✅ SOLUTIONS
Class 5
Chapter 2: Fractions
Math Mela · NCERT Solutions
Class 5Math Mela (NCERT)Chapter 2
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🍫 Warm-up Questions
Is Tamanna correct that ⅓ of one chocolate can be bigger than ½ of the other?
Solution
Yes, she can be correct — IF the two chocolates are different sizes.
Looking at the picture: the first chocolate has 4 pieces (2×2), and ½ of it = 2 pieces. The second chocolate has 6 pieces (2×3), and ⅓ of it = 2 pieces. But since the SECOND chocolate bar is physically bigger (6 pieces vs 4 pieces), its 2 pieces (⅓) can be bigger in actual size than the first bar's 2 pieces (½)!
⚠️ Important Lesson
We can only directly compare fractions like ⅓ and ½ (and say one is "bigger") when they are parts of the SAME-sized whole. Here, the wholes are different, so simple fraction comparison doesn't apply to actual size.Playing with a Grid — Shade 1/8 of Grid A (red), 1/6 of Grid B (blue), 1/12 of Grid C (yellow). Find 1/3 in any grid.
Solution
Each grid has 8 columns × 6 rows = 48 equal cells.
| Grid | Fraction | Cells to shade | Working |
|---|---|---|---|
| A (red) | 1/8 | 6 cells | 48 ÷ 8 = 6 (e.g., one full column) |
| B (blue) | 1/6 | 8 cells | 48 ÷ 6 = 8 (e.g., one full row) |
| C (yellow) | 1/12 | 4 cells | 48 ÷ 12 = 4 (e.g., a small 2×2 block) |
Grid A: 1/8 shaded (one full column = 6 cells)
Finding 1/3: since 1/3 of 48 = 16 cells, and 1/6 = 8 cells (one row in Grid B), 1/3 = exactly TWO rows (16 cells) in the same grid — double the 1/6 shaded amount!
Is 1/3 equal to 2/6? Fraction pattern discovery.
Solution
Yes! When a whole is divided into 3 equal parts and 1 is shaded, that's the same shaded area as dividing it into 6 equal parts (by splitting each of the 3 parts into 2) and shading 2 of them.
1/3
2/6
1/3 = 2/6 — these are called equivalent fractions: different names for the same amount.
Continuing the pattern from the picture (1/3, 2/6, 3/9, 4/12):
1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 6/18 = 7/21 = 8/24 = ... = 16/48 (24) ... = 24/72 (36)
💡 Pattern: multiply both numerator and denominator of 1/3 by the same number — 1×8/3×8=8/24, 1×12/3×12=12/36.
For 2/5 pattern (2/5, 4/10, ...):
2/5 = 4/10 = 6/15 = 8/20 = 20/50 = 40/100
✍️ Let Us Do — Equivalent Fractions
Q1. Fill in the blanks with equivalent fractions.
Solution(other correct answers also possible)
| Fraction | One equivalent chain |
|---|---|
| (a) 1/7 | 1/7 = 2/14 = 3/21 |
| (b) 2/3 | 2/3 = 4/6 = 6/9 |
| (c) 3/4 | 3/4 = 6/8 = 9/12 |
| (d) 3/5 | 3/5 = 6/10 = 9/15 |
Q2. Tick (✓) the pairs that are equivalent.
Solution
| Pair | Check | Equivalent? |
|---|---|---|
| (a) 2/3 and 3/4 | 2/3≈0.67, 3/4=0.75 — different | ❌ No |
| (b) 3/5 and 6/10 | 3×2=6, 5×2=10 — matches! | ✅ Yes |
| (c) 4/12 and 2/6 | 4/12=1/3, 2/6=1/3 — same! | ✅ Yes |
| (d) 6/9 and 1/3 | 6/9=2/3, but 1/3 is different | ❌ No |
Q3. Fill in the boxes so the fractions become equivalent.
Solution
| Given | Working | Answer |
|---|---|---|
| (a) 2/5 = ?/10 | 10÷5=2, so 2×2=4 | 2/5 = 4/10 |
| (b) 3/4 = ?/16 | 16÷4=4, so 3×4=12 | 3/4 = 12/16 |
| (c) 4/7 = 8/? | 8÷4=2, so 7×2=14 | 4/7 = 8/14 |
| (d) 5/9 = 25/? | 25÷5=5, so 9×5=45 | 5/9 = 25/45 |
⚖️ Let Us Do — Same Denominator
Compare using < and > signs.
SolutionSame denominator → bigger numerator wins
| Part | Comparison | Answer |
|---|---|---|
| (a) | 1/4 ___ 3/4 | 1/4 < 3/4 |
| (b) | 3/5 ___ 4/5 | 3/5 < 4/5 |
| (c) | 5/7 ___ 2/7 | 5/7 > 2/7 |
| (d) | 7/8 ___ 3/8 | 7/8 > 3/8 |
| (e) | 5/10 ___ 6/10 | 5/10 < 6/10 |
| (f) | 2/6 ___ 1/6 | 2/6 > 1/6 |
⚖️ Let Us Do — Same Numerator
Compare using < and > signs.
SolutionSame numerator → SMALLER denominator wins
| Part | Comparison | Answer |
|---|---|---|
| (a) | 3/8 ___ 3/7 | 3/8 < 3/7 |
| (b) | 4/9 ___ 4/10 | 4/9 > 4/10 |
| (c) | 2/7 ___ 2/5 | 2/7 < 2/5 |
| (d) | 5/7 ___ 5/6 | 5/7 < 5/6 |
| (e) | 6/9 ___ 6/10 | 6/9 > 6/10 |
| (f) | 7/9 ___ 7/11 | 7/9 > 7/11 |
💡 Think of pizza slices: if the SAME number of slices are cut from two pizzas, the pizza cut into FEWER total slices has BIGGER slices!
🥙 Let Us Do — Fractions Greater Than 1
Paratha story problems (from the chapter)
Solution
| Person | Pieces eaten | Working | Parathas eaten |
|---|---|---|---|
| Maa | 5 pieces of 1/2 | 5/2 = 2 + 1/2 | 2½ parathas |
| Radhika | 6 pieces of 1/2 | 6/2 = 3 | 3 parathas |
| Dadiji | 7 pieces of 1/2 | 7/2 = 3 + 1/2 | 3½ parathas |
| Raman | 6 pieces of 1/2 | 6/2 = 3 | 3 parathas |
| Baba | 5 pieces of 1/2 | 5/2 = 2 + 1/2 | 2½ parathas |
Total parathas made that day (Raman 6 + Dadaji 7 + Baba 5 pieces, all halves): (6+7+5) ÷ 2 = 18 ÷ 2 = 9 parathas
Dadaji: 9 pieces of 1/4 → 9/4 = 2 + 1/4 = 2¼ parathas
| Person | Pieces of 1/4 | Parathas eaten |
|---|---|---|
| Raman | 7 | 7/4 = 1¾ |
| Radhika | 6 | 6/4 = 1½ |
| Maa | 8 | 8/4 = 2 |
| Dadiji | 10 | 10/4 = 2½ |
| Baba | 12 | 12/4 = 3 |
Total parathas made: (7+6+8+10+12) ÷ 4 = 43 ÷ 4 = 10¾ parathas
Pizza: Raman's total share = his own 1/3 + Dadiji's 1/3 + Dadaji's 1/3 = 3/3 = 1 whole pizza. He could only eat 2 slices, so he gave 1 slice (1/3) to Radhika.
Radhika's total = her own 1/3 + Maa's 1/3 + Baba's 1/3 + Raman's gift 1/3 = 4/3 = 1⅓ pizza
Radhika's total = her own 1/3 + Maa's 1/3 + Baba's 1/3 + Raman's gift 1/3 = 4/3 = 1⅓ pizza
Q1. Show 2/3 & 5/3, 3/4 & 5/4, 4/8 & 9/8 using parathas & number lines.
Solution — Method
For each pair, draw a number line from 0 to beyond 2, split into the given number of equal parts, and mark the fraction:
0
2/3
1
5/3
2
2/3 is less than 1 whole paratha. 5/3 = 1 whole + 2/3 more = 1⅔ parathas (more than 1 paratha).
Similarly: 5/4 = 1¼ parathas (just over 1), and 9/8 = 1⅛ parathas (just over 1) — both greater than one whole.
Q2. Circle the fractions greater than 1 from the list.
Solution
List: 7/9, 2/5, 5/4, 3/9, 2/3, 7/3, 7/11, 13/11, 9/4, 5/7, 4/9, 12/5, 9/4, 12/8
A fraction is greater than 1 exactly when the numerator is bigger than the denominator. Circle these:
5/4 7/3 13/11 9/4 12/5 12/8
(9/4 appears twice in the list — circle both!) All the rest (7/9, 2/5, 3/9, 2/3, 7/11, 5/7, 4/9) have numerator smaller than denominator, so they are all less than 1.
🎯 Let Us Do — Reference to 1
Compare using 1 as a reference.
Solution
| Part | Fraction 1 vs 1 | Fraction 2 vs 1 | Answer |
|---|---|---|---|
| (a) | 8/7 > 1 | 9/15 < 1 | 8/7 > 9/15 |
| (b) | 13/20 < 1 | 17/15 > 1 | 13/20 < 17/15 |
| (c) | 7/6 > 1 | 8/8 = 1 | 7/6 > 8/8 |
| (d) | 6/6 = 1 | 19/12 > 1 | 6/6 < 19/12 |
| (e) | 12/9 > 1 | 4/5 < 1 | 12/9 > 4/5 |
| (f) | 15/5 = 3 | 16/4 = 4 | 15/5 < 16/4 |
💡 Part (f): both are >1, so simplify fully (15/5=3, 16/4=4) and compare whole numbers.
🎯 Let Us Do — Reference to ½
Q1. Circle the fractions equal to ½.
Solution
List: 2/4, 3/5, 5/7, 7/14, 5/10, 8/16, 5/9, 6/12, 10/20, 6/8
A fraction equals ½ exactly when 2 × numerator = denominator. Circle:
2/4 7/14 5/10 8/16 6/12 10/20
(3/5, 5/7, 5/9, 6/8 are NOT equal to ½.)
Q2. Circle the fractions less than half.
Solution
List: 3/9, 2/4, 12/15, 8/15, 11/12, 3/15, 4/8, 1/3, 7/11, 11/16, 15/31, 6/18
Less than half means 2 × numerator < denominator. Circle:
3/9 3/15 1/3 15/31 6/18
(2/4 and 4/8 are exactly half, NOT less than half, so don't circle those.)
Q3. Compare fractions using ½ as reference where possible.
Solution
| Pair | vs ½ | Answer |
|---|---|---|
| 2/9 and 4/7 | 2/9<½ (since 2×2=4<9); 4/7>½ (2×4=8>7) | 2/9 < 4/7 |
| 11/14 and 7/20 | 11/14>½ (22>14); 7/20<½ (14<20) | 11/14 > 7/20 |
| 5/7 and 3/9 | 5/7>½ (10>7); 3/9=1/3<½ | 5/7 > 3/9 |
| 6/7 and 4/10 | 6/7>½ (12>7); 4/10=2/5<½ (8<10) | 6/7 > 4/10 |
| 9/17 and 3/15 | 9/17>½ (18>17, just barely); 3/15=1/5<½ | 9/17 > 3/15 |
| 7/12 and 3/11 | 7/12>½ (14>12); 3/11<½ (6<11) | 7/12 > 3/11 |
| 1/3 and 5/9 | 1/3<½ (2<3); 5/9>½ (10>9) | 1/3 < 5/9 |
| 3/9 and 4/7 | 3/9=1/3<½; 4/7>½ (8>7) | 3/9 < 4/7 |
💡 Quick test: double the numerator and compare to the denominator. Bigger → fraction > ½. Smaller → fraction < ½. Equal → exactly ½.
🐜 Try This & Fun with Relations
If an ant is 1/4 cm long, what is the total length of 16 such ants in a line?
Solution
Length of 16 ants = 16 × 1/4 cm = 16/4 cm = 4 cm
0
1
2
3
4
Since 4 ants of 1/4 cm make exactly 1 cm, 16 ants (4 groups of 4) make 4 cm in total.
Fun with Relations: If the only brother of your father's sister had a child, what is that child's relation to you?
Solution
Let's break it down step by step:
1
"Father's sister" = your aunt (Bua/Foi)
2
"The only brother of your father's sister" = your aunt's only brother = that IS your own father! (since your father is indeed his sister's brother)
3
So "his child" = your father's child = YOU or your sibling!
The child's relationship to you is: brother or sister (sibling)! 🎉