Fractions
Equivalent fractions, comparing fractions, and fractions bigger than one whole, explained with food, ribbons, and number lines.
- Why we can compare fractions only when the “whole” is the same
- What equivalent fractions are and how to make them
- How to compare fractions with the same denominator or the same numerator
- Fractions bigger than 1, like 5/2 = 2½ (mixed numbers)
- Quick comparing using 1 and ½ as “reference points”
🍉 Let’s Begin: Is Half Always Bigger?
Kabir got half of a small melon. His sister Pihu got one-third of a huge watermelon. Kabir said, “I got ½ and you got only ⅓. Mine is bigger!”
Pihu laughed. “Look at the plates!” Her piece of watermelon was clearly bigger.
Who is right? Pihu! ½ is bigger than ⅓ only when both come from the same whole. A third of something big can be more than half of something small.
🟰 Part 1: Equivalent Fractions
Fold a paper strip into 2 equal parts and colour 1 part. That’s ½. Now fold it once more. The strip now has 4 parts, and the coloured part covers 2 of them. That’s 2/4. Fold again: 4 out of 8 parts, so 4/8.
The coloured part never changed! Only the number of pieces changed.
½ = 2/4 = 4/8
Fractions that show the same amount with different numbers are called equivalent fractions.
| Strip | Pieces | Coloured | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Halves | ½ | ½ | 1/2 | ||||||
| Fourths | ¼ | ¼ | ¼ | ¼ | 2/4 | ||||
| Eighths | ⅛ | ⅛ | ⅛ | ⅛ | ⅛ | ⅛ | ⅛ | ⅛ | 4/8 |
The shortcut
2/5 = 4/10 = 6/15 = 8/20 = 20/50
Whatever you do to the bottom (denominator), do the same to the top (numerator).
How to check if two fractions are equivalent
Is 3/4 equal to 9/12? Ask: “What did 4 get multiplied by to become 12?” It’s ×3. Now check the top: 3 × 3 = 9 ✅. Yes, they are equivalent.
Is 2/3 equal to 4/9? 3 × 3 = 9, but 2 × 3 = 6, not 4 ❌. So they are not equivalent.
½ is not equal to 2/3. ✅ Only multiply (or divide) top and bottom by the same number.
⚖️ Part 2: Comparing Fractions
Same denominator (same-size pieces)
A cake is cut into 8 equal pieces. Riya ate 3 pieces (3/8), Manu ate 5 pieces (5/8). All pieces are the same size, so whoever has more pieces has more cake.
5/8 > 3/8, so Manu ate more.
Rule: Same bottom number? Compare the top numbers. Bigger top = bigger fraction.
Same numerator (same number of pieces)
Two same-size rotis. One is cut into 4 pieces, the other into 6 pieces. Aman takes 3 pieces from the first roti (3/4). Neha takes 3 pieces from the second (3/6).
Both have 3 pieces, but a quarter piece is bigger than a sixth piece (fewer people sharing = bigger piece). So 3/4 > 3/6.
Rule: Same top number? The fraction with the smaller bottom number is bigger.
✅ Cutting into 10 pieces makes each piece smaller. 1/4 > 1/10.
🫓 Part 3: Fractions Bigger Than 1
At a wedding, rotis are cut in halves. Chacha eats 7 half-rotis. How many rotis is that?
2 halves make 1 roti. So 7 halves = 3 full rotis (6 halves) + 1 half left.
7/2 = 3 + ½ = 3½ rotis
When the top number is bigger than the bottom number, the fraction is more than 1 whole. 3½ is called a mixed number (a whole number and a fraction together).
On a number line
Divide each gap between 0, 1, 2, 3, 4 into 2 equal parts. Now jump in halves: ½, 2/2 (=1), 3/2, 4/2 (=2), 5/2, 6/2 (=3), 7/2. You land halfway between 3 and 4.
11/4 → 11 ÷ 4 = 2, remainder 3 → 2¾ | 10/3 → 3, remainder 1 → 3⅓
🎯 Part 4: Comparing Using 1 and ½
Using 1 as a reference
Compare 9/10 and 5/4. Is either one more than a whole?
- 9/10: top is smaller than bottom → less than 1
- 5/4: top is bigger than bottom → more than 1
So 9/10 < 5/4. No drawing needed!
Using ½ as a reference
A fraction is exactly half when the top is half of the bottom: 3/6, 4/8, 10/20.
- Double = bottom → exactly ½ (5/10: 5 × 2 = 10)
- Double < bottom → less than ½ (4/11: 8 < 11)
- Double > bottom → more than ½ (5/9: 10 > 9)
Compare 4/11 and 5/9: 4/11 is less than ½, and 5/9 is more than ½. So 4/11 < 5/9.
❌ Common Mistakes to Avoid
✅ Check that the wholes are the same first.
✅ More pieces = smaller pieces. 1/5 > 1/8.
✅ 9 ÷ 4 = 2 remainder 1, so 9/4 = 2¼.
✅ Multiply top and bottom by the same number.
✏️ Practice Time
Try these on your own first, then check your answer below each question.
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Page 17 · Tamanna’s chocolatesCan ⅓ be bigger than ½?
Making a whole
½ = 2/4 = 3/6 = 4/8 = 6/12
Equivalent fractions using the kit
- Q1 (a) ⅓ = 2/6 = 3/9 = 4/12 (b) ¼ = 2/8 = 3/12 = 4/16 (c) ⅕ = 2/10 = 3/15 = 4/20 (d) ⅙ = 2/12 = 3/18 = 4/24
- Pattern: multiply the top and bottom by the same number.
- Q2 A: 2 sixths make ⅓
- Q2 B: (a) 2 eighths make ¼ (b) 4 eighths make ½
- Q2 C: (a) 6 twelfths make ½ (b) 4 make ⅓ (c) 3 make ¼ (d) 2 make ⅙
Make a whole with the kit (sample answers)
- ⅙ and 1/12: 4 pieces of ⅙ + 4 pieces of 1/12 (4/6 + 4/12 = 1)
- 1/12, ¼ and ½: ½ + ¼ + 3 pieces of 1/12 (6/12 + 3/12 + 3/12 = 12/12)
- Five same-size pieces: 5 pieces of ⅕
- Any seven pieces: ½ + 6 pieces of 1/12, or ¼ + ¼ + 5 pieces of 1/10 (2/4 + 5/10 = 1). Many answers are possible!
Equivalent to ⅓ and ⅖
⅖ = 4/10 = 6/15 = 8/20 = 20/50 = 40/100
The pattern: both numbers are multiplied by the same number.
Fill, tick, and complete
- Q1 (sample answers): (a) 1/7 = 2/14 (b) 2/3 = 4/6 (c) 3/4 = 6/8 (d) 3/5 = 6/10
- Q2: (a) 2/3 and 3/4 ✗ (b) 3/5 and 6/10 ✓ (c) 4/12 and 2/6 ✓ (d) 6/9 and 1/3 ✗ (6/9 = 2/3)
- Q3: (a) 2/5 = 4/10 (b) 3/4 = 12/16 (c) 4/7 = 8/14 (d) 5/9 = 25/45
Same denominator and same numerator
4/6 or 4/5 of a paratha? The one who ate 4/5 ate more, since a fifth is bigger than a sixth.
Same numerator: (a) 3/8 < 3/7 (b) 4/9 > 4/10 (c) 2/7 < 2/5 (d) 5/7 < 5/6 (e) 6/9 > 6/10 (f) 7/9 > 7/11
How many parathas?
- Dadiji: 7 halves = 7/2 = 3½ parathas
- Raman: 6 halves = 3 · Dadaji: 7 halves = 3½ · Baba: 5 halves = 2½
- Total for these three: 18 halves = 9 parathas
Quarter pieces
- Dadaji: 9/4 = 2¼ · Raman: 7/4 = 1¾ · Radhika: 6/4 = 1½ · Maa: 8/4 = 2 · Dadiji: 10/4 = 2½ · Baba: 12/4 = 3
- Total pieces: 9 + 7 + 6 + 8 + 10 + 12 = 52 quarters = 13 parathas (without Dadaji’s 9 pieces, 43/4 = 10¾)
Sharing pizza slices
Greater than one
Q2: Greater than 1: 9/4, 9/4, 5/4, 7/3, 13/11, 12/5, 12/8. (Top bigger than bottom.)
Less than 1: 7/9, 3/9, 2/5, 7/11, 4/9, 5/7, 2/3
Compare using 1
(a) 8/7 > 9/15 (b) 13/20 < 17/15 (c) 7/6 > 8/8 (8/8 is exactly 1) (d) 6/6 < 19/12 (e) 12/9 > 4/5 (f) 15/5 < 16/4 (both more than 1: 15/5 = 3 and 16/4 = 4)
Half and less than half
Q2: Less than ½: 3/9, 1/3, 3/15, 6/18, 15/31
(2/4 and 4/8 are exactly ½. 12/15, 8/15, 11/12, 7/11, 11/16 are more than ½.)
Compare using ½
In each pair, one fraction is more than ½ and the other is less than ½.
Ant line and a relation puzzle
Your father’s sister’s only brother is your father. So his child is you (or your brother or sister)!
👨👩👧 Tips for Parents
- At meals, cut rotis into halves and quarters and ask, “How many rotis did you eat?”
- Fold paper strips together to show ½ = 2/4 = 4/8.
- Ask, “Would you rather have ⅓ of this pizza or ¼?” Let your child explain why.