Solved Exercises on Fractions Introduction in Grade 1

Master fractions: parts of a whole, equal parts, fraction notation, comparing fractions, and visual representations through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Parts of a whole
Exercise 1
Look at this pizza:
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If the pizza is cut into 4 equal pieces and you eat 1 piece, what fraction of the pizza did you eat?
Definition:

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

Fraction identification method:
  1. Count the total number of equal parts (denominator)
  2. Count the number of parts being considered (numerator)
  3. Write the fraction as numerator/denominator
Total parts
4
Parts eaten
1
Fraction
1/4
Step 1: Identify the whole

The whole pizza is divided into 4 equal pieces

Step 2: Count the total parts

Total parts = 4 (the bottom number of the fraction)

Step 3: Count the parts eaten

Parts eaten = 1 (the top number of the fraction)

Step 4: Write the fraction

1 out of 4 parts = 1/4

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You ate 1/4 of the pizza
Final answer:

You ate 1/4 of the pizza

Applied rules:

• Equal parts: All parts must be the same size for a fraction

• Numerator: Number of parts being considered

• Denominator: Total number of equal parts in the whole

2 Equal parts
Exercise 2
Look at this apple:
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The apple is cut into 3 pieces. Are these equal parts? If yes, what fraction does each piece represent?
Definition:

Equal parts: Parts that are the same size and shape in a whole object.

Pieces
3
Equal?
Yes
Each piece
1/3
Step 1: Check if pieces are equal

All 3 pieces of the apple look the same size → Yes, they are equal

Step 2: Count total equal parts

There are 3 equal parts in total

Step 3: Determine fraction for each piece

Each piece is 1 out of 3 equal parts = 1/3

Step 4: Verify

3 pieces of 1/3 each = 3 × 1/3 = 1 whole apple ✓

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Each piece is 1/3 of the apple
Final answer:

Yes, the pieces are equal. Each piece represents 1/3 of the apple.

Applied rules:

• Equal parts: Essential for fractions to work correctly

• Sum of parts: All fractional parts should add up to 1 whole

• Uniformity: Same size and shape for each part

3 Fraction notation
Exercise 3
Look at this pie:
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The pie is cut into 4 equal pieces. If 2 pieces are shaded, write the fraction of the pie that is shaded.
Definition:

Fraction notation: Written as numerator/denominator where numerator is the number of parts taken and denominator is the total number of equal parts.

Shaded parts
2
Total parts
4
Fraction
2/4
Step 1: Count the shaded parts

Number of shaded pieces = 2 (this is the numerator)

Step 2: Count total equal parts

Total pieces = 4 (this is the denominator)

Step 3: Write the fraction

Shaded parts over total parts = 2/4

Step 4: Read the fraction

"Two-fourths" means 2 out of 4 equal parts

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2/4
The fraction of the pie that is shaded is 2/4
Final answer:

The fraction of the pie that is shaded is 2/4

Applied rules:

• Numerator: Top number shows how many parts are taken

• Denominator: Bottom number shows total equal parts

• Reading fractions: Say numerator first, then denominator

Rules and methods, laws,...
Fraction = Numerator / Denominator
Fraction Notation
Part of Whole
Part = Part/Whole
How much of the whole is taken
Equal Parts
All parts = Same Size
Essential for fractions
Sum of Parts
All parts = 1 whole
Fractions add up to 1
Key definitions:

Whole: Complete object or group

Part: Portion of a whole

Equal parts: Same size portions

Numerator: Top number in fraction (parts taken)

Denominator: Bottom number in fraction (total parts)

Complete methodology:
  1. Identify the whole: Find the complete object or set
  2. Check for equal parts: Ensure all parts are the same size
  3. Count total parts: This becomes the denominator
  4. Count parts of interest: This becomes the numerator
  5. Write the fraction: Numerator over denominator
Tip 1: Always make sure parts are equal before making fractions.
Tip 2: The bigger the denominator, the smaller each part becomes.
Tip 3: Draw pictures to visualize fractions better.
Tip 4: Practice with real objects like pizzas, cakes, or paper.
Common errors: Not checking for equal parts, mixing up numerator and denominator, forgetting that all parts must be equal.
Key notes: Fractions describe parts of a whole, always need equal parts, numerator tells "how many", denominator tells "out of how many".
Rules to remember:

• Equal parts rule: All parts must be the same size

• Numerator rule: Top number shows how many parts are taken

• Denominator rule: Bottom number shows total number of equal parts

• Whole rule: All fractional parts together make 1 whole

• Comparison rule: Larger denominators mean smaller parts

Solution: Exercises 4 to 5
4 Comparing fractions
Exercise 4
Which is larger?
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1/2
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2/4
Compare 1/2 and 2/4
Definition:

Equivalent fractions: Different fractions that represent the same amount.

Fraction 1
1/2
Fraction 2
2/4
Result
Equal
Step 1: Visualize 1/2

Half of a cake = 1 out of 2 equal pieces

Step 2: Visualize 2/4

Two-fourths of a cake = 2 out of 4 equal pieces

Step 3: Compare the amounts

Both represent the same amount of cake!

Step 4: Conclusion

1/2 = 2/4 (they are equivalent fractions)

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1/2
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2/4
1/2 = 2/4
Final answer:

1/2 and 2/4 are equal - they represent the same amount.

Applied rules:

• Visual comparison: Draw pictures to compare fractions

• Equivalence: Different fractions can represent same amount

• Denominator effect: More parts means smaller individual parts

5 Adding fractions
Exercise 5
If you eat 1/4 of a pizza and your friend eats 1/4 of the same pizza, what fraction of the pizza did you both eat together?
Definition:

Adding fractions: Combine parts of the same whole to find total amount taken.

First part
1/4
Second part
1/4
Total
2/4
Step 1: Identify what's being added

You ate 1/4 and friend ate 1/4 of the same pizza

Step 2: Add the numerators

1/4 + 1/4 = (1+1)/4 = 2/4

Step 3: Keep the same denominator

Since both fractions refer to the same whole (cut into 4), denominator stays 4

Step 4: Simplify if possible

2/4 can be simplified to 1/2

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Together you ate 2/4 (or 1/2) of the pizza
Final answer:

You both ate 2/4 (or 1/2) of the pizza together.

Applied rules:

• Add numerators: When denominators are the same, add top numbers

• Keep denominator: Don't change the bottom number

• Simplification: Reduce fractions to simplest form when possible

Fraction Concepts, Laws, and Methods Guide
Fraction = Part / Whole
Fraction Concept
Key definitions:

Whole: Complete object or group that can be divided into parts

Part: Individual portion of a whole object or group

Equal parts: Parts that are identical in size and shape

Numerator: Top number in a fraction showing how many parts are taken

Denominator: Bottom number in a fraction showing total number of equal parts

Equivalent fractions: Different fractions that represent the same amount

Unit fraction: Fraction with numerator of 1 (like 1/2, 1/3, 1/4)

Complete methodology:
  1. Identify the whole: Locate the complete object or set being divided
  2. Verify equal parts: Ensure all divisions are the same size
  3. Count total parts: Determine the denominator (bottom number)
  4. Count relevant parts: Determine the numerator (top number)
  5. Write the fraction: Present as numerator/denominator
  6. Simplify if needed: Reduce to lowest terms
Tip 1: Always check that parts are equal before forming fractions.
Tip 2: The larger the denominator, the smaller each individual part becomes.
Tip 3: Draw pictures or use manipulatives to visualize fractions.
Tip 4: Remember: numerator = how many parts, denominator = out of how many total.
Tip 5: Equivalent fractions represent the same amount even though they look different.
Tip 6: Practice with real-life examples like sharing food or dividing groups.
Common errors: Forgetting to check for equal parts, confusing numerator and denominator, thinking larger denominators mean larger amounts, not recognizing equivalent fractions.
Key notes: Fractions describe parts of a whole, require equal divisions, numerator tells "how many", denominator tells "out of how many", all parts together equal 1 whole.
Real-world applications: Cooking measurements, sharing items fairly, time divisions, money calculations, and many daily activities involve fractions.
Laws and rules to know:

• Equality requirement: All parts must be equal for valid fractions

• Numerator function: Shows how many parts are being considered

• Denominator function: Shows total number of equal parts in the whole

• Whole completion: All fractional parts combined equal 1 whole

• Size relationship: Larger denominators create smaller individual parts

• Addition rule: Add numerators when denominators are the same

• Equivalence law: Different fractions can represent the same quantity

• Comparison principle: With same denominator, larger numerator means larger fraction

Questions & Answers

Question: I don't understand why we need equal parts for fractions. Why can't some parts be bigger than others?

Answer: Great question! Equal parts are essential for fractions because they allow us to make fair comparisons and accurate measurements.

Think of it this way: If you and your friend are sharing a pizza, and one slice is huge while another is tiny, how would you know if it's fair? With equal parts, everyone gets the same-sized piece.

Examples of why equal parts matter:

  • If a circle is divided into 4 parts where 3 are small and 1 is large, taking 1 part doesn't tell us exactly how much we got
  • With 4 equal parts, we know exactly that 1 part is 1/4 of the whole
  • Equal parts allow us to say that 2/4 is exactly half of something

This is why when learning fractions, we always emphasize that the parts must be the same size and shape!

Question: Why is 1/4 smaller than 1/2? Doesn't 4 seem bigger than 2?

Answer: This is a very common confusion! The key is to focus on the denominator (bottom number) - it tells you how many equal parts the whole is divided into.

Think of it like this:

  • 1/2 means: 1 part out of 2 equal parts (each part is big)
  • 1/4 means: 1 part out of 4 equal parts (each part is small)

If you cut a pizza into 2 pieces, each piece is big. If you cut the same pizza into 4 pieces, each piece is smaller. So 1/2 of a pizza is more than 1/4 of the same pizza.

Remember: The larger the denominator, the smaller each individual part becomes!

Question: How can I help my child understand fractions better at home?

Answer: There are many fun ways to practice fractions at home!

Activities to try:

  • Cut food into equal parts: pizzas, sandwiches, apples, etc.
  • Use toys or blocks to create groups and take parts
  • Draw shapes and shade parts
  • Play games with fraction cards
  • Cook together using measuring cups (1/2 cup, 1/4 cup)

Start with simple unit fractions like 1/2, 1/3, 1/4 and gradually move to fractions with numerators greater than 1. Make it visual and hands-on!