DECIMAL FRACTIONS EXERCISE 3 (SOLUTION 101 TO 110)

101.  Given expression = (1.49 x 1.49 x 10 – 0.51 x 0.51x 10)/1.49 x 10 – 0.51x 10)

       =10[(1.49)² - (0.51)²]/10(1.49 – 0.51) = (1.49 + 0.51) = 2.

102.  Given expression = (a² -b²) / (a + b) (a – b) = (a² -b²)/ (a²/² = 1.

103.  Given expression = 5.32 x (56 + 44)/(7.66 + 2.34) (7.66 – 2.34) = 5.32 x 100 /10x5.32 = 10.

104.  Given expression = [(0.6)² ]² - [(0.5)²]²/(0.6)² + (0.5)²= (0.6)² ] - [(0.5)²][(0.6)² + 

        (0.5)/(0.6)² + (0.5)²

      = (0.6)² - (0.5)² = (0.6 + 0.5) (0.6 -0.5) = (1.1 x 0.1) = 0.11.

105.  Given expression = (7.5 x 7.5 +2 x 7.5 x 2.5 + 2.5 x 2.5)

  = (a² + 2ab + b²) =(a + b)² = (7.5 + 2.5)²= 10²= 100.

106.  0.2 x0.2 + 0.02  x 0.02 -0.4x0.02  =0.2 x 0.2 +  0.02 x 0.02 – 2x 0.2- 0.02

    = (a² + b² - 2ab) = (a – b)² = (0.2 – 0.02)²

    = (0.18)²

Given expression = (0.18 x 0.18)/0.36 = 0.09.

107.  Given expression = (11.98)² + (0.02)² + 11.98 x X.

    For the given expression to be a perfect t square, we must have

111.98 x X =2 x 11.98 x 0.2 or x = 0.04.

108.   Given expression = (a – b)² + (a +b)²/a² + b² = 2 (a² + b²/(a² + b²) = 2.

109.  Given expression = (a + b)² + (a – b)²/ a b =4ab/a b = 4.

120.  Given expression = (0.051)³ + (0.041)³/(0.051)² - (0.051 x 0.041) + (0.041)² = (a³ +   b³/a² - a b + b²).

  = (a +b) = (0.051) + 0.041) = (0.041)