Solved Exercises on Fractions on a Number Line Worksheet with Answers in Grade 3

Comprehensive practice worksheet on fractions on a number line: solving various problems with detailed solutions and visual aids.

Complete Summary: Fractions on a Number Line

Definitions

Fraction: A number that represents a part of a whole. It has a numerator (top number) and a denominator (bottom number).

Number Line: A straight line with numbers placed at equal intervals, showing the position of numbers.

Fraction on Number Line: A way to show fractions visually by placing them at specific points on a number line.

Unit Fraction: A fraction with numerator 1 (like 14).

Equivalent Fractions: Fractions that have different numerators and denominators but represent the same value.

Position Value: The position of a fraction on the number line corresponds to its value relative to other numbers.

Core Rules and Laws

Denominator Rule: The denominator tells how many equal parts to divide the interval between 0 and 1 into.

Numerator Rule: The numerator tells how many parts to count from 0.

Equal Spacing Rule: All parts on the number line must be the same size.

Position Rule: Fractions farther from 0 have greater values.

Whole Equals One: When the numerator equals the denominator, the fraction equals 1.

Zero Rule: When the numerator is 0, the fraction equals 0.

Step-by-Step Method

  1. Identify the fraction: Determine the numerator and denominator
  2. Draw the number line: Mark 0 and 1 with equal spacing
  3. Divide the interval: Split the space between 0 and 1 into equal parts based on the denominator
  4. Count segments: Move from 0 by the number of segments equal to the numerator
  5. Mark the point: Place a dot at the calculated position
  6. Label the point: Write the fraction at the marked location

Examples (Simple to Advanced)

Simple: 12 → Divide line into 2 parts, count 1 from 0

Intermediate: 34 → Divide line into 4 parts, count 3 from 0

Advanced: Mixed numbers like 112 → Go to 1, then divide next segment into 2 parts, count 1

Tips, Tricks, and Common Pitfalls

Tips: Always divide into equal parts, use a ruler for accuracy, start counting from 0.

Tricks: Equivalent fractions share the same position on the number line.

Common Pitfalls: Unequal segment spacing, counting from wrong starting point, confusing numerator and denominator.

Key Notes for Memorization

Memory Aid: "Divide by bottom, count by top" - denominator first, then numerator.

Visual Memory: Fractions are points on the line, not the spaces between marks.

Quick Check: The fraction ab is located at (a÷b)×100% of the distance from 0 to 1.

Practice Worksheet: Fractions on a Number Line

Exercise 1: Plot 13 on the number line below:

0
1/3
2/3
1
1/3

Answer: The point is located at one-third of the distance from 0 to 1

Exercise 2: Which fraction is larger: 25 or 35? Use the number line to compare.

0
1/5
2/5
3/5
4/5
1
2/5
3/5

Answer: 35 is larger because it is farther from 0 on the number line

Exercise 3: Show that 24 and 12 are equivalent using number lines.

0
1/4
2/4
3/4
1
2/4
0
1/2
1
1/2

Answer: Both fractions are located at the same position (50%) on their respective number lines, proving they are equivalent

Exercise 4: Plot the mixed number 134 on a number line from 0 to 2.

0
1/4
2/4
3/4
1
1 1/4
1 2/4
1 3/4
2
1 3/4

Answer: The point is located at 1.75, which is 3/4 of the way from 1 to 2

Exercise 5: Compare 46 and 23 using number lines.

0
1/6
2/6
3/6
4/6
5/6
1
4/6
0
1/3
2/3
1
2/3

Answer: Both fractions are equivalent since they occupy the same position (66.67%) on their respective number lines

Solution: Exercises 1 to 3
1 Basic Fraction Placement
Exercise 1
Plot 25 on a number line from 0 to 1.
Definition:

Fraction placement: A fraction ab is placed by dividing the number line from 0 to 1 into b equal parts and counting a parts from 0.

0
1/5
2/5
3/5
4/5
1
2/5
Method for placing fractions on number lines:
  1. Draw a line from 0 to 1 with equal spacing
  2. Divide the line into equal parts based on the denominator (5 parts)
  3. Count the number of parts from 0 based on the numerator (2 parts)
  4. Mark the point at the counted position
Step 1: Identify the fraction: 25
Step 2: Divide the number line into 5 equal parts
Step 3: Count 2 parts from 0
Step 1: Read the fraction

25 means 2 parts out of 5 equal parts

Step 2: Divide the line

Split the line from 0 to 1 into 5 equal segments

Step 3: Count from 0

Move 2 segments from 0 (the second mark)

Step 4: Mark the position

Place a point at the second division mark

25 is located at 40% of the distance from 0 to 1
Final answer:

25 is marked at the second fifth on the number line

Applied rules:

• Denominator rule: Tells how many equal parts to divide the whole

• Numerator rule: Tells how many parts to count from 0

• Equal spacing: Each segment must be exactly the same size

2 Comparing Fractions
Exercise 2
Which fraction is larger: 34 or 23? Use number lines to compare.
Definition:

Comparing fractions: Determining which fraction is larger by their positions on a number line, where the fraction farther from 0 is greater.

0
1/4
2/4
3/4
1
3/4
0
1/3
2/3
1
2/3
Step 1: Draw separate number lines

Create one line divided into 4 parts for 34 and another into 3 parts for 23

Step 2: Place each fraction

34 goes at the 3rd mark (75%), 23 goes at the 2nd mark (66.67%)

Step 3: Compare positions

Since 75% > 66.67%, 34 is farther from 0

Step 4: Draw conclusion

Therefore 34 > 23

34 > 23
Final answer:

34 is larger than 23

Applied rules:

• Position comparison: The fraction farther from 0 is greater

• Equivalent fractions: Fractions at the same position represent the same value

• Cross multiplication: ab vs cd → compare a×d vs b×c

3 Equivalent Fractions
Exercise 3
Show that 12, 24, and 36 are equivalent using number lines.
Definition:

Equivalent fractions: Different fractions that represent the same value and occupy the same position on a number line.

0
1/2
1
1/2
0
1/4
2/4
3/4
1
2/4
0
1/6
2/6
3/6
4/6
5/6
1
3/6
Step 1: Draw three separate number lines

One divided into 2 parts, one into 4 parts, one into 6 parts

Step 2: Place each fraction

12 at 50%, 24 at 50%, 36 at 50%

Step 3: Observe the positions

All three fractions are located at the exact same position (50%)

Step 4: Conclude equivalence

Since all fractions share the same position, they are equivalent

12 = 24 = 36
Final answer:

12, 24, and 36 are equivalent fractions

Applied rules:

• Equivalent fractions rule: Same position on number line means same value

• Simplification: 24 simplifies to 12 by dividing numerator and denominator by 2

• Multiplication rule: Multiply numerator and denominator by same number to get equivalent fraction

Rules and methods, laws,...
ab = a×nb×n
Equivalent Fractions
Rule 1
12 of n = n ÷ 2
Half of a number
Rule 2
13 of n = n ÷ 3
Third of a number
Rule 3
nn of m = m
All of a number
Key definitions:

Numerator: The top number in a fraction (how many parts taken)

Denominator: The bottom number in a fraction (total equal parts)

Whole number: Any positive integer including zero

Equivalent: Having the same value despite different appearance

Complete methodology:
  1. Identify the fraction: Determine numerator and denominator
  2. Draw the number line: Mark 0 and 1 with equal spacing
  3. Divide the interval: Split 0 to 1 into equal parts based on denominator
  4. Count segments: Move from 0 by numerator number of segments
  5. Mark the point: Place point at calculated position
  6. Verify the answer: Check if it makes sense in the context
Tip 1: Always divide by the denominator first, then multiply by the numerator.
Tip 2: Use visual models to understand the concept before calculating.
Tip 3: The answer should be smaller than the original number (unless fraction > 1).
Tip 4: Check your answer by seeing if the parts add up to the whole.
Common errors: Multiplying before dividing, confusing numerator and denominator roles.
Key insights: Fractions of numbers connect multiplication and division concepts.
Formulas to know by heart:

• Fraction of a number: ab of n = (n ÷ b) × a

• Half of a number: 12 of n = n ÷ 2

• Third of a number: 13 of n = n ÷ 3

Solution: Exercises 4 to 5
4 Adding Fractions Using Number Lines
Exercise 4
Add 14 + 24 using a number line.
Definition:

Adding fractions: Moving along the number line by the amount of each fraction, starting from the first fraction's position.

0
1/4
2/4
3/4
1
Start: 1/4
End: 3/4
Step 1: Start at the first fraction: 14
Step 2: Move by the second fraction: 24
Step 3: Calculate: 14 + 24 = 34
Step 1: Identify the problem

We need to add 14 and 24 using the number line

Step 2: Start at the first fraction

Place a marker at 14 (25% of the way from 0 to 1)

Step 3: Move by the second fraction

Move forward by 24 (50% of the total distance)

Step 4: Land at the sum

The final position is at 34

14 + 24 = 34
Final answer:

14 + 24 = 34

Applied rules:

• Addition on number line: Start at first fraction, move distance of second fraction

• Same denominators: Add numerators, keep denominator the same

• Visual confirmation: Number line shows the actual distance moved

5 Mixed Numbers on Number Lines
Exercise 5
Show the mixed number 123 on a number line from 0 to 2.
Definition:

Mixed number: A combination of a whole number and a fraction (like 123 = 1 + 23)

0
1/3
2/3
1
1 1/3
1 2/3
2
1 2/3
Step 1: Identify the mixed number

123 means 1 whole + 23 of another whole

Step 2: Locate the whole number part

Find 1 on the number line (the first whole unit)

Step 3: Add the fractional part

From 1, move 23 of the next unit (2 out of 3 segments)

Step 4: Mark the final position

Place the point at 123 (166.67% of the way from 0 to 2)

123 = 53 located at 166.67% of the distance from 0 to 2
Final answer:

123 is located at the 5th third mark between 0 and 2

Applied rules:

• Mixed number conversion: 123 = 53

• Number line extension: Extend beyond 1 to accommodate mixed numbers

• Position calculation: Mixed number = whole part + fractional part

Questions & Answers

Question: Why do I divide first and then multiply when finding fractions of numbers? Can't I multiply first?

Answer: Great question! You divide first because the fraction tells you to split the number into equal parts first. Here's why:

  • Division finds the size of each part: If you want 23 of 15, first find how big one-third is: 15 ÷ 3 = 5
  • Multiplication finds the total of selected parts: Then take 2 of those parts: 5 × 2 = 10
  • Order matters: 15 ÷ 3 × 2 = 10, but 15 × 2 ÷ 3 = 10 too, but the thinking process is clearer when you divide first

Think of it as: "First, figure out how big each piece is, then count how many pieces you want."

Question: My child sometimes gets confused when the denominator doesn't divide evenly into the whole number. How should we handle that?

Answer: At the 3rd grade level, focus on problems where the division results in a whole number. For example, use 13 of 12 rather than 13 of 10.

If you encounter a situation where the division doesn't result in a whole number, you can explain that some fractions of numbers result in parts, but for now, stick to problems that divide evenly. The key is ensuring students master the basic concept before moving to more complex scenarios.

Look for whole numbers that are multiples of the denominator to ensure clean division results.

Question: How can I quickly check if I did the fraction problem correctly?

Answer: Here are quick checking strategies:

  • Size check: Your answer should usually be smaller than the original number (unless the fraction is greater than 1)
  • Reasonableness: Does the answer make sense in the context of the problem?
  • Reversibility: If 23 of 15 is 10, then 10 should represent 2 out of 3 equal parts of 15
  • Estimation: Round numbers to check if your answer is close to what you'd expect

Always ask yourself: "Does this answer seem reasonable?" before moving on.