Question

find
$\frac{ - 4}{5} \times \frac{3}{7} \times \frac{15}{16} ( \frac{ - 14}{9} )$
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Answer 1

Answer

We have

$\frac{ - 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times ( \frac{ - 14}{9} )$

$= - ( \frac { (4 \times 3)}{(5 \times ) } ) \times ( \frac{15 \times ( - 14)}{16 \times 9} )$

$= \frac{ - 12}{35} \times ( \frac{ - 35}{24} ) = \frac{ - 12 \times ( - 13)}{35 \times 24} = \frac{1}{2}$

We can also do this method

$\frac{ - 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times ( \frac{ - 14}{9} )$

$= ( \frac{ - 4}{5} \times \frac{15}{16} ) \times ( \frac{3}{7} \times ( \frac{ - 14}{9} )using \: commutativity \: and \: associativity$

$= \frac{ - 3}{4} \times ( \frac{ - 2}{3} ) = \frac{1}{2}If we want to convert 1/2 into =0.5$

Properties used to find answer are commutative and associative

Extra information

Communicative

For any two rational numbers a, b, a+b=a+a Rational numbers are commutative under +nand xn (addition and multiplication)

Associative

For any three rational numbers a, b, c a+(b+c)=(a+b)+c Rational numbers are associative Under +n and xn(addition and multiplication )

Answer 2

METHOD 1:

By rearranging the terms:

$- \frac{4}{5} \times \frac{3}{7} \times \frac{15}{16} \times - \frac{14}{9}$

$= - \frac{4}{5} \times \frac{15}{16} \times \frac{3}{7} \times - \frac{14}{9} \\ \\ = - \frac{3}{4} \times - \frac{2}{3} \\ \\ = \frac{1}{2} = 0.5$

Property used:

Commutative Property of rational numbers under multiplication:

We can change the order in which rational numbers are arranged for multiplication without changing the final product. This property of rational numbers is called commutative property and is used for making operations on rational numbers easier. Rational numbers are commutative under addition and multiplication.

METHOD 2:

Direct Multiplication:

$- \frac{4}{5} \times \frac{3}{7} \times \frac{15}{16} \times - \frac{14}{9} \\ \\ = - \frac{12}{35} \times -\frac{210}{144} \\ \\ = - \frac{12}{35} \times - \frac{35}{24} \\ \\ = \frac{1}{2}=0.5$

Therefore, the final answer is 0.5.