Verify- 3-4- -5-6-7-8 - 3-4-5-6 -7-8By which property- it holds true-

nbsp;3/4+ ( 5/6+7/8 )= ( 3/4+ 5/6 )+7/8 L.H.S =3/4+ ( 5/6+7/8 ) =3/4+ ( 20+21/24 ) =3/4 + nbsp;1/24 =19/24 nbsp; .........(1) R.H.S =(3/4+ 5/6) +7/8 ...

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Standard VII

Mathematics

Problems Involving Difference of Fractions

Verify: 3/4+ ...

Question

Verify:
$\frac{3}{4} + (\frac{- 5}{6} + \frac{7}{8}) = (\frac{3}{4} + \frac{- 5}{6}) + \frac{7}{8}$
By which property, it holds true.

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Solution

$\frac{3}{4} + (\frac{- 5}{6} + \frac{7}{8}) = (\frac{3}{4} + \frac{- 5}{6}) + \frac{7}{8}$
$L . H . S = \frac{3}{4} + (\frac{- 5}{6} + \frac{7}{8})$
$= \frac{3}{4} + (\frac{- 20 + 21}{24})$
$= \frac{3}{4} + \frac{1}{24}$
$= \frac{19}{24} . . . . . . . . . (1)$
$R . H . S = (\frac{3}{4} + \frac{- 5}{6}) + \frac{7}{8}$
$= (\frac{9 - 10}{12}) + \frac{7}{8}$
$= \frac{- 1}{12} + \frac{7}{8}$
$= \frac{- 2 + 21}{24}$
$= \frac{19}{24} . . . . . . . . (i i)$
From (i) and (ii) LHS = RHS .
Hence verified.
This is assosciative law of addition.

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Similar questions

Q. Verify:

\frac{3}{4} + (\frac{- 5}{6} + \frac{7}{8}) = (\frac{3}{4} + \frac{- 5}{6}) + \frac{7}{8}

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Q. Verify:

\frac{3}{4} + (\frac{- 5}{6} + \frac{7}{8}) = (\frac{3}{4} + \frac{- 5}{6}) + \frac{7}{8}

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Q. Which property of multiplication is illustrated by :

\frac{- 4}{3} \times (\frac{- 6}{5} + \frac{8}{7}) = (\frac{- 4}{3} \times \frac{- 6}{5}) + (\frac{- 4}{3} \times \frac{8}{7})

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. Name the property of multiplication illustrated by

\frac{- 4}{3} \times (\frac{6}{5} + \frac{8}{7}) = (\frac{- 4}{3} \times \frac{6}{5}) + (\frac{- 4}{3} \times \frac{8}{7})

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Verify: 34+(−56+78)=(34+−56)+78 By which property, it holds true.

34+(−56+78)=(34+−56)+78 L.H.S =34+(−56+78) =34+(−20+2124) =34+124 =1924.........(1) R.H.S =(34+−56)+78 =(9−1012)+78 =−112+78 =−2+2124 =1924........(ii) From (i) and (ii) LHS = RHS . Hence verified. This is assosciative law of addition.

Verify:
$\frac{3}{4} + (\frac{- 5}{6} + \frac{7}{8}) = (\frac{3}{4} + \frac{- 5}{6}) + \frac{7}{8}$
By which property, it holds true.