Question

Please ans this question
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Answer 1

Simplifying 14(a)

Given:$\frac{13}{11}\times(-\frac{14}{11})+\frac{3}{11}(\frac{-7}{5})+(\frac{-13}{11})\times\frac{34}{5}$

To Simplify the given equation

Solution,

Multiplying the fractions

$\frac{(13\times-14)}{(11 \times 11)}+\frac{3}{11}\times\frac{-7}{5}+\frac{-13}{11}\times \frac{34}{5}$

Simplifying the arithmetic

$\frac{-182}{(11\times11)}+\frac{3}{11}\times\frac{-7}{5}+\frac{-13}{11}\times\frac{34}{5}$

$\frac{-182}{121}+\frac{3}{11}\times\frac{-7}{5}+\frac{-13}{11}\times\frac{34}{5}$

Multiplying the fractions

$\frac{-182}{121}+\frac{(3\times-7)}{(11\times5)}+\frac{-13}{11}\times\frac{34}{5}$

$\frac{-182}{121}+\frac{-21}{55}+\frac{-13}{11}\times\frac{34}{5}$

Grouping the like terms

$(\frac{-182}{121}+\frac{-21}{55})+\frac{-13}{11}\times\frac{34}{5}$

Finding the L.C.M

$\frac{(-182\times5)}{(121\times5)}+\frac{(-21\times11)}{(55\times11)}+\frac{-13}{11} \times\frac{34}{5}$

Multiplying the denominator and numerator

$\frac{(-182\times5)}{605}+\frac{(-21\times11)}{605}+\frac{-13}{11}\times\frac{34}{5}$

$\frac{-910}{605}+\frac{-231}{605}+\frac{-13}{11}\times\frac{34}{5}$

Adding the fractions

$\frac{(-910+-231)}{605}+\frac{-13}{11}\times\frac{34}{5}$

$\frac{-1141}{605}+\frac{-13}{11}\times\frac{34}{5}$

Multiplying the fractions

$\frac{-1141}{605}+\frac{(-13\times34)}{(11\times5)}$

$\frac{-1141}{605}+\frac{-442}{55}$

Finding L.C.M

$\frac{-1141}{605}+\frac{(-442\times11)}{(55\times11)}$

$\frac{-1141}{605}+\frac{-4862}{605}$

Combining the fractions

$\frac{(-1141+-4862)}{605}$

$\frac{-6003}{605}$

Final Answer:$\frac{-6003}{605}$

Simplifying 14(b)

Given:$\frac{6}{5}\times\frac{3}{7}-\frac{1}{5}\times\frac{3}{7}$

To Simplify the given equation

Solution,

Multiplying the fractions

$(\frac{6\times3}{5\times7})+-(\frac{1}{5}\times\frac{3}{7})$

Simplifying the arithmetic

$\frac{18}{35}+-(\frac{1}{5}\times\frac{3}{7})$

Multiplying the fractions

$\frac{18}{35}+-(\frac{1\times3}{5\times7})$

$\frac{18}{35}+-\frac{3}{35}$

Simplifying the arithmetic

$\frac{18}{35} +\frac{-3}{35}$

Adding the fractions

$\frac{(18+-3)}{35}$

$\frac{15}{35}$

Using H.C.F in both the numerator and denominator

$\frac{(3\times5)}{(7\times5)}$

$\frac{3}{7}$

Final Answer: $\frac{3}{7}$