Chapter focus: A fraction represents a part of a whole or a part of a collection. This chapter builds a strong understanding of numerator, denominator, equivalent fractions, comparison and operations with fractions.

🎯 Learning Goals

• Understand fractions as parts of a whole and parts of a collection.
• Identify numerator and denominator.
• Recognise proper, improper and mixed fractions.
• Find equivalent fractions.
• Compare and order fractions.
• Add and subtract fractions in appropriate cases.
• Solve fraction problems in everyday situations.

🍕 1. What Is a Fraction?

A fraction describes equal parts of a whole or collection. In 3/5, the numerator 3 tells how many parts are considered and the denominator 5 tells how many equal parts make the whole.

🔢 2. Types of Fractions

• Proper fraction: numerator is less than denominator, e.g. 3/7.
• Improper fraction: numerator is greater than or equal to denominator, e.g. 9/5.
• Mixed fraction: a whole number together with a proper fraction, e.g. 1 4/5.

🔄 3. Equivalent Fractions

Equivalent fractions have the same value even though their numerators and denominators are different.

Example: 1/2 = 2/4 = 3/6 = 4/8.

Multiplying or dividing the numerator and denominator by the same non-zero number gives an equivalent fraction.

⚖️ 4. Comparing Fractions

When denominators are equal, compare the numerators. For example, 5/8 is greater than 3/8.

When numerators are equal, the fraction with the smaller denominator is greater. For example, 3/5 is greater than 3/7.

For other cases, fractions can be converted to equivalent fractions with a common denominator.

➕ 5. Adding Fractions

For fractions with the same denominator, add the numerators and keep the denominator.

2/7 + 3/7 = 5/7

For unlike denominators, first express the fractions with a common denominator when required.

➖ 6. Subtracting Fractions

For fractions with the same denominator, subtract the numerators and keep the denominator.

6/9 − 2/9 = 4/9

📋 Worked Examples

Example 1 – Identify the Parts

In 7/10, numerator = 7 and denominator = 10.

Example 2 – Equivalent Fraction

Find a fraction equivalent to 3/4 with denominator 12.

Multiply numerator and denominator by 3: 3×3 / 4×3 = 9/12.

Example 3 – Add Like Fractions

3/8 + 2/8 = 5/8.

Example 4 – Compare

Compare 5/9 and 7/9. Since denominators are equal, compare numerators. Therefore 7/9 > 5/9.

Example 5 – Mixed Number

2 1/3 means 2 whole units and one-third of another unit.

🧠 Fraction Reasoning

1. Why must the parts of a whole be equal when a fraction is used to represent them?
2. Why does multiplying both numerator and denominator by the same number not change the value?
3. Is 4/4 a proper fraction? Explain.
4. Which is greater: 1/2 or 1/3? Explain without converting to decimals.
5. Why must we use a common denominator when adding unlike fractions?

📝 Important Practice Questions

1. Define numerator and denominator.
2. Classify 2/7, 9/4 and 3 1/5 as proper, improper or mixed.
3. Write three fractions equivalent to 2/3.
4. Compare 5/8 and 7/8.
5. Compare 2/3 and 2/5.
6. Add 3/11 and 5/11.
7. Subtract 2/9 from 7/9.
8. Convert 11/4 into a mixed fraction.
9. Write 3 2/5 as an improper fraction.
10. Give one real-life situation where fractions are used.

🔥 Competency / HOTS Questions

1. A cake is divided into 8 equal pieces. Riya eats 3 pieces and Aman eats 2. What fraction remains?
2. Two students say 2/4 and 1/2 are different because their numbers are different. Explain who is correct.
3. Arrange 1/2, 3/4 and 2/3 from smallest to greatest and explain your method.
4. Can a proper fraction ever be greater than 1? Explain.
5. A student adds 1/3 + 1/4 as 2/7. Explain the mistake and give the correct result.

🧩 MCQ Practice

1. In 5/9, the denominator is — A. 5 B. 9 C. 14 D. 4
2. Which is a proper fraction? A. 7/4 B. 4/4 C. 3/8 D. 9/5
3. Which is equivalent to 1/2? A. 2/3 B. 3/6 C. 4/6 D. 5/8
4. Which is greater? A. 3/8 B. 5/8 C. 2/8 D. 1/8
5. 2/7 + 3/7 = — A. 5/14 B. 6/7 C. 5/7 D. 1/7
6. 7/9 − 2/9 = — A. 5/9 B. 5/18 C. 9/5 D. 4/9
7. 11/4 as a mixed fraction is — A. 2 3/4 B. 2 1/4 C. 3 1/4 D. 4 2/3
8. Which statement is true? A. 1/2 < 1/3 B. 1/2 = 1/3 C. 1/2 > 1/3 D. cannot compare

Answer Key: 1-B, 2-C, 3-B, 4-B, 5-C, 6-A, 7-B, 8-C

📄 Printable Worksheet

1. Identify numerator and denominator in five given fractions.
2. Classify a list of fractions as proper, improper or mixed.
3. Write three equivalent fractions for 3/5.
4. Compare 4/7 and 6/7.
5. Compare 3/4 and 3/8.
6. Add 4/9 and 2/9.
7. Subtract 3/10 from 9/10.
8. Convert 13/5 to a mixed fraction.
9. Convert 2 3/7 to an improper fraction.
10. Create a fraction word problem and solve it.

🔁 Quick Revision Table

✅ Chapter Mastery Checklist

• ☐ I can identify numerator and denominator.
• ☐ I can classify fractions.
• ☐ I can find equivalent fractions.
• ☐ I can compare and order fractions.
• ☐ I can add and subtract like fractions.
• ☐ I can convert between improper and mixed fractions.
• ☐ I can solve real-life fraction problems.

🔗 Continue Learning

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