Simplify the following using distributive property of multiplication over addition and subtraction:
1) - 3/75/12+11/12(-3/7)
2) 4/58/13-5/134/5
*= multiply

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Solution

Answer :

Simplify :

1 ) $- \frac{3}{7} \times \frac{5}{12} + \frac{11}{12} \times (- \frac{3}{7})$

We apply distributive property and get

$\Rightarrow - \frac{3}{7} \times (\frac{5}{12} + \frac{11}{12}) \Rightarrow - \frac{3}{7} \times (\frac{5 + 11}{12}) \Rightarrow - \frac{3}{7} \times \frac{16}{12} \Rightarrow - \frac{1}{7} \times \frac{16}{4} \Rightarrow - \frac{1}{7} \times 4 \Rightarrow - \frac{4}{7} (A n s)$

2 ) $\frac{4}{5} \times \frac{8}{13} - \frac{5}{13} \times \frac{4}{5}$

We apply distributive property and get

$\Rightarrow \frac{4}{5} \times (\frac{8}{13} - \frac{5}{13}) \Rightarrow \frac{4}{5} \times (\frac{8 - 5}{13}) \Rightarrow \frac{4}{5} \times \frac{3}{13} \Rightarrow \frac{12}{65} (A n s)$

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Q. Simplify the expression

12 \times (13 - 5)

using distributive property of multiplication.

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

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) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

Evaluate :

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} (i i i) \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7}$

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Simplify the following using distributive property of multiplication over addition and subtraction: 1) - 3/7*5/12+11/12*(-3/7) 2) 4/5*8/13-5/13*4/5 *= multiply

Simplify the following using distributive property of multiplication over addition and subtraction:
1) - 3/75/12+11/12(-3/7)
2) 4/58/13-5/134/5
*= multiply