Question

please tell me this it's of maths​

Answer 1

We need to find:

$\sf{\Bigg[ \dfrac{1}{2} \div \bigg(1\dfrac{1}{7} +\dfrac{11}{14} \bigg) \Bigg] + \Bigg[ 3\dfrac{1}{3} \:of\: \dfrac{6}{15}-\dfrac{2}{9}\Bigg]}$

Let us start with solving the brackets. The first bracket:

$\bf{\Bigg[ \dfrac{1}{2} \div \bigg(1\dfrac{1}{7} +\dfrac{11}{14} \bigg) \Bigg]}$

We convert the mixed fraction in the brackets to an improper fraction.

$\sf{=\Bigg[ \dfrac{1}{2} \div \bigg(\dfrac{8}{7} +\dfrac{11}{14} \bigg) \Bigg]}$

In order to add the two fractions, we convert them into like fractions, by making the denominators same.

$\sf{=\Bigg[ \dfrac{1}{2} \div \bigg(\dfrac{(8\times2)+11}{7\times2} \bigg) \Bigg]}$

Simplifying,

$\sf{=\Bigg[ \dfrac{1}{2} \div \dfrac{27}{14} \Bigg]}$

To divide the fractions, we multiply the dividend fraction with the reciprocal of the divisor fraction.

$\sf{=\Bigg[ \dfrac{1}{2} \times \dfrac{14}{27} \Bigg]}$

To multiply fractions, we multiply the numerators of the fraction with the numerator of the other and the denominator of the fraction with the denominator of the other.

$\sf{=\dfrac{1\times14}{2\times27}=\dfrac{14}{54}= \dfrac{7}{27}}$

Now, the other bracket:

$\bf{\Bigg[ 3\dfrac{1}{3} \:of\: \bigg(\dfrac{6}{15}-\dfrac{2}{9}\bigg)\Bigg]}$

The LCM of the denominators 9 and 15 is 45 (9 x 5 = 45 = 15 x 3). We multiply the numerators by the same number as we multiply the denominators. And then, we subtract the numerators.

$\sf{=\Bigg[ 3\dfrac{1}{3} \:of\: \bigg(\dfrac{(6\times3)-(2\times5)}{45}\bigg)\Bigg]}$

Simplifying,

$\sf{=3\dfrac{1}{3} \:of\: \dfrac{8}{45}}$

'Of' represents multiplication, so it can further be simplified into

$\sf{=\dfrac{10}{3}\times\dfrac{8}{45}}$

Cutting 10 by 45,

$\sf{=\dfrac{2}{3} \times \dfrac{8}{9}}$

Now multiplying the numerator with the numerator and the denominator with the denominator,

$\sf{=\dfrac{2\times8}{3\times9}=\dfrac{16}{27}}$

Perfect! From solving both the brackets, we have got two like fractions and now we have to add them, which is:

$\sf{=\dfrac{7}{27}+\dfrac{16}{27}}$

$\sf{=\dfrac{7+16}{27}=\dfrac{23}{27}}$

Thus we get the answer.

$\bf{\Bigg[ \dfrac{1}{2} \div \bigg(1\dfrac{1}{7} +\dfrac{11}{14} \bigg) \Bigg] + \Bigg[ 3\dfrac{1}{3} \:of\: \dfrac{6}{15}-\dfrac{2}{9}\Bigg]=\dfrac{23}{27}}$

Answer 2

Question :

To find the value of $\left\{\frac{1}{2}\div \left( 1 \frac{1}{7}+\frac{11}{14}\right) \right\} +3\frac{1}{3} \: \textsf{of} \frac{6}{15}-\frac{2}{9}$

Solution :

$\left\{\frac{1}{2}\div \left( 1 \frac{1}{7}+\frac{11}{14}\right) \right\} +3\frac{1}{3} \: \textsf{of} \frac{6}{15}-\frac{2}{9}$

Lets divide the question into 3 parts.

First Part :

$\left\{\frac{1}{2}\div \left( 1 \frac{1}{7}+\frac{11}{14}\right) \right\} \\\\ 1 \frac{1}{7} = \frac{7\times1+1}{7}= \frac{8}{7}\\\\\left\{\frac{1}{2}\div \left( \frac{8}{7}+\frac{11}{14}\right) \right\}\\\\\\\textsf{LCM = 14}\\\\\left\{\frac{1}{2}\div \left( \frac{8}{7}\times\frac{2}{2}+\frac{11}{14}\right) \right\}\\\\\\\left\{\frac{1}{2}\div \left( \frac{16}{14}+\frac{11}{14}\right) \right\}\\\\\\\left\{\frac{1}{2}\div \left( \frac{16+11}{14}\right) \right\}$

$\left\{\frac{1}{2}\div \left( \frac{27}{14}\right) \right\}\\\\\textsf{Reciprocal of }\frac {27}{14}\textsf{is}\frac {14}{27}\\\\\left\{\frac{1}{2}\times\left( \frac{14}{27}\right) \right\}\\\\\\\left\{\left( \frac{7}{27}\right) \right\}$

Second Part :

$3\frac{1}{3} \: \textsf{of}\:( \frac{6}{15}-\frac{2}{9})\\\\\textsf{LCM=45}\\\\3\frac{1}{3} \: \textsf{of} \:(\frac{6}{15}\times\frac{3}{3}-\frac{2}{9}\times\frac{5}{5})\\\\\\3\frac{1}{3} \: \textsf{of} \:(\frac{18}{45}-\frac{10}{45})\\\\\\3\frac{1}{3} \: \textsf{of}\:( \frac{18-10}{45})\\\\\\3\frac{1}{3} \: \textsf{of}\:(\frac{8}{45})\\\\3\frac{1}{3}=\frac{3\times3+1}{3}=\frac{10}{3}\\\\\\\frac{10}{3}\: \textsf{of}\:(\frac{8}{45})$

$(\textsf{of means }\times)\\\\\\\frac{10}{3}\times\frac{8}{45}\\\\\\=\frac{2}{3}\times\frac{8}{9}\\\\\\=\frac{16}{27}$

Third Part :

Add first and second parts

$\frac{7}{27}+\frac{16}{27}\\\\\\=\frac{7+16}{27}\\\\\\=\frac{23}{27}$

Answer :

$\left\{\frac{1}{2}\div \left( 1 \frac{1}{7}+\frac{11}{14}\right) \right\} +3\frac{1}{3} \: \textsf{of} \frac{6}{15}-\frac{2}{9} = \frac{23}{27}$

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