Which of the following expressions show that rational numbers are associative under multiplication- a 2-3-6-7-3-5-2-3-6-7-3-5 b 2-3-6-7-3-5-2-3-3-5-6-7 c 2-3-6-7-3-5-3-5-2-3-6-7 d 2-3-6-7-3-5-6-7-2-3-3-5

Given, 2/3× ( 6/7×3/5 ) = ( 2/3× 6/7 ) ×3/5 [by associative property under multiplication a × (b × c) = (a × b) × c] ⇒2/3× 18/35 = 12/21×3/5 So, a × (b × ...

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Standard VIII

Mathematics

Associative Property of Rational Numbers

Which of the ...

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Question 6

Which of the following expressions show that rational numbers are associative under multiplication.
(a) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5}$
(b) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = \frac{2}{3} \times (\frac{3}{5} \times \frac{- 6}{7})$
(c) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{3}{5} \times \frac{2}{3}) \times \frac{- 6}{7}$
(d) $(\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5} = (\frac{- 6}{7} \times \frac{2}{3}) \times \frac{3}{5}$

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Solution

Given, $\frac{2}{3} \times (- \frac{6}{7} \times \frac{3}{5}) = (\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5}$ [by associative property under multiplication $a \times (b \times c) = (a \times b) \times c$ ]
$\Rightarrow \frac{2}{3} \times \frac{- 18}{35} = \frac{- 12}{21} \times \frac{3}{5}$
So, $a \times (b \times c) = (a \times b) \times c$
Hence, the given expression shows that rational numbers are associative under multiplication i.e option (a).

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Question 6

Which of the following expressions show that rational numbers are associative under multiplication.
(a) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5}$
(b) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = \frac{2}{3} \times (\frac{3}{5} \times \frac{- 6}{7})$
(c) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{3}{5} \times \frac{2}{3}) \times \frac{- 6}{7}$
(d) $(\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5} = (\frac{- 6}{7} \times \frac{2}{3}) \times \frac{3}{5}$

2/3 x [-6/7+4/5]=[ 2/3 x 4/5] x (-6/7)

Q. Simplify each of the following by rationalizing the denominator

\frac{6 - 4 \sqrt{2}}{6 + 4 \sqrt{2}}

\frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} + \sqrt{5}}

\frac{1}{3 \sqrt{2} - 2 \sqrt{3}}

\frac{3 \sqrt{5} - \sqrt{7}}{3 \sqrt{3} + \sqrt{2}}

Q. Name the property of rational numbers illustrated by the given statement.

\frac{- 3}{2} \times \frac{5}{4} + \frac{- 3}{2} \times \frac{- 7}{6} = \frac{- 3}{2} \times (\frac{5}{4} + \frac{- 7}{6})

Question 91

Following are the numbers of members in 25 families of a village :6, 8, 7, 7, 6, 5, 3, 2, 5, 6, 8, 7, 7, 4, 3, 6, 6, 6, 7, 5, 4, 3, 3, 2, 5 Prepare a frequency distribution table for the data using class intervals 0-2, 2-4 etc.

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Associative Property of Rational Numbers

Standard VIII Mathematics

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Question 6 Which of the following expressions show that rational numbers are associative under multiplication. (a) 23×(−67×35)=(23×−67)×35 (b) 23×(−67×35)=23×(35×−67) (c) 23×(−67×35)=(35×23)×−67 (d) (23×−67)×35=(−67×23)×35

Given, 23×(−67×35)=(23×−67)×35 [by associative property under multiplication a×(b×c)=(a×b)×c] ⇒23×−1835=−1221×35 So, a×(b×c)=(a×b)×c Hence, the given expression shows that rational numbers are associative under multiplication i.e option (a).