Name the property of multiplication illustrated by each of the following statements-i -158 -127-127 -158ii -23 - 79 -95-23 - 79 -95iii -34 x-56-78-34 -56-34 - 78iv -169 - 1-1 -169-169v -1115 - 15-11-15-11 -1115-1vi -75 - 0-0

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Standard VIII

Mathematics

Associative Property of Rational Numbers

Name the prop...

Question

Name the property of multiplication illustrated by each of the following statements:
(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$
(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$
(iii) $\frac{- 3}{4} \times (\frac{- 5}{6} + \frac{7}{8}) = (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$
(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$
(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$
(vi) $\frac{- 7}{5} \times 0 = 0$

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Solution

Commutative property

Associative property

Distributive property

Property of multiplicative identity

Property of multiplicative inverse

Multiplicative property of 0

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Q. Name the property of multiplication shown by each of the following statements:
(i)

\frac{- 12}{5} \times \frac{3}{4} = \frac{3}{4} \times \frac{- 12}{5}

(ii)

\frac{- 8}{15} \times 1 = \frac{- 8}{15}

(iii)

(\frac{- 2}{3} \times \frac{7}{8}) \times \frac{- 5}{7} = \frac{- 2}{3} \times (\frac{7}{8} \times \frac{- 5}{7})

(iv)

\frac{- 2}{3} \times 0 = 0

(v)

\frac{2}{5} \times (\frac{- 4}{5} + \frac{- 3}{10}) = (\frac{2}{5} \times \frac{- 4}{5}) + (\frac{2}{5} \times \frac{- 3}{10})

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

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

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

Q. Convert
the following table into cumulative frequency table.

X	$11$	$12$	$23$	$34$	$56$	$78$
F	$0$	$1$	$2$	$3$	$5$	$6$

Q. Mark the correct alternative in each of the following:

Which of the following is correct?

(a)

\frac{2}{3} < \frac{3}{5} < \frac{11}{15}

(b)

\frac{3}{5} < \frac{2}{3} < \frac{11}{15}

(c)

\frac{11}{15} < \frac{3}{5} < \frac{2}{3}

(d)

\frac{3}{5} < \frac{11}{15} < \frac{2}{3}

Simplify each of the following and write as a rational number of the form $\frac{p}{q}$ :
(i) $\frac{3}{4} + \frac{5}{6} + \frac{- 7}{8}$
(ii) $\frac{2}{3} + \frac{- 5}{6} + \frac{- 7}{9}$
(iii) $\frac{- 11}{2} + \frac{7}{6} + \frac{- 5}{8}$
(iv) $\frac{- 4}{5} + \frac{- 7}{10} + \frac{- 8}{15}$
(v) $\frac{- 9}{10} + \frac{22}{15} + \frac{13}{- 20}$
(vi) $\frac{5}{3} + \frac{3}{- 2} + \frac{- 7}{3} + 3$

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Name the property of multiplication illustrated by each of the following statements: (i) -158×-127=-127×-158 (ii) -23×79×-95=-23×79×-95 (iii) -34×-56+78=-34×-56+-34×78 (iv) -169×1=1×-169=-169 (v) -1115×15-11=15-11×-1115=1 (vi) -75×0=0

Commutative property Associative property Distributive property Property of multiplicative identity Property of multiplicative inverse Multiplicative property of 0

Commutative property

Associative property

Distributive property

Property of multiplicative identity

Property of multiplicative inverse

Multiplicative property of 0