Solved Exercises on Fractions Number Lines Worksheets in Grade 3

Master fractions on number lines: representing fractions, comparing fractions, equivalent fractions, and mixed numbers through these 5 detailed exercises with printable worksheet elements.

Complete Summary: Fractions on Number Lines

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.

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

Mixed Number: A combination of a whole number and a fraction (like 112).

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

Core Rules and Laws

Denominator Rule: The denominator tells how many equal parts to divide the whole into.

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

Position Rule: On a number line, fractions farther from 0 are greater.

Equivalence Rule: Equivalent fractions always land at the same position on the number line.

Comparison Rule: Cross multiply to compare fractions: ab vs cd → compare a×d vs b×c.

Worksheet Rule: Always divide the number line into equal segments before placing any fractions.

Step-by-Step Method

  1. Identify the fraction: Determine numerator and denominator
  2. Draw the number line: Mark 0 and 1 with equal spacing
  3. Divide the line: Split 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: 213 → Go to 2, then divide next segment into 3 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; larger numerators mean farther from 0 when denominators are equal.

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

Key Notes for Memorization

Memory Aid: "Denominator divides, Numerator counts" - D=divide, N=numbers to count.

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

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

Practice Worksheet: Fractions on Number Lines

Exercise 1: Place 14 on the number line below:

0
1/4
2/4
3/4
1

Answer: Mark the point at 25% of the line (first division mark)

Exercise 2: Which fraction is larger: 25 or 35? Explain using the number line concept.

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

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

Answer: Both fractions will be at the same position (50%) on their respective number lines.

Solution: Exercises 1 to 3
1 Basic Fraction Placement
Exercise 1
Show 35 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.

Method for placing fractions on number lines:
  1. Identify the denominator (5) to determine how many equal parts to divide the interval
  2. Divide the number line from 0 to 1 into 5 equal segments
  3. Count 3 segments from 0 (numerator = 3)
  4. Mark the point at that location
0
1/5
2/5
3/5
4/5
1
3/5
Step 1: Identify the fraction

35 means 3 parts out of 5 equal parts

Step 2: Divide the number line

From 0 to 1, divide into 5 equal segments (denominator = 5)

Step 3: Count the parts

Count 3 segments from 0 (numerator = 3)

Step 4: Mark the point

Place a point at the third division mark

35 is located at 60% of the distance from 0 to 1
Final answer:

35 is marked at the three-fifths point 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 on Number Lines
Exercise 2
Compare 45 and 34 using number lines.
Definition:

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

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

Create one line divided into 5 parts for 45 and another into 4 parts for 34

Step 2: Place each fraction

45 goes at the 4th mark (80%), 34 goes at the 3rd mark (75%)

Step 3: Compare positions

45 is at 80% and 34 is at 75%

Step 4: Draw conclusion

Since 80% > 75%, 45 > 34

45 > 34
Final answer:

45 is greater than 34

Applied rules:

• Position comparison: The fraction farther from 0 is greater

• Cross multiplication: 45 vs 34 → 4×4 vs 5×3 → 16 vs 15 → 16 > 15

• Visual verification: Number lines confirm the mathematical comparison

3 Equivalent Fractions on Number Lines
Exercise 3
Show that 36, 48, and 510 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
1/6
2/6
3/6
4/6
5/6
1
3/6
0
1/8
2/8
3/8
4/8
5/8
6/8
7/8
1
4/8
0
1/10
2/10
3/10
4/10
5/10
6/10
7/10
8/10
9/10
1
5/10
Step 1: Draw three separate number lines

One divided into 6 parts, one into 8 parts, one into 10 parts

Step 2: Place each fraction

36 at 50%, 48 at 50%, 510 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

36 = 48 = 510
Final answer:

36, 48, and 510 are equivalent fractions

Applied rules:

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

• Simplification: 36 = 12 by dividing numerator and denominator by 3

• 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
ab < cd
If a×d < b×c
Rule 2
ab = cd
If a×d = b×c
Rule 3
ab > cd
If a×d > b×c
Key definitions:

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

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

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

Complete methodology:
  1. Identify the fraction: Recognize numerator and denominator
  2. Draw the number line: Mark 0 and 1, divide into equal parts
  3. Count segments: Move from 0 by numerator number of segments
  4. Mark the point: Place point at calculated position
Tip 1: Always divide the number line into equal segments based on the denominator.
Tip 2: Larger numerators mean points farther from 0 when denominators are equal.
Tip 3: Equivalent fractions always land at the same position on the number line.
Tip 4: Use cross multiplication to compare fractions quickly.
Common errors: Unequal segment spacing, counting from wrong starting point, confusing numerator and denominator.
Key insights: Number lines provide visual confirmation of fraction relationships and equivalence.
Formulas to know by heart:

• Equivalent fractions: ab = a×nb×n

• Comparison rule: ab vs cd depends on a×d vs b×c

• Number line positioning: Position = (numerator ÷ denominator) × 100%

Solution: Exercises 4 to 5
4 Adding Fractions Using Number Lines
Exercise 4
Add 25 + 15 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
1/5
2/5
3/5
4/5
1
Start: 2/5
End: 3/5
Step 1: Start at the first fraction

Place a marker at 25 (40% of the way from 0 to 1)

Step 2: Move by the second fraction

Move forward by 15 (20% of the total distance)

Step 3: Calculate the final position

Starting at 25 and moving 15 lands at 35

Step 4: Verify the addition

25 + 15 = 35 (same denominators, add numerators)

25 + 15 = 35
Final answer:

25 + 15 = 35

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 134 on a number line from 0 to 2.
Definition:

Mixed number: A combination of a whole number and a fraction (like 134 = 1 + 34)

0
1/4
2/4
3/4
1
1 1/4
1 2/4
1 3/4
2
1 3/4
Step 1: Identify the mixed number

134 means 1 whole + 34 of another whole

Step 2: Extend the number line

Since we need to show up to 2, extend the line beyond 1 to include 134

Step 3: Locate the whole number part

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

Step 4: Add the fractional part

From 1, move 34 of the next unit (3 out of 4 segments)

Step 5: Mark the final position

Place the point at 134 (175% of the way from 0 to 2)

134 = 74 located at 175% of the distance from 0 to 2
Final answer:

134 is located at the 7th fourth mark between 0 and 2

Applied rules:

• Mixed number conversion: 134 = 74

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

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

Questions & Answers

Question: I don't understand why 24 and 12 are the same size on the number line even though they look different. Can you explain?

Answer: Great question! These fractions are called equivalent fractions. Here's why they're the same:

  • Think of a pizza cut into 4 pieces. If you eat 2 pieces, you ate 24 of the pizza.
  • Now imagine the same pizza cut into 2 pieces. If you eat 1 piece, you ate 12 of the pizza.
  • But 24 and 12 represent the same amount of pizza!

On the number line, both fractions land at the exact same spot - halfway between 0 and 1. The mathematical rule is: multiply or divide both numerator and denominator by the same number, and you get an equivalent fraction.

Example: 12 × 22 = 24

Question: My child struggles with placing fractions on number lines. What's the best way to help them visualize this concept?

Answer: Here are effective strategies to help visualize fractions on number lines:

  • Physical models: Use rulers, measuring cups, or paper strips folded into equal parts
  • Real-world examples: Show distances walked (halfway to school), time (quarter past the hour)
  • Visual aids: Draw multiple number lines with different divisions (halves, thirds, fourths)
  • Step-by-step approach: Always divide first, then count, then mark

Start with simple unit fractions like 12, 13, 14 before moving to other numerators. Practice regularly with hands-on activities.

Encourage your child to say: "I need to divide into [denominator] equal parts, then count [numerator] parts from zero."

Question: How do I compare fractions like 23 and 34 using number lines when they have different denominators?

Answer: To compare fractions with different denominators on number lines, find a common denominator. Here's how:

To compare 23 and 34:

  • Find the least common denominator (LCD) of 3 and 4, which is 12
  • Convert 23 to 812 (multiply by 44)
  • Convert 34 to 912 (multiply by 33)
  • Draw a number line divided into 12 equal parts
  • Mark 812 and 912 - you'll see 34 is farther from 0

Therefore: 23 < 34