Solved Exercises on Fractions Number Line Printable in Grade 3

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

Solution: Exercises 1 to 3
1 Representing Fractions on Number Lines
Exercise 1
Show 14 on a number line from 0 to 1.
Definition:

Fraction on number line: A fraction represents a part of a whole, shown as a point on a number line where the distance from 0 indicates the value.

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

14 means 1 part out of 4 equal parts

Step 2: Divide the number line

From 0 to 1, divide into 4 equal segments (denominator = 4)

Step 3: Count the parts

Count 1 segment from 0 (numerator = 1)

Step 4: Mark the point

Place a point at the first division mark

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

14 is marked at the first quarter 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 26 and 13 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
1/6
2/6
3/6
4/6
5/6
1
2/6
0
1/3
2/3
1
1/3
Step 1: Draw separate number lines

Create one line divided into 6 parts for 26 and another into 3 parts for 13

Step 2: Place each fraction

26 goes at the 2nd mark, 13 goes at the 1st mark

Step 3: Compare positions

Both fractions are at the same position (33.33%) on their respective number lines

Step 4: Draw conclusion

Since both points are at the same distance from 0, the fractions are equivalent

26 = 13
Final answer:

26 and 13 are equivalent fractions

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 = cd if a×d = b×c

3 Equivalent Fractions on Number Lines
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
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 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

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

Step 2: Move by the second fraction

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

Step 3: Calculate the final position

Starting at 14 and moving 24 lands at 34

Step 4: Verify the addition

14 + 24 = 34 (same denominators, add numerators)

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 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 quarter 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