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Question

Simplify:
(a) 23+17 (b) 310+715 (c) 49+27 (d)57+13

(e) 45+23 (f) 3413 (g) 5613

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Solution

(a) 23+17

Now, LCM of 3 and 7 is 21. [LCM of co-prime numbers is their product]

=2×73×7+1×37×3=1421+321

=1721

(b) 310+715

We will first find the LCM of the given denominators.

210,1535,1555,51

LCM of 10 and 15=2×3×5=30

=3×1510×15+7×1015×10

=45150+70150

=45+70150

=115150

=2330

(c) 49+27

Since, 9 and 7 are co prime numbers, therefore, their LCM will be 9×7=63

=4×79×7+2×97×9

=28+1863

=4663

(d) 57+13

Since, 7 and 3 are co prime numbers, their LCM will be their product ie. 21

=5×37×3+1×73×7

=1521+721

=2221

(e) 45+23

Since, 5 and 3 are are co prime numbers their LCM will be their product ie. 15

=4×35×3+2×53×5

=1215+1015

=2215

(f) 3413

Since, 4 and 3 are co prime numbers their LCM will be their product ie. 12.

=3×34×31×43×4

=912412

=512

(g) 5613

Since, 6 is the multiple of 3 their LCM will be 6

=561×23×2

=5626

=36

=12


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