OC fractions on a number line: 10 practice questions

Quick Answer

To read a fraction on a number line, count the equal spaces between 0 and 1 to get the denominator, then count the spaces from 0 to the point to get the numerator. This page from Braintree Coaching Australia has ten original questions for Year 3–4 children preparing for the NSW Opportunity Class (OC) test, two worked models, and a reason for every wrong option. It is free, needs no sign-up, and takes about 25 minutes including review.

Who is this fraction practice for?

This set suits a Year 3 or Year 4 child who can name simple fractions such as 1/2 and 3/4 and is starting to meet fractions greater than 1. It is skill practice for mathematical reasoning. It is not a copy of official test items, and we do not claim a question like these will appear on the real test.

The NSW Department of Education describes the Opportunity Class Placement Test as a computer-based test with three sections: Reading, Mathematical Reasoning and Thinking Skills. All questions are multiple choice. The department's own OC practice tests are the place to see the real format.

How do you place a fraction on a number line? Two worked models

Model 1: count spaces, not marks

A number line runs from 0 to 1. It is cut into 4 equal parts, so it has 5 tick marks (including the marks at 0 and 1). Point P sits on the first tick mark after 0.

1. Count the equal spaces between 0 and 1. There are 4, so each space is one quarter.
2. Count the spaces from 0 to P. There is 1.
3. P is at 1/4.

A child who counts tick marks gets 5 and writes 1/5. The marks are the fence posts. The fractions measure the gaps between them.

Model 2: fractions past 1

A number line runs from 0 to 2. Each whole is cut into 2 equal parts. Point Q sits on the third tick mark after 0.

1. Look at one whole only (0 to 1). It has 2 equal spaces, so each space is one half.
2. Count spaces from 0 to Q. There are 3.
3. Q is at 3/2, which is the same as 1 1/2.

The trap here is counting all 4 spaces on the line and writing 3/4. The denominator comes from one whole, not from the length of the line you happen to be shown.

The questions

Work on paper. Draw the number line each time, even if you think you can see the answer.

Question 1. A number line from 0 to 1 is cut into 4 equal parts. Point P is on the third tick mark after 0. Where is P?

• A. 3/5
• B. 1/3
• C. 3/4
• D. 3/3

Question 2. A number line from 0 to 1 is cut into 5 equal parts. Point Q is on the second tick mark after 0. Where is Q?

• A. 2/5
• B. 2/6
• C. 2/4
• D. 1/2

Question 3. A number line runs from 0 to 2. Each whole is cut into 3 equal parts. Point R is on the fourth tick mark after 0. Where is R?

• A. 4/6
• B. 1 1/4
• C. 3/4
• D. 1 1/3

Question 4. Which fraction is closer to 1 on a number line: 5/6 or 7/8?

• A. 5/6
• B. 7/8
• C. They are the same distance from 1
• D. It is impossible to tell

Question 5. A number line shows only three marks: 0, 1/2 and 1. Point S is exactly halfway between 1/2 and 1. Where is S?

• A. 2/3
• B. 3/4
• C. 1/4
• D. 1 1/2

Question 6. A number line from 0 to 1 is cut into 10 equal parts. Point T is on the sixth tick mark after 0. Which fraction is at the same place as T?

• A. 3/5
• B. 6/11
• C. 1/6
• D. 2/3

Question 7. Which list shows 1/2, 3/8 and 3/4 in order from left to right on a number line?

• A. 1/2, 3/4, 3/8
• B. 3/4, 1/2, 3/8
• C. 3/8, 1/2, 3/4
• D. 3/8, 3/4, 1/2

Question 8. A number line shows the section from 2 to 3. It is cut into 4 equal parts. Point V is on the first tick mark after 2. Where is V?

• A. 1/4
• B. 2 1/5
• C. 2 1/2
• D. 2 1/4

Question 9. A frog starts at 0 on a number line. Each jump is 2/5 long. Where is the frog after 3 jumps?

• A. 6/15
• B. 1 1/5
• C. 1 2/5
• D. 3/5

Question 10. Point W is at 2/3 and point X is at 5/6 on the same number line. How far apart are they?

• A. 1/6
• B. 3/3
• C. 3/6
• D. 1/3

Answers and worked explanations

Check one question at a time. For each wrong answer, find the option your child chose and read why it is tempting.

Question 1: C, 3/4. Four equal spaces make quarters. P is three spaces from 0. Option A (3/5) counts the 5 tick marks. Option B (1/3) uses the 3 as the denominator. Option D (3/3) equals 1, which is the far end of the line.

Question 2: A, 2/5. Five equal spaces make fifths, and Q is two spaces along. Option B (2/6) counts 6 tick marks. Option C (2/4) leaves out one space. Option D (1/2) is a guess from "about the middle"; half of 5 spaces would be 2 1/2 spaces along.

Question 3: D, 1 1/3. Each whole has 3 spaces, so each space is one third. Four spaces from 0 is 4/3, which is 1 1/3. Option A (4/6) treats the whole line from 0 to 2 as one whole. Option B (1 1/4) uses the 4 from "fourth mark" as the denominator. Option C (3/4) swaps the two numbers.

Question 4: B, 7/8. 5/6 is 1/6 away from 1. 7/8 is 1/8 away from 1. An eighth is smaller than a sixth, so 7/8 is closer. Option A is chosen by children who think a smaller denominator always means a bigger fraction. Option C comes from noticing both are "one part short" without comparing the size of the part. Option D gives up too early: changing both fractions to twenty-fourths (20/24 and 21/24) settles it.

Question 5: B, 3/4. The gap from 1/2 to 1 is one half. Half of that gap is one quarter. 1/2 + 1/4 = 3/4. Option A (2/3) is a common guess for "between a half and one". Option C (1/4) gives the size of the step, not the position. Option D (1 1/2) adds a half to 1 instead of to 1/2.

Question 6: A, 3/5. T is at 6/10. Dividing the top and bottom by 2 gives 3/5, so 6/10 and 3/5 share one spot on the line. Option B (6/11) counts 11 tick marks. Option C (1/6) reads "sixth mark" as one sixth. Option D (2/3) is close in size (about 0.67) but is not equal to 0.6.

Question 7: C, 3/8, 1/2, 3/4. Change all three to eighths: 1/2 = 4/8 and 3/4 = 6/8. In order: 3/8, 4/8, 6/8. Option A puts 3/8 last because 8 is the biggest denominator. Option B is the correct order backwards (right to left). Option D places 3/4 before 1/2.

Question 8: D, 2 1/4. The section from 2 to 3 is one whole cut into 4 spaces, so each space is one quarter. One space after 2 is 2 1/4. Option A (1/4) forgets the line starts at 2. Option B (2 1/5) counts 5 tick marks. Option C (2 1/2) is the middle of the section, two spaces along.

Question 9: B, 1 1/5. Three jumps of 2/5 is 2/5 + 2/5 + 2/5 = 6/5. Five fifths make 1, with one fifth left over: 1 1/5. Option A (6/15) multiplies the denominator by 3 as well. Option C (1 2/5) is 7/5, one fifth too far. Option D (3/5) counts the jumps but forgets each jump is two fifths long.

Question 10: A, 1/6. Change 2/3 to sixths: 2/3 = 4/6. Then 5/6 − 4/6 = 1/6. Option B (3/3) subtracts top from top and bottom from bottom (5 − 2 and 6 − 3). Option C (3/6) subtracts the numerators only. Option D (1/3) is the size of one third, not the gap between the points.

What mistake patterns should we look for?

Tally which kind of error came up. Each one needs a different fix.

Pattern	Seen in	What to practise next
Counted tick marks instead of spaces	Questions 1, 2, 6, 8	Draw lines and number the spaces, not the marks
Lost track of which whole the line shows	Questions 3, 8	Circle one whole (0 to 1, or 2 to 3) before counting
Compared denominators only	Questions 4, 7	Change fractions to the same denominator first
Did arithmetic on tops and bottoms separately	Questions 9, 10	Say the fraction in words: "two fifths and two fifths"

Can my child try the skill on a new task?

Draw a number line from 0 to 2 and cut each whole into quarters. Mark these three points: 3/4, 1 1/2 and 5/4.

Self-check: counting tick marks after 0, 3/4 is on the third mark, 5/4 is on the fifth mark and 1 1/2 is on the sixth mark. If 5/4 landed on the fifth mark between 0 and 1, go back to Model 2.

What should we do after this set?

• If two or more answers showed the same pattern in the table, repeat only those questions tomorrow with new numbers. Do not sit a full test yet.
• For mixed OC practice with worked solutions, open the OC practice tests guide.
• For full papers to sit under time, see the OC past papers page.
• The free mock tests need a free classroom account. Create one only when your child is ready for a timed sitting.
• If you want a structured set of full OC tests after that, see what the OC course includes and check it matches your child's entry year before buying.

Sources and review

Official source (checked 2026-10-05): NSW Department of Education, Opportunity Class practice tests: the test is computer-based with three multiple-choice sections (Reading, Mathematical Reasoning, Thinking Skills).

Where the questions came from: all ten questions and both models are original Braintree Coaching Australia material written for this page. None is taken from an official or third-party paper.

Author: James Rush, content writer, Braintree Coaching Australia.

Answer check: every answer was solved a second time, independently of the author, before publication. A named teacher review has not yet been recorded for this set. If you find an error, please tell us.

Last updated: 2026-10-05.