भिन्न के प्रकार
Types of Fractions
A fraction represents equal parts of a whole. In 3/4 the denominator 4 tells how many equal parts the whole is divided into, and the numerator 3 tells how many are taken. The word 'equal' carries the whole concept — unequal parts are not fractions at all.
The kinds of fractions
| Type | Meaning | Example |
|---|---|---|
| Proper | Numerator less than denominator; value less than 1 | 3/5 |
| Improper | Numerator greater than or equal to denominator | 7/4 |
| Mixed | A whole number with a proper fraction | 1 3/4 |
| Like | Same denominator | 2/9 and 5/9 |
| Unlike | Different denominators | 2/3 and 4/5 |
| Equivalent | Different numbers, same value | 1/2, 2/4, 5/10 |
| Unit | Numerator is 1 | 1/7 |
Equivalent fractions
Multiply or divide numerator and denominator by the same non-zero number
2/3 = 4/6 = 6/9 = 10/15. This is the single most useful fraction skill, because it underlies comparison, addition of unlike fractions and simplification. A fraction is in its lowest terms when the HCF of numerator and denominator is 1.
Comparing fractions
- Like fractions: the one with the larger numerator is larger. 5/9 is greater than 2/9.
- Same numerator: the one with the smaller denominator is larger, because the whole is cut into fewer pieces. 3/5 is greater than 3/8.
- Otherwise, convert to a common denominator using the LCM, or cross-multiply.
- Between any two fractions there are infinitely many fractions — a fact that surprises children and is worth showing.
Fractions in a Class 3-5 classroom
Fractions must be met in three forms before the symbol makes sense: as part of a whole (half a chapati), as part of a collection (three of the twelve children), and as a point on the number line (1/2 lies exactly between 0 and 1). Children who meet only the first form are helpless when a question asks for two-thirds of a group of nine.
The misconception that matters
Children carry whole-number rules into fractions. Because 8 is bigger than 5, they conclude 1/8 is bigger than 1/5. The cure is not a rule but an experience: cut one chapati into five parts and another into eight, and let them pick a piece.
✗ 1/8 is greater than 1/5 because 8 is greater than 5. | ✓ 1/5 is greater; more parts means each part is smaller.
✗ 2/6 and 1/3 are different amounts. | ✓ They are equivalent fractions with the same value.
संकेत: भिन्न में हर (denominator) बताता है कितने बराबर भाग, अंश (numerator) बताता है कितने लिए गए।
Fractions give 2-3 questions across the Maths and Maths pedagogy sections, and the pedagogy questions are usually about the misconception above. Expect an item that names a child's error and asks what it shows. The commonest trap in the content questions is comparing unit fractions, where the larger denominator looks like the larger value. Remember also that the parts must be equal for a figure to represent a fraction; CTET has used a diagram of unequal parts as a distractor.
Frequently asked questions
What is the difference between a proper and an improper fraction?
In a proper fraction the numerator is smaller than the denominator, so the value is less than one. In an improper fraction the numerator is equal to or greater than the denominator, so the value is one or more.
Why is 1/5 greater than 1/8?
Because the denominator tells how many equal parts the whole is divided into. Dividing into eight parts makes each part smaller than dividing into five, so one part out of five is more than one part out of eight.
How do you find equivalent fractions?
Multiply or divide both the numerator and the denominator by the same non-zero number. This changes the numbers but not the value, which is why 1/2, 2/4 and 5/10 all represent the same quantity.
60-second recap
- A fraction needs equal parts; denominator = number of parts, numerator = parts taken.
- Proper, improper, mixed, like, unlike, equivalent and unit fractions.
- Equivalent fractions: multiply or divide both parts by the same number.
- Same numerator: smaller denominator means larger fraction.
- Main misconception: applying whole-number size rules to fractions.