Verify- 3-4- -5-6-7-8 - 3-4-5-6 -7-8-4 MARKS-

Concept : 1 Mark Simplification : 2 Marks Verification : 1 Mark 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 + ...

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Byju's Answer

Standard VII

Mathematics

Addition and Subtraction of Rational Numbers

Verify: 3/4+ ...

Question

Verify:
$\frac{3}{4} + (\frac{- 5}{6} + \frac{7}{8}) = (\frac{3}{4} + \frac{- 5}{6}) + \frac{7}{8}$
[4 MARKS]

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Solution

Concept : 1 Mark
Simplification : 2 Marks
Verification : 1 Mark

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

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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}

[4 MARKS]

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. 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.

In a Mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table using tally marks.

8	1	3	7	6	5	5	4	4	2
4	9	5	3	7	1	6	5	2	7
7	3	8	4	2	8	9	5	8	6
7	4	5	6	9	6	4	4	6	6

(a) Find how many students obtained marks equal to or more than7.

(b) How many students obtained marks below 4?

Q. The following data gives the marks of 20 students in Mathematics (X) and statistics (Y), each out of 10, expressed as (x, y). Construct an ungrouped frequency distribution, considering single numbers as a class:

(2, 7), (3, 8), (4, 9), (2, 8), (5, 6), (5, 7), (4, 9), (3, 8), (4, 8), (2, 9), (3, 8), (4, 8), (5, 6), (4, 7),

(4, 7), (4, 6), (5, 6), (5, 7), (4, 6), (5, 5).

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Verify: 34+(−56+78)=(34+−56)+78 [4 MARKS]

Concept : 1 Mark Simplification : 2 Marks Verification : 1 Mark 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.

Verify:
$\frac{3}{4} + (\frac{- 5}{6} + \frac{7}{8}) = (\frac{3}{4} + \frac{- 5}{6}) + \frac{7}{8}$
[4 MARKS]