12

    Compare 1/4 and 7/9. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: <

    Rename as 9/36 and 28/36. Compare numerators: 1/4 < 7/9.

    1/47/9
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  13. A13

    Calculate 5/10 − 4/10. Give the answer in simplest form.

    Reveal explanation

    Answer: 1/10

    Both fractions use 10ths. 5 − 4 pieces make 1/10 of a whole after simplification.

    5/104/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  14. A14

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

    Reveal explanation

    Answer: 3/4

    First rename 1/2 as 2/4. Add 1/4 to get 3/4 = 3/4.

    1/21/4
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  15. A15

    Draw or explain why 7/8 and 28/32 represent the same amount.

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 8 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 7/8 = 28/32.

    7/828/32
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  16. A16

    Complete the equivalent fraction: 1/3 = ?/6.

    Reveal explanation

    Answer: 2

    Subdivide each of the 3 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 1/3 = 2/6.

    1/32/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  17. A17

    Simplify 18/24 fully.

    Reveal explanation

    Answer: 3/4

    Divide numerator and denominator by their greatest common factor 6. The equivalent simplest fraction is 3/4.

    18/24
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  18. A18

    Compare 1/8 and 5/8. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: <

    Rename as 1/8 and 5/8. Compare numerators: 1/8 < 5/8.

    1/85/8
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  19. A19

    Compare 4/5 and 3/7. Write > or < and justify using equal parts.

    Reveal explanation

    Answer: >

    Rename as 28/35 and 15/35. Compare numerators: 4/5 > 3/7.

    4/53/7
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  20. A20

    Calculate 2/5 + 2/5. Give the answer in simplest form.

    Reveal explanation

    Answer: 4/5

    Both fractions use 5ths. 2 + 2 pieces make 4/5 of a whole after simplification.

    2/52/5
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  21. A21

    Find 2/3 + 5/6; rename parts and simplify.

    Reveal explanation

    Answer: 3/2

    First rename 2/3 as 4/6. Add 5/6 to get 9/6 = 3/2.

    2/35/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  22. A22

    Draw or explain why 4/5 and 8/10 represent the same amount.

    Reveal explanation

    Answer: They are equal

    Subdivide each of the 5 equal parts into 2 pieces. That multiplies shaded parts and total parts by 2, so 4/5 = 8/10.

    4/58/10
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  23. A23

    Complete the equivalent fraction: 1/8 = ?/32.

    Reveal explanation

    Answer: 4

    Subdivide each of the 8 equal parts into 4 pieces. That multiplies shaded parts and total parts by 4, so 1/8 = 4/32.

    1/84/32
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  24. A24

    Simplify 4/6 fully.

    Reveal explanation

    Answer: 2/3

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

    4/6
    Each full bar represents the same-sized whole; shaded parts show the fraction.
  25. A25

    Explain why reducing 6/24 by dividing numerator and denominator by 3 preserves the value.

    Reveal explanation

    Answer: 2/8

    Grouping numerator and denominator into threes gives 2/8; both represent the same share of the same whole.

  26. A26

    A student changes 2/8 to 4/8 and says the fractions are equivalent. Is this correct? Give the correct denominator if the numerator doubles.

    Reveal explanation

    Answer: 4/16

    No. Both numerator and denominator must be multiplied by 2 to preserve the same portion: 2/8 = 4/16.

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