Let’s solve each problem step by step.
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Problem 1: Find the equivalent fraction of 2/3 using the number lines.
We are given two number lines:
- Top line: marked in thirds → 0, 1/3, 2/3, 3/3 (which is 1), etc.
- Bottom line: marked in twelfths → 0, 1/12, 2/12, ..., up to 12/12.
We need to find what fraction on the bottom line matches 2/3 on the top line.
Look at where 2/3 is on the top line — it’s the second mark after 0.
Now look directly below that point on the bottom line. What fraction is there?
Count the marks on the bottom line:
From 0 to 2/3, how many twelfths?
Since 1 whole = 12/12, then 1/3 = 4/12 (because 12 ÷ 3 = 4).
So 2/3 = 2 × 4/12 =
8/12.
✔ So, 2/3 = 8/12.
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Problem 2: Find the equivalent fraction of 2/4 using the number lines.
Top line: marked in fourths → 0, 1/4, 2/4, 3/4, 4/4.
Bottom line: marked in eighths → 0, 1/8, 2/8, ..., 8/8.
Where is 2/4 on the top line? It’s halfway between 0 and 1.
Look directly below that point on the bottom line — what fraction is there?
Since 1/4 = 2/8 (because 8 ÷ 4 = 2), then 2/4 = 2 × 2/8 =
4/8.
Also, you can see visually: 2/4 is the same as 1/2, and 4/8 is also 1/2.
✔ So, 2/4 = 4/8.
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Problem 3: Find the equivalent fraction of 2/6 using the number lines.
Top line: marked in sixths → 0, 1/6, 2/6, 3/6, ..., 6/6.
Bottom line: marked in thirds → 0, 1/3, 2/3, 3/3.
Where is 2/6 on the top line? It’s the second mark after 0.
Look directly below that point on the bottom line — what fraction is there?
Note: 2/6 simplifies to 1/3 (divide numerator and denominator by 2).
On the bottom line, 1/3 is the first mark after 0.
Visually, 2/6 lines up with 1/3.
✔ So, 2/6 = 1/3.
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Final Answer:
1. 8/12
2. 4/8
3. 1/3
Parent Tip: Review the logic above to help your child master the concept of identifying fractions on a number line worksheet.
