PROBLEMS ON SIMPLIFYING COMPLEX FRACTIONS

Evaluate each expression.

Problem 1 :

2 + 23-65· (-2)

Solution :

Given, 2 + 23-65· (-2)= 2 + 23 × -56 · (-2)= 2 + 13 × -53 · (-2)= 2 - 59· (-2)= 2 + 109 = 21+ 109 = 21 × 99+ 109 = 189 + 109= 289

Problem 2 :

-116 - 74(-2) - 1

Solution :

Given, -116 - 74(-2) - 1= -116 × 22 - 74 × 33-3= -2212 - 2112-3= -2212 - 2112 × -13= -4312 × -13= 4336

Problem 3 :

-43 - 22 · -25

Solution :

Given, -43 - 22 · -25= -43 - 212 · -25= -43 - 21 × 33-45= -43 - 63 -45 = -103 -45= -103 × -54= 5012= 256

Problem 4 :

-56 + 213 - 45

Solution :

Given, -56 + 213 - 45= -56 + 213 × 55 - 45 × 33= -56 + 2515 - 1215= -56 + 25 - 1215= -56 + 2 -715= -56 + 2 × -157 = -56 - 307 = -56 × 77 - 307 × 66= -3542 - 18042 = -21542

Problem 5 :

1162- 2-12

Solution :

Given,1162- 2-12= 12136- 2-12= 12136- 21-12= 12136- 21 × 3636-12= 12136- 7236-12= 4936-12= 4936 × -21= -9836= -4918

Problem 6 :

-85 - -53 · 116-32

Solution :

Given, -85 - -53 · 116-32= -85 + 5518-32= -85 × 1818 + 5518 × 55-32= -14490 + 27590-32= 13190-32= 13190 × -23= -262270= -131135

Problem 7 :

-32 + -54 + 1412

Solution :

Given, -32 + -54 + 1412= -32 + -44 12= -32 + -1 12= -32 + (-1 × 2)= -32 - 2=-32 - 21 × 22= -32 - 42= -3 - 42= -72

Problem 8 :

-525 + 74 · 2

Solution :

Given, -525 + 74 · 2= -525 + 144 = -525 × 44 + 144 × 55 = -5820 + 7020 = -58 + 7020= -5 7820= -51 × 2078= -10078= -5039

Problem 9 :

23 - 53-13 - -95 - 32

Solution :

Given, 23 - 53-13 - -95 - 32= 2 - 53-13 × 55 - -95 × 33 - 32= -33-515 - -2715 - 32= -33 -5 + 2715 - 32= -1 2215 - 32= -11 × 1522 - 32= -1522 - 32= -1522 - 32 × 1111= -1522 - 3322= -15 - 3322 = -4822= -2411

Problem 10 :

-43 - 7512 - (-1) · (-1)

Solution :

Given, -43 - 7512 - (-1) · (-1)= -43 - 7512 + 1 · (-1)= -43 - 7512 + 11 · (-1)= -43 - 7512 + 11 × 22 · (-1)= -43 - 7512 + 22 · (-1)= -43 - 75 32 · (-1)= -43 - 75 × 23· (-1)= -43 - 1415 · (-1)= -43 + 1415= -43 × 55 + 1415= -2015 + 1415= -20 + 1415= -615= -25

Problem 11 :

-32 · -35 - 5(-1) - -12

Solution :

Given, -32 · -35 - 5(-1) - -12= -32 · -35 - 51-1 + 12= -32 · -35 - 51 × 55-1 + 12= -32 · -35 - 255-1 + 12= -32 · -35 - 255-11 + 12= -32 · -35 - 255-11 × 22 + 12= -32 · (-3 - 25)5-11 × 22 + 12= -32 · -285-22 + 12= -32 · -285-12= -32 ·-285 × -21= -32 ·565= -16810 = -845

Problem 12 :

43 · (-1)-16 - 12

Solution :

Given, 43 · (-1)-16 - 12= -43-16 - 112= -43-16 - 11 × 662= -43-16 - 662= -43 -762= -43 4936= -43 × 3649= -41 × 1249 = -4849

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