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Fractions and Decimals

Question
CBSEENMA7000738

Solve:

(i)  2-35 (ii) 4+78 (iii) 35+27

(iv)  911-415 (v) 710+25+32  (vi)  223+312

(vii)   812-358

Solution

(i)  2-35=2×55-35= 10-35=75

(ii)   4+78=4*88+78 = (4×8)+78 = 398=478

(iii)  35+27=3×75×7+2×57×5=21+1035=3135

(iv)  911-415=9×1511×15-4×1115×11= 135-44165=91165

(v)   710+25+32 = 710+2×25×2+7+4+1510=2610=135=235

(vi)  223+312= 83+72=8×23×2+7×32×3=16+216=376=616

(vii)   812-358=172-298=17×42×4-298=68-298=398=478

Question
CBSEENMA7000739

Arrange the following in descending order:

(i)29,23,821 (ii) 15,37,710

Solution

(i)  29, 23,821

Changing them to like fractions, we obtain

 29=2×79×7=146323=2×213×21=4263821=8×321×3=2463

Since 42>24>14,

 23>821>29(ii)  15,37, 710

Changing them to like fractions, we obtain

15=1×145×14=147037=3×107×10=3070710=7×710×7=4970

As 49 > 30>14,

 7010>37>15

Question
CBSEENMA7000740

In a “magic square”, the sum of the numbers in each row, in each column and along the diagonal is the same. Is this a magic square?

411

911

211

(Along the first row  411+911+211+511)

311

511

711

811

111

611

 

Solution

Along the first row, sum =  411+911+211=1511

Along the second row, sum = 311+511+711=1511

Along the third row, sum = 811+111+611=1511

Along the first column, sum = 411+311+811=1511

Along the second column, sum = 911+511+111=1511

Along the third column, sum =211+711+611=1511

Along the first diagonal, sum = 411+511+611=1511

Along the second diagonal, sum =211+511+811=1511

Since the sum of the numbers in each row, in each column, and along the diagonals is the same, it is a magic square.

Question
CBSEENMA7000741

A rectangular sheet of paper is 1212cm long and 1023cm wide.

Find its perimeter.

Solution

Length =1212 cm = 252cm

Breadth = 1023 cm = 323 cm

Perimeter = 2 × (Length + Breadth)

=2×252+323=2×(25×3)+(32×2)6=2×75+646=2×1396=1393=4613 cm