1-2 - 1 - -1-2-3-2-5-2-7-2-

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Standard VII

Mathematics

Problems Involving Difference of Fractions

1/2 - 1 = ___...

Question

1/2 - 1 = ____

-1/2

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3/2

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5/2

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7/2

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$(i) \frac{6}{5} x^{2} - \frac{4}{5} x^{3} + \frac{5}{6} + \frac{3}{2} x from \frac{x^{3}}{3} - \frac{5}{2} x^{2} + \frac{3}{5} x + \frac{1}{4}$

$(i i) \frac{5 a^{2}}{2} + \frac{3 a^{3}}{2} + \frac{a}{3} - \frac{6}{5} from \frac{1}{3} a^{3} - \frac{3}{4} a^{2} - \frac{5}{2}$

$(i i i) \frac{7}{4} x^{3} + \frac{3}{5} x^{2} + \frac{1}{2} x + \frac{9}{2} from \frac{7}{2} - \frac{x}{3} - \frac{x^{2}}{5}$

$(i v) \frac{y^{3}}{3} + \frac{7}{3} y^{2} + \frac{1}{2} y + \frac{1}{2} from \frac{1}{3} - \frac{5}{3} y^{2}$

$(v) \frac{2}{3} a c - \frac{5}{7} a b + \frac{2}{3} b c from \frac{3}{2} a b - \frac{7}{4} a c - \frac{5}{6} b c$

Simplify each of the following: $(i) x^{2} - 3 x + 5 - \frac{1}{2} (3 x^{2} - 5 x + 7) (i i) [5 - 3 x + 2 y - (2 x - y)] - (3 x - 7 y + 9) (i i i) \frac{11}{2} x^{2} y - \frac{9}{4} x y^{2} + \frac{1}{4} x y - \frac{1}{14} y^{2} x + \frac{1}{15} y x^{2} + \frac{1}{2} x y (i v) (\frac{1}{3} y^{2} - \frac{4}{7} y + 11) - (\frac{1}{7} y - 3 + 2 y^{2}) - (\frac{2}{7} y - \frac{2}{3} y^{2} + 2) (v) - \frac{1}{2} a^{2} b^{2} c + \frac{1}{3} a b^{2} c - \frac{1}{4} a b c^{2} - \frac{1}{5} c b^{2} a^{2} + \frac{1}{6} c b^{2} a - \frac{1}{7} c^{2} a b + \frac{1}{8} c a^{2} b .$

In each of the following determine rational numbers a and b :

(i) $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a - b \sqrt{3}$

(ii) $\frac{4 + \sqrt{2}}{2 + \sqrt{2}} = a - \sqrt{b}$

(iii) $\frac{3 + \sqrt{2}}{3 - \sqrt{2}} = a + b \sqrt{2}$

(iv) $\frac{5 + 3 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

(v) $\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77}$

(vi) $\frac{4 + 3 \sqrt{5}}{4 - 3 \sqrt{5}} = a + b \sqrt{5}$

Multiply :

$(i) 8 a b^{2} b y - 4 a^{3} b^{4} (i i) \frac{2}{3} a b b y - \frac{1}{4} a^{2} b (i i i) - 5 c d^{2} b y - 5 c d^{2} (i v) 4 a a n d (6 a + 7) (v) - 8 x a n d (4 - 2 x - x^{2}) (v i) 2 a^{2} - 5 a - 4 a n d - 3 a . (v i i) x + 4 b y x - 5 (v i i i) 5 a - 1 b y 7 a - 3 (i x) 12 a + 5 b b y 7 a - b (x) x^{2} + x + 1 b y 1 - x (x i) 2 m^{2} - 3 m - 1 a n d 4 m^{2} - m - 1 (x i i) a^{2}, a b a n d b^{2} (x i i i) a b x, - 3 a^{2} x a n d 7 b^{2} x^{3} (x i v) - 3 b x, - 5 x y a n d - 7 b^{3} y^{2} (x v) (- \frac{3}{2} x^{5} y^{3}) a n d (\frac{4}{9} a^{2} x^{3} y) (x v i) (- \frac{2}{3} a^{7} b^{2}) a n d (- \frac{9}{4} a b^{5}) (x v i i) (2 a^{3} - 3 a^{2} b^{2}) a n d (- \frac{1}{2} a b^{2}) (x v i i i) (2 x + \frac{1}{2} y) a n d (2 x - \frac{1}{2} y)$

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