What this chapter is about
A fraction is a way to show a part of a whole. When you cut a roti into 4 equal pieces and eat 1 piece, you have eaten 1/4 of the roti. The bottom number tells how many equal parts the whole is divided into. The top number tells how many parts you are talking about.
In Class 6, you learn to read, write and compare fractions. You also learn about different types of fractions and how to add or subtract fractions that have the same bottom number. This helps you in daily life when you share food, measure lengths, or handle money.
After studying this chapter, you should be able to write fractions for parts of shapes or groups, compare two fractions to see which is bigger, and do simple addition and subtraction with fractions.
Key ideas
- A fraction has two parts: the numerator (top number) shows how many parts you have; the denominator (bottom number) shows how many equal parts the whole is divided into.
- Fractions like 1/2, 1/3, 1/4, 1/5 where the numerator is 1 are called unit fractions.
- A proper fraction has a numerator smaller than its denominator, like 3/5. An improper fraction has a numerator equal to or greater than its denominator, like 7/4.
- A mixed number combines a whole number and a fraction, like 2 and 1/3.
- Equivalent fractions look different but show the same amount. For example, 1/2 and 2/4 are equivalent because both mean half.
- To compare fractions with the same denominator, look at the numerators. The fraction with the bigger numerator is bigger.
- To add or subtract fractions with the same denominator, keep the denominator and add or subtract the numerators.
Formulas and facts to remember
- Fraction = Numerator / Denominator. The numerator tells how many parts; the denominator tells the total equal parts.
- Equivalent fractions: Multiply or divide both numerator and denominator by the same number. Example: 1/2 = 2/4 = 3/6.
- Comparing fractions with the same denominator: The one with the larger numerator is larger. Example: 5/7 > 3/7.
- Adding fractions with the same denominator: a/c + b/c = (a + b)/c. Example: 2/9 + 4/9 = 6/9.
- Subtracting fractions with the same denominator: a/c − b/c = (a − b)/c. Example: 5/8 − 3/8 = 2/8.
- Changing improper fraction to mixed number: Divide numerator by denominator. The quotient is the whole part; the remainder over the denominator is the fraction part.
Worked examples
Example 1: Writing a fraction
Seema has 8 mangoes. She gives 3 mangoes to her friend. What fraction of the mangoes did she give away?
Step 1: Total mangoes = 8. This is the denominator. Step 2: Mangoes given = 3. This is the numerator. Step 3: Fraction given away = 3/8.
Example 2: Finding an equivalent fraction
Find a fraction equivalent to 2/5 with denominator 15.
Step 1: We need to change 5 to 15. Since 5 × 3 = 15, multiply denominator by 3. Step 2: Multiply numerator by the same number: 2 × 3 = 6. Step 3: Equivalent fraction = 6/15.
Example 3: Adding fractions
Ravi drank 2/7 of a bottle of water in the morning and 3/7 in the afternoon. How much did he drink in total?
Step 1: Both fractions have the same denominator, 7. Step 2: Add the numerators: 2 + 3 = 5. Step 3: Keep the denominator: Total = 5/7 of the bottle.
Common mistakes
- Writing 3/8 as 8/3 → Remember: the part you are talking about goes on top; the total equal parts go at the bottom.
- Thinking 1/4 is bigger than 1/2 because 4 is bigger than 2 → With the same numerator, a larger denominator means smaller parts; so 1/4 is less than 1/2.
- Adding denominators when adding fractions (2/5 + 1/5 = 3/10) → Keep the denominator the same; add only the numerators: 2/5 + 1/5 = 3/5.
- Forgetting to multiply both numerator and denominator when finding equivalent fractions → Always multiply or divide both by the same number.
- Writing an improper fraction like 9/4 as a mixed number by just putting a line (9/4 = 9 and 4) → Divide: 9 ÷ 4 = 2 remainder 1, so 9/4 = 2 and 1/4.
Quick revision
- Fraction = part / whole (numerator / denominator).
- Unit fraction has 1 on top; proper fraction has numerator less than denominator.
- To get equivalent fractions, multiply or divide top and bottom by the same number.
- Compare fractions with the same denominator by comparing numerators.
- Add or subtract fractions with the same denominator by working only with the numerators.
- Improper fraction to mixed number: divide and write quotient with remainder over denominator.