Exercise 3-E — Fractions 🧁

🔑 Yaad rakho!

a/b × c/d = ac/bd

a/b ÷ c/d = a/b × d/c

Mixed → Improper: a b/c = (ac+b)/c

Simplify = HCF se divide karo

Question 1

Evaluate (Fraction ke saath multiply/add karo)

Evaluate — (a), (b), (c), (d) — Click karke dekho! 👆

Part (a)

Part (b)

Part (c)

Part (d)

Part (a) — Question

(3−77 × 2227) + (4−63 × 10268)

Pehla bracket solve karo: 3−77 × 2227
Simplify karo: 3 aur 27 mein 3 common hai → 1−77 × 229
Phir 22 aur 77 mein 11 common hai → 1−7 × 29 = −2/63
Doosra bracket: 4−63 × 10268
4 aur 68 mein 4 common → 1−63 × 10217
102 aur 17 mein 17 common → 1−63 × 61 = −6/63
Ab dono add karo (same denominator 63): −263 + −663 = −863

✅ Answer = −8/63

💡 Seedha multiply karo top×top aur bottom×bottom. Pehle simplify karo toh numbers chhote rehte hain!

Part (b) — Question

(716 × −6442) + (6−45 × 135126)

Pehla bracket: 716 × −6442
16 aur 64 mein 16 common → 71 × −442
7 aur 42 mein 7 common → 11 × −46 = −2/3
Doosra bracket: 6−45 × 135126
6 aur 126 mein 6 common → 1−45 × 13521
135 aur 45 mein 45 common → 3−1 × 121 = −1/7
Add karo: −23 + −17
LCM of 3,7 = 21: −1421 + −321 = −1721

✅ Answer = −17/21

💡 LCM nikaalke add karo jab denominators alag hon!

Part (c) — Question

(1235 × 14744) + (6−90 ÷ 36132) − (524 × 7255)

Pehla bracket: 1235 × 14744
12 aur 44 mein 4 common → 335 × 14711
147 aur 35 mein 7 common → 35 × 2111 = 6355
Doosra bracket (division hai!): 6−90 ÷ 36132
Division = multiply by reciprocal: 6−90 × 13236
6 aur 36 mein 6 common, 90 aur 132 mein 6 common:
1−15 × 226 = 22−90 = −11/45
Teesra bracket: 524 × 7255
5 aur 55 mein 5 common, 24 aur 72 mein 24 common:
11 × 311 = 3/11
Final: 6355 + (−1145) − 311
LCM(55, 45, 11) = 495
= 567495 + −121495 − 135495
= 567 − 121 − 135495 = 311495

✅ Answer = 311/495

💡 Division wale bracket mein: flip karke multiply karo! ÷ b/c = × c/b

Part (d) — Question

(1334 × 17078) + (1435 × −2×556) − (72132 ÷ 1822)

Pehla bracket: 1334 × 17078
13 aur 78 mein 13 common → 134 × 1706
34 aur 170 mein 34 common → 11 × 56 = 5/6
Doosra bracket: 1435 × −1056 (kyunki −2×5 = −10)
14 aur 56 mein 14 common → 135 × −104
10 aur 35 mein 5 common → −27×4 = −1/14
Teesra bracket (division): 72132 ÷ 1822
= 72132 × 2218
72 aur 18 mein 18 common, 22 aur 132 mein 22 common:
= 46 × 11 = 2/3
Final: 56 + (−114) − 23
LCM(6, 14, 3) = 42
= 3542 − 342 − 2842 = 442 = 221

✅ Answer = 2/21

Question 2

Nihal ka Growth 📏

Nihal was 19¼ inches at birth. At 3 months he measured 23½ inches. Find his growth.

Samajhte hain Growth = Baad ki height − Pehle ki height. Bas subtraction karna hai mixed fractions mein!

Birth height = 19¼ = 77/4 inches
(19×4 + 1 = 77)
3-month height = 23½ = 47/2 inches
(23×2 + 1 = 47)
Growth = 47/2 − 77/4
LCM(2,4) = 4
= 94/4 − 77/4 = 17/4
17/4 = 4¼ inches

✅ Growth = 4¼ inches

💡 Mixed fraction ko improper mein badlo pehle: a b/c = (a×c + b)/c. Phir minus karo!

Question 3

Manisha ke Cupcakes 🧁

Manisha uses 2¾ cups of flour per batch. She bakes 8 batches. Total flour?

Samajhte hain Ek batch mein 2¾ cups lagti hai. 8 batches ke liye? Multiply karo! 8 × 2¾

2¾ ko improper fraction mein badlo: 2¾ = 11/4
(2×4 + 3 = 11)
8 × 11/4 = 88/4
88/4 = 22

✅ Total flour = 22 cups

💡 "Har ek mein X hai, n items hain" → n × X karo. Multiplication ka kaam hai!

Question 4

Vikram & Anna ka Fence 🏡

Fence section = 4⅔ feet long. Square garden with side 10 feet. How many sections needed?

Samajhte hain Square garden ka perimeter = 4 × side. Phir total length ÷ ek section ki length = kitne sections chahiye.

Square ka perimeter = 4 × 10 = 40 feet
Ek section = 4⅔ = 14/3 feet
(4×3 + 2 = 14)
Sections = 40 ÷ 14/3 = 40 × 3/14 = 120/14 = 60/7
60/7 = 8 remainder 4 → yaani 8 complete sections + thoda aur
Toh unhe 9 sections khareedne padenge (last wala cut karenge)

✅ Sections needed = 9 (ceiling of 60/7 = 8.57)

💡 Agar 8.57 sections chahiye, toh poore 9 khareedne padenge — aadha section toh milta nahi store mein! 😄

Question 5

John ka Mobile Phone 📱

Original price = ₹49,000. Sale price = 5/7 of original. How much does John pay?

Samajhte hain "Five-sevenths of original price" matlab original ka 5/7 hissa. Multiply karo!

Sale price = 57 × 49,000
= 5 × 49,0007 = 5 × 7,000
= ₹35,000

✅ John pays = ₹35,000

💡 "X ka 5/7 nikalo" = 5/7 × X. Pehle 7 se divide karo, phir 5 se multiply!

Question 6

Sohini ki Bicycle 🚴

Speed = 63⅓ km/h. Distance = 3½ km. How much time?

Formula yaad karo Time = Distance ÷ Speed. (Waqt = Doori ÷ Raftar)

Speed = 63⅓ = 190/3 km/h
(63×3 + 1 = 190)
Distance = 3½ = 7/2 km
Time = 7/2190/3 = 72 × 3190 = 21380 hours
Convert to minutes: 21380 × 60 = 1260380 = 63/19 minutes ≈ 3.3 minutes

✅ Time = 21/380 hours = 63/19 minutes

💡 Time = Distance / Speed. Division mein ulta karke multiply karo! Bahut chhota time hai kyunki speed bahut zyada hai.

Question 7

Anshul ki Short Story ✍️

Written 9⅖ pages. 1.5 hours to write one page. Total hours spent?

Samajhte hain Ek page = 1.5 ghante. Total pages = 9⅖. Total time = pages × time per page.

Pages = 9⅖ = 47/5
(9×5 + 2 = 47)
Time per page = 1.5 = 3/2 hours
Total time = 475 × 32 = 14110
141/10 = 14.1 hours = 14 hours 6 minutes

✅ Total time = 141/10 = 14.1 hours

💡 1.5 = 3/2 likho fraction mein — calculation easy ho jaati hai! Phir simply multiply karo.

Exercise 3 – E