Using bodmas rule ⇒ 4 / 5 ÷ 7 / 15 of 8 / 9 #160; ⇒ 4 / 5 ÷ 7× 8 / 15× 9 #160; ⇒ 4 / 5 ÷ 56 / 15× 9 #160; ⇒ 4 × 1 5 × ...

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Standard X

Mathematics

Frequency

45÷715 of 8...

Question

$\frac{4}{5} \div \frac{7}{15}$ of $\frac{8}{9}$ .

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Solution

$U s i n g b o d m a s r u l e \Rightarrow \frac{4}{5} \div \frac{7}{15} o f \frac{8}{9} \Rightarrow \frac{4}{5} \div \frac{7 \times 8}{15 \times 9} \Rightarrow \frac{4}{5} \div \frac{56}{15 \times 9} \Rightarrow \frac{4 \times 15 \times 9}{5 \times 56} = \frac{27}{14} A n s . B O D M A S - B O D M A S i s a a c r o n y m a n d i t s t a n d s f o r b r a c k e t, o f, d i v i s i o n, m u l t i p l i c a t i o n,$ $a d d i t i o n, a n d s u b t r a c t i o n . I t l a i n s t h e o r d e r o f o p e r a t i o u s t o s o l v e a n d r e s s i o n, a c c o r d i n g t o B O D M A S r u l e .$

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$Name the multiplication property of rational numbers shown below: (i) \frac{3}{5} \times \frac{- 8}{9} = \frac{- 8}{9} \times \frac{3}{5} (i i) \frac{- 3}{4} \times (\frac{5}{7} \times \frac{- 8}{15}) = (\frac{- 3}{5} \times \frac{5}{7}) \times \frac{- 8}{15} (i i i) \frac{4}{5} \times (\frac{3}{- 8} + \frac{- 4}{7}) = \frac{4}{5} \times \frac{3}{- 8} + \frac{4}{5} \times \frac{- 4}{7} (i v) \frac{- 7}{5} \times \frac{5}{- 7} = 1 (v) \frac{8}{- 9} \times 1 = 1 \times \frac{8}{- 9} = \frac{8}{- 9} (v i) \frac{- 3}{4} \times 0 = 0$

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. The property under addition used in each of the following are
(i)

(\frac{- 3}{7}) + \frac{1}{9} = \frac{1}{9} + (\frac{- 3}{7})

(ii)

\frac{4}{9} + (\frac{7}{8} + \frac{1}{2}) = (\frac{4}{9} + \frac{7}{8}) + \frac{1}{2}

(iii)

8 + \frac{7}{10} = \frac{7}{10} + 8

(iv)

(\frac{- 7}{15}) + 0 = \frac{- 7}{15} = 0 + (\frac{- 7}{15})

(v)

\frac{2}{5} + (\frac{- 2}{5}) = 0

(i) Commutative
(ii) Associative
(iii) Commutative
(iv) Additive identity
(v) Additive inverse.

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

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

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45÷715 of 89.

Usingbodmasrule⇒45÷715of89⇒45÷7×815×9⇒45÷5615×9⇒4×15×95×56=2714Ans.BODMAS−BODMASisaacronymanditstandsforbracket,of,division,multiplication, addition,andsubtraction.Itlainstheorderofoperatioustosolveandression,accordingtoBODMASrule.

$\frac{4}{5} \div \frac{7}{15}$ of $\frac{8}{9}$ .