Chapter - 2- EXERCISE 2.2 - Basic Geometrical Ideas (NCERT Class 6th Maths Solution)

1. Find the sum by suitable rearrangement:
    (a) 837 + 208 + 363                 (b) 1962 + 453 + 1538 + 647

Solution/Explanation:

(a) 837+208+363${\displaystyle 837+208+363}$
= (837+363)+208${\displaystyle (837+363)+208}$
=1200+208${\displaystyle =1200+208}$
=1408${\displaystyle =1408}$ answer
(b)1962+453+1538+647${\displaystyle 1962+453+1538+647}$
=(1962+1538)+(453+647)${\displaystyle =(1962+1538)+(453+647)}$
=3500+1100${\displaystyle =3500+1100}$
=4600
2. Find the product by suitable rearrangement:
     (a) 2 × 1768 × 50                                           (b) 4 × 166 × 25                                                                   (c) 8 × 291 × 125                                           (d) 625 × 279 × 16                                                               (e) 285 × 5 × 60                                             (f) 125 × 40 × 8 × 25

Solution/Explanation:

(a) 2⋅1768⋅50${\displaystyle 2\cdot 1768\cdot 50}$
=(2⋅50)⋅1768=176800${\displaystyle =(2\cdot 50)\cdot 1768=176800}$
(b) 4⋅166⋅25${\displaystyle 4\cdot 166\cdot 25}$
=(4⋅25)⋅166${\displaystyle =(4\cdot 25)\cdot 166}$
=100⋅166=16600${\displaystyle =100\cdot 166=16600}$
(c) 8⋅291⋅125${\displaystyle 8\cdot 291\cdot 125}$
=(8⋅125)⋅291${\displaystyle =(8\cdot 125)\cdot 291}$
=1000⋅291=291000${\displaystyle =1000\cdot 291=291000}$
(d) 625⋅279⋅16${\displaystyle 625\cdot 279\cdot 16}$
=(625⋅16)⋅279=10000⋅279${\displaystyle =(625\cdot 16)\cdot 279=10000\cdot 279}$
=2790000${\displaystyle =2790000}$
(e) 285⋅5⋅60${\displaystyle 285\cdot 5\cdot 60}$
=285⋅(5⋅60)=285⋅300${\displaystyle =285\cdot (5\cdot 60)=285\cdot 300}$
=85500${\displaystyle =85500}$
(f) 125⋅40⋅8⋅25=(125⋅8)⋅(40⋅25)${\displaystyle 125\cdot 40\cdot 8\cdot 25=(125\cdot 8)\cdot (40\cdot 25)}$
=1000⋅1000${\displaystyle =1000\cdot 1000}$
=1000000

3. Find the value of the following:
(a) 297 × 17 + 297 × 3                                    (b) 54279 × 92 + 8 × 54279                                            (c) 81265 × 169 – 81265 × 69                         (d) 3845 × 5 × 782 + 769 × 25 × 218

Solution/Explanation:

(a)297⋅17+297⋅3${\displaystyle 297\cdot 17+297\cdot 3}$
=297(17+3)=297⋅20${\displaystyle =297(17+3)=297\cdot 20}$
=5940${\displaystyle =5940}$ answer
(b)54279⋅92+8⋅54279${\displaystyle 54279\cdot 92+8\cdot 54279}$
=54279(92+8)=54279⋅100${\displaystyle =54279(92+8)=54279\cdot 100}$
=5427900${\displaystyle =5427900}$
(c)81265⋅169−81265⋅69${\displaystyle 81265\cdot 169-81265\cdot 69}$
=81265(169−69)=81265⋅100${\displaystyle =81265(169-69)=81265\cdot 100}$
=8126500${\displaystyle =8126500}$
(d)3845⋅5⋅782+769⋅25⋅218${\displaystyle 3845\cdot 5\cdot 782+769\cdot 25\cdot 218}$
=3845⋅5⋅782+(769⋅5)⋅5⋅218${\displaystyle =3845\cdot 5\cdot 782+(769\cdot 5)\cdot 5\cdot 218}$
=3845⋅5⋅782+3845⋅5⋅218${\displaystyle =3845\cdot 5\cdot 782+3845\cdot 5\cdot 218}$
=3845⋅5(782+218)=19225⋅1000${\displaystyle =3845\cdot 5(782+218)=19225\cdot 1000}$
=19225000${\displaystyle =19225000}$

${\displaystyle \mathrm{<br>}}$

4. Find the product using suitable properties.
(a) 738 × 103                   (b) 854 × 102               (c) 258 × 1008                     (d) 1005 × 168

Solution/Explanation:

(a) 738 × 103 = 738 × (100 + 3)

= 738 × 100 + 738 × 3 (Distributive property)

= 73800 + 2214 = 76014

(b) 854 × 102 = 854 × (100 + 2)

= 854 × 100 + 854 × 2

= 85400 + 1708 = 87108 (Distributive property)

(c) 258 × 1008 = 258 × (1000 + 8)

= 258 × 1000 + 258 × 8 (Distributive property)

= 258000 + 2064 = 260064

(d) 1005 × 168 = (1000 + 5) × 168

= 1000 × 168 + 5 × 168 (Distributive property)

= 168000 + 840 = 168840

5. A taxi driver filled his car petrol tank with 40 litres of petrol on Monday. The next day, he filled the tank with 50 litres of petrol. If the petrol costs ` 44 per litre, how much did he spend in all on petrol?

Solution/Explanation:

Petrol filled on Monday = 40 liters
Petrol filled on next day = 50 liters
Total petrol filled = 90 liters
Now, Cost of 1 liter petrol = Rs. 44
Cost of 90 liters petrol = 44 x 90
= 44 x (100 – 10)
= 44 x 100 – 44 x 10
= 4400 – 440
= Rs. 3960
Therefore, he spent Rs. 3960 on petrol.

6. A vendor supplies 32 litres of milk to a hotel in the morning and 68 litres of milk in the evening. If the milk costs ` 45 per litre, how much money is due to the vendor per day? 

Solution/Explanation:

Amount of milk supplied in the morning = 

Amount of milk supplied in the evening = 

 Total amount of petrol = 

Cost of 1 litre of milk = 

 Cost of  of milk = 

7. Match the following: 

(i) 425 × 136 = 425 × (6 + 30 +100)                              (a) Commutativity under multiplication.

 (ii) 2 × 49 × 50 = 2 × 50 × 49                                        (b) Commutativity under addition. 

(iii) 80 + 2005 + 20 = 80 + 20 + 2005                            (c) Distributivity of multiplication over addition. 

Solution/Explanation:

(i) 425 x 136 = 425 x (6 + 30 + 100)           (c) Distributivity of multiplication over addition 

(ii) 2 x 49 x 50 = 2 x 50 x 49                      (a) Commutivity under multiplication 

(iii) 80 + 2005 + 20 = 80 + 20 + 2005        (b) Commutivity under addition