3B · Chapter 9 · consolidation
Practice
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.
- A1
A same-sized whole is split into 3 equal parts and 2 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 2/3
The denominator counts all 3 equal parts; the numerator counts the 2 shaded parts. In simplest form this is 2/3.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A2
Between 0 and 1, a line is split into 5 equal intervals. What fraction is at the 3rd tick after 0?
Reveal explanation
Answer: 3/5
Each interval represents 1/5. Moving 3 intervals from zero reaches 3/5, or 3/5 in simplest form.
An interval from zero to one divided into equal segments. - A3
Compare 1/5 and 2/5. Write > or <.
Reveal explanation
Answer: <
Both fractions use pieces of size 1/5, so compare 1 pieces with 2 pieces: 1/5 < 2/5.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A4
Compare 1/6 and 1/12. Write > or <.
Reveal explanation
Answer: >
There are 1 pieces in each fraction, but 1/6 is a larger piece than 1/12 when the whole is identical.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A5
A same-sized whole is split into 8 equal parts and 1 part is shaded. What fraction is shaded?
Reveal explanation
Answer: 1/8
The denominator counts all 8 equal parts; the numerator counts the 1 shaded parts. In simplest form this is 1/8.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A6
Between 0 and 1, a line is split into 8 equal intervals. What fraction is at the 5th tick after 0?
Reveal explanation
Answer: 5/8
Each interval represents 1/8. Moving 5 intervals from zero reaches 5/8, or 5/8 in simplest form.
An interval from zero to one divided into equal segments. - A7
Compare 5/10 and 3/10. Write > or <.
Reveal explanation
Answer: >
Both fractions use pieces of size 1/10, so compare 5 pieces with 3 pieces: 5/10 > 3/10.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A8
Compare 4/10 and 4/12. Write > or <.
Reveal explanation
Answer: >
There are 4 pieces in each fraction, but 1/10 is a larger piece than 1/12 when the whole is identical.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A9
A same-sized whole is split into 12 equal parts and 7 parts are shaded. What fraction is shaded?
Reveal explanation
Answer: 7/12
The denominator counts all 12 equal parts; the numerator counts the 7 shaded parts. In simplest form this is 7/12.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A10
Between 0 and 1, a line is split into 3 equal intervals. What fraction is at the 2nd tick after 0?
Reveal explanation
Answer: 2/3
Each interval represents 1/3. Moving 2 intervals from zero reaches 2/3, or 2/3 in simplest form.
An interval from zero to one divided into equal segments. - A11
Compare 5/10 and 9/10. Write > or <.
Reveal explanation
Answer: <
Both fractions use pieces of size 1/10, so compare 5 pieces with 9 pieces: 5/10 < 9/10.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A12
Compare 2/5 and 2/10. Write > or <.
Reveal explanation
Answer: >
There are 2 pieces in each fraction, but 1/5 is a larger piece than 1/10 when the whole is identical.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A13
A same-sized whole is split into 3 equal parts and 1 part is shaded. What fraction is shaded?
Reveal explanation
Answer: 1/3
The denominator counts all 3 equal parts; the numerator counts the 1 shaded parts. In simplest form this is 1/3.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A14
Between 0 and 1, a line is split into 4 equal intervals. What fraction is at the 1st tick after 0?
Reveal explanation
Answer: 1/4
Each interval represents 1/4. Moving 1 intervals from zero reaches 1/4, or 1/4 in simplest form.
An interval from zero to one divided into equal segments. - A15
Compare 2/4 and 1/4. Write > or <.
Reveal explanation
Answer: >
Both fractions use pieces of size 1/4, so compare 2 pieces with 1 pieces: 2/4 > 1/4.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A16
Compare 1/8 and 1/12. Write > or <.
Reveal explanation
Answer: >
There are 1 pieces in each fraction, but 1/8 is a larger piece than 1/12 when the whole is identical.
Each full bar represents the same-sized whole; shaded parts show the fraction. - A17
A student marks 1/7 at the first tick on a 0-to-1 line but drew only 6 equal intervals. Explain and correct the model.
Reveal explanation
Answer: 7 equal intervals
To show 1/7, the full unit length must be divided into 7 equal intervals, not 6.
- A18
A ribbon is split into 7 equal pieces; 5 are colored. Another ribbon is twice as long but also has 5 colored of 7 equal pieces. Are the colored lengths equal?
Reveal explanation
Answer: No
Equal fractions of differently sized wholes need not represent equal physical lengths.