Find using distributivity- -3 marks-713 -315 - -59 -713

According to distributive property: (a × b) + (a × c)= a×(b + c) (1 mark) nbsp; ⇒(713) ×(315)+( 59) ×(713) =(713) ×(315 59) =(713) ×(9 2545) (1 mark ...

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Byju's Answer

Standard XII

Mathematics

Cartesian Product

Find using di...

Question

Find using distributivity: [3 marks]

$(\frac{7}{13}) \times (\frac{3}{15}) + (\frac{- 5}{9}) \times (\frac{7}{13})$

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Solution

According to distributive property:

$(a \times b) + (a \times c) = a \times (b + c) (1 mark) \Rightarrow (\frac{7}{13}) \times (\frac{3}{15}) + (\frac{- 5}{9}) \times (\frac{7}{13}) = (\frac{7}{13}) \times (\frac{3}{15} - \frac{5}{9}) = (\frac{7}{13}) \times (\frac{9 - 25}{45}) (1 mark) = (\frac{7}{13}) \times (\frac{- 16}{45})$

$= \frac{- 112}{585} (1 mark)$

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Similar questions

Q. Without adding, find the sum
(i)

1 + 3 + 5 + 7 + 9

(ii)

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

(iii)

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Without adding find the sum

(i) 1 + 3 + 5 + 7 + 9

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

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. Using suitable rearrangement, find the sum.

\frac{4}{7} + (\frac{- 4}{9}) + \frac{3}{7} + (\frac{- 13}{9})

Simplify:

((13/9) × (-15/2)) + ((7/3) × (8/5)) + ((3/5) × (1/2)) (2 marks)

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Find using distributivity: [3 marks] (713)×(315)+(−59)×(713)

According to distributive property: (a×b)+(a×c)=a×(b+c) (1 mark)⇒(713)×(315)+(−59)×(713)=(713)×(315−59)=(713)×(9−2545) (1 mark)=(713)×(−1645) =−112585 (1 mark)

Find using distributivity: [3 marks]

$(\frac{7}{13}) \times (\frac{3}{15}) + (\frac{- 5}{9}) \times (\frac{7}{13})$