Solved Exercises on Fractions Part of a Whole Worksheets PDF in Grade 3

Comprehensive practice worksheets on fractions part of a whole: solving various problems with detailed solutions and visual aids.

Complete Summary: Fractions Part of a Whole

Definitions

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

Whole: The complete object or set that is being divided into equal parts.

Fraction of a Whole: A way to show how many parts of a complete object or set are being considered.

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

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

Part-Whole Relationship: The connection between a part and the whole it comes from.

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 consider from the whole.

Equal Parts Rule: All parts of the whole must be the same size when creating fractions.

Whole Equals One: When all parts are taken together, the fraction equals 1 whole (nn = 1).

Part-Whole Relationship: The fraction ab means a parts out of b total equal parts.

Visual Confirmation: Pictures and diagrams help verify fraction calculations.

Step-by-Step Method

  1. Identify the whole: Determine what object or set is being divided
  2. Count total parts: Find how many equal parts the whole is divided into
  3. Count selected parts: Find how many parts meet the criteria
  4. Write the fraction: Express as selectedtotal
  5. Verify the answer: Check if it makes sense in context

Examples (Simple to Advanced)

Simple: Circle divided into 4 parts, 1 part shaded = 14

Intermediate: Rectangle divided into 6 parts, 3 parts shaded = 36

Advanced: Set of 12 items, 8 items selected = 812

Tips, Tricks, and Common Pitfalls

Tips: Always ensure parts are equal, count carefully, start with unit fractions.

Tricks: Use visual models like circles, rectangles, or groups to make fractions concrete.

Common Pitfalls: Unequal part sizes, miscounting parts, confusing numerator and denominator.

Key Notes for Memorization

Memory Aid: "Denominator divides, Numerator names" - D=divide, N=name how many.

Visual Memory: Fractions show parts of a complete object or group.

Quick Check: The fraction ab means a out of b total parts.

Practice Worksheet: Fractions Part of a Whole

Exercise 1: Shade 34 of the circle below:

Answer: 3 out of 4 equal parts are shaded

Exercise 2: What fraction of the rectangle is shaded?

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Answer: 24 of the rectangle is shaded

Exercise 3: Show 26 using the objects below:

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Answer: 2 out of 6 stars are selected

Exercise 4: Which fraction is larger: 12 or 34?

Answer: 34 is larger because it represents more parts of the same whole

Exercise 5: Are 24 and 12 equivalent fractions?

Answer: Yes, they are equivalent because both represent the same portion of a whole

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Solution: Exercises 1 to 3
1 Fractions of Circles
Exercise 1
What fraction of the circle is shaded if 5 out of 8 equal parts are shaded?
Definition:

Fraction of a circle: The fraction shaded partstotal parts represents how much of the circle is shaded.

Method for finding fractions of circles:
  1. Count the total number of equal parts in the circle
  2. Count the number of shaded or selected parts
  3. Write the fraction as shaded partstotal parts
Step 1: Identify total parts

The circle is divided into 8 equal parts (denominator = 8)

Step 2: Count shaded parts

5 parts are shaded (numerator = 5)

Step 3: Write the fraction

Fraction = 58

58 of the circle is shaded
Final answer:

58 of the circle is shaded

Applied rules:

• Part-whole relationship: Numerator = shaded parts, Denominator = total parts

• Equal parts requirement: All parts must be the same size for valid fractions

• Visual confirmation: Picture confirms the fraction calculation

2 Fractions of Rectangles
Exercise 2
A rectangle is divided into 6 equal parts. 4 parts are colored blue. What fraction of the rectangle is blue?
Definition:

Fraction of a rectangle: The fraction colored partstotal parts represents how much of the rectangle is colored.

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Step 1: Identify total parts

The rectangle is divided into 6 equal parts (denominator = 6)

Step 2: Count colored parts

4 parts are colored blue (numerator = 4)

Step 3: Write the fraction

Fraction = 46

46 of the rectangle is blue
Final answer:

46 of the rectangle is blue

Applied rules:

• Part-whole relationship: Numerator = colored parts, Denominator = total parts

• Equal parts requirement: All parts must be the same size for valid fractions

• Visual confirmation: Diagram confirms the fraction calculation

3 Fractions of Sets
Exercise 3
There are 10 apples in a basket. 7 apples are red. What fraction of the apples are red?
Definition:

Fraction of a set: The fraction red applestotal apples represents how many items in the set have the specified characteristic.

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Step 1: Identify total items

There are 10 apples in total (denominator = 10)

Step 2: Count red apples

7 apples are red (numerator = 7)

Step 3: Write the fraction

Fraction = 710

710 of the apples are red
Final answer:

710 of the apples are red

Applied rules:

• Set fraction rule: Numerator = items with characteristic, Denominator = total items

• Part-whole relationship: Applies to collections of objects too

• Counting accuracy: Careful counting ensures correct fraction

Rules and methods, laws,...
partwhole = selected itemstotal items
Fraction of a Whole
Rule 1
nn = 1
All parts equal the whole
Rule 2
0n = 0
No parts selected
Rule 3
ab = a×nb×n
Equivalent fractions
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 whole: Determine what object or set is being divided
  2. Count total parts: Find how many equal parts the whole is divided into
  3. Count selected parts: Find how many parts meet the criteria
  4. Write the fraction: Express as selectedtotal
Tip 1: Always ensure all parts are equal when dividing a whole.
Tip 2: Use visual models like circles, rectangles, or groups to make fractions concrete.
Tip 3: Start with unit fractions before moving to other numerators.
Tip 4: Remember that fractions apply to shapes, sets, and quantities equally.
Common errors: Unequal part sizes, miscounting parts, confusing numerator and denominator.
Key insights: Fractions connect parts to wholes in meaningful ways across all contexts.
Formulas to know by heart:

• Fraction of a whole: selected partstotal parts

• Whole equals one: nn = 1

• Nothing selected: 0n = 0

Solution: Exercises 4 to 5
4 Comparing Fractions
Exercise 4
Which fraction is larger: 34 or 23?
Definition:

Comparing fractions: Determining which fraction is larger by comparing their positions on a number line or finding common denominators.

Step 1: Find common denominators

LCM of 4 and 3 is 12: 34 = 912 and 23 = 812

Step 2: Compare numerators

Since 9 > 8, 912 > 812

Step 3: Draw conclusion

Therefore 34 > 23

34 is larger than 23
Final answer:

34 is larger than 23

Applied rules:

• Comparison rule: Convert to common denominators to compare

• Visual confirmation: Diagrams show 34 covers more area than 23

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

5 Equivalent Fractions
Exercise 5
Show that 24 and 12 are equivalent fractions.
Definition:

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

Step 1: Simplify 24

Divide numerator and denominator by 2: 24 = 12

Step 2: Verify with cross multiplication

2 × 2 = 4 and 4 × 1 = 4, so 4 = 4 ✓

Step 3: Visual confirmation

Both fractions cover the same area of their respective circles

24 = 12
Final answer:

24 and 12 are equivalent fractions

Applied rules:

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

• Simplification: 24 = 12 by dividing numerator and denominator by 2

• Cross multiplication: a×d = b×c for equivalent fractions

Questions & Answers

Question: Why do the parts have to be equal when we make fractions? Can't I just count any parts?

Answer: Great question! The parts must be equal because fractions are about fair sharing and equal portions. Here's why:

  • Consistency: Equal parts ensure that everyone gets the same amount
  • Comparison: We can only compare fractions accurately when parts are equal
  • Mathematical accuracy: 14 means one out of four equal parts, not just any one part

Think of sharing a cake - if some pieces are bigger than others, it's not fair! Fractions work the same way - equal parts make the math work properly.

Question: My child is struggling to understand that 24 and 12 are the same. How can I help?

Answer: This is a common challenge! Here are effective ways to help your child understand equivalent fractions:

  • Visual demonstrations: Use paper folding, pizza slices, or chocolate bars to show they represent the same amount
  • Real-world examples: Half a pizza vs. two quarters of the same pizza
  • Pattern recognition: Show that 1×2=2 and 2×2=4, so 12 = 24
  • Hands-on activities: Use fraction tiles, circles, or rectangles to physically manipulate

The key is showing that different fractions can represent the same portion of a whole object.

Question: How do I know which number goes on top and which goes on bottom in a fraction?

Answer: Here's a helpful memory trick for remembering fraction parts:

  • Numerator (top number): Think "N" for "Number" - it tells HOW MANY parts we have
  • Denominator (bottom number): Think "D" for "Divide" - it tells INTO HOW MANY equal parts the whole is divided

Remember: "Numerator Names" how many parts, "Denominator Denotes" how many total parts. So if you have 3 pieces out of 8 total pieces, it's 38.