1- What should be added to
(1/2+1/3+1/5) to get 2
2-Find [3/115/6]-[9/124/3] +[5/13*6/15]
3- Divide the sum of 65/12 and 8/3 by their difference.
4- If a= 3 and b= 5 find the value of [ a/5+b/a]^a-2

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Solution

1- What should be added to

(1/2+1/3+1/5) to get 2
$\frac{1}{2} + \frac{1}{3} + \frac{1}{5} = \frac{15 + 10 + 6}{30} = \frac{31}{30}$
Let x be the quantity to be added to 31/30 to get 2.
$x + \frac{31}{30} = 2; x = 2 - \frac{31}{30} = \frac{60 - 31}{30} = \frac{29}{30}$

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Similar questions

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

Q. Find

(\frac{3}{11} \times \frac{5}{6}) - (\frac{9}{12} \times \frac{4}{3}) + (\frac{5}{13} \times \frac{6}{15})

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Q. Simplify:
(i)

\frac{11}{12} \div (\frac{5}{9} \times \frac{18}{25})

(ii)

(2 \frac{1}{2} \times \frac{8}{10}) \div (1 \frac{1}{2} + \frac{5}{8})

(iii)

\frac{15}{16}

(\frac{5}{6} - \frac{1}{2}) \div \frac{10}{11}

(iv)

\frac{9}{8} \div \frac{3}{5}

(\frac{3}{4} + \frac{3}{5})

(v)

\frac{2}{5} \div {\frac{1}{5} o f [\frac{3}{4} - \frac{1}{2}] - 1}

(vi)

(1 \frac{3}{4} \times 3 \frac{1}{7}) - (4 \frac{3}{8} \div 5 \frac{3}{5})

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

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1- What should be added to(1/2+1/3+1/5) to get 22-Find [3/11*5/6]-[9/12*4/3] +[5/13*6/15]3- Divide the sum of 65/12 and 8/3 by their difference.4- If a= 3 and b= 5 find the value of [ a/5+b/a]a-2

1- What should be added to (1/2+1/3+1/5) to get 2 12+13+15=15+10+630=3130 Let x be the quantity to be added to 31/30 to get 2. x+3130=2;x=2-3130=60-3130=2930

1- What should be added to
(1/2+1/3+1/5) to get 2
2-Find [3/115/6]-[9/124/3] +[5/13*6/15]
3- Divide the sum of 65/12 and 8/3 by their difference.
4- If a= 3 and b= 5 find the value of [ a/5+b/a]^a-2

1- What should be added to

(1/2+1/3+1/5) to get 2
$\frac{1}{2} + \frac{1}{3} + \frac{1}{5} = \frac{15 + 10 + 6}{30} = \frac{31}{30}$
Let x be the quantity to be added to 31/30 to get 2.
$x + \frac{31}{30} = 2; x = 2 - \frac{31}{30} = \frac{60 - 31}{30} = \frac{29}{30}$