Question

simplify :

the person who answers step by step will be marked as brainlist...​

Answer 1

Answer:

$\frac{-3}{2}$ x $\frac{-6}{5} + \frac{2}{3}+ (\frac{5}{6}$÷$\frac{7}{6})$

$\frac{-3}{2}$ x $\frac{-6}{5} + \frac{2}{3}+ (\frac{5}{6}$ x $\frac{6}{7})$

$\frac{-3}{2}$ x $\frac{-6}{5} + \frac{2}{3}+ \frac{5}{7}$

$\frac{18}{10} +\frac{2}{3}+\frac{5}{7}$

$\frac{189}{105}+\frac{70}{105} + \frac{75}{105}$

$\frac{334}{105}$

$3\frac{19}{105}$

Step-by-step explanation:

You have to do according to BODMAS.

( ), of, /, x, +, -

So, in this sum you have to first do the division.

$\frac{5}{6}$÷$\frac{7}{6}$

01. you have to change the / sign to multiplication.

02. While you change the sign, the second fraction should be written as reciprocal. (Turn upside down)

$\frac{5}{6}$ x $\frac{6}{7}$

01. While multiplying fractions numerator should be multiplied with numerator and denominator should be multiplied with denominator.

So,

5 x 6 = 30

6 x 7 = 42

$\frac{30}{42}$

Now you have to simplify the answer

For that you have to see whether they have any common factors.

30 = 1, 2, 3, 5, 6, 10, 15, 30

42 = 1, 2, 3, 6, 7, 14, 21, 42

There are many common factors. (2,3 and 6)

If there are more than one, then you have to choose the largest number. (In this case:6)

Next you have to divide both by 6 (Highest common factor)

30 / 6 = 5

42 / 6 = 7

So, $\frac{5}{7}$

Both don't have any common factors, because both are prime numbers. So, 5/7 is the final answer for 5/6 ÷ 7/6

$\frac{-3}{2}$ x $\frac{-6}{5} + \frac{2}{3}+\frac{5}{7}$

According to BODMAS, next you have to do the multiplication

$\frac{-3}{2}$  x $\frac{-6}{5}$

-3 x -6 = 18

2 x 5 = 10

*While multiplying note that if two numbers have same signs then the answer will come inn +ve. If they have different signs, then the answer will come in -ve.

So,

$\frac{18}{10}$

Factors of 18 and 10 are,

18 = 1, 2, 3, 6, 9, 18

10 = 1, 2, 5, 10

Only common factor is 2

So,

18 / 2 = 9

10 / 2 = 5

Final answer for  $\frac{-3}{2}$  x $\frac{-6}{5}$ is $\frac{9}{5}$

$\frac{9}{5}$  $+ \frac{2}{3}+\frac{5}{7}$

While adding or subtracting fractions you have to note that the denominators must be equal. If not we have to find the LCM and make all the denominators equal.

All, 5,3 and 7 are prime numbers. So to find the LCM we have to multiply the three of them

5 x 3 x 7

=105

*Whatever changes you make to denominator should also be made to numerator.

01) If denominator 5 changes as 105, that means it is multiplied by 21 (105/5). So, numerator 9 should also be multiplied by 21.

9 x 21 = 189    

02) If denominator 3 changes as 105, that means it is multiplied by 35 (105/3). So, numerator2 should also be multiplied by 35.

2 x 35 = 70

03) If denominator 7 changes as 105, that means it is multiplied by 15 (105/7). So, numerator 5 should also be multiplied by 15.

5 x 15 = 75

So, the fractions are,

$\frac{189}{105}+\frac{70}{105} + \frac{75}{105}$

If you add the values in numerator

$\frac{334}{105}$

334= 2 x 167

105= 3 x 5 x 7

As nothing are common, Highest Common Factor is 1. If we divide any number by 1, the result is same. So, as 334/105 is an improper fraction we can give it as mixed number.

334/105 =

Quotient (Answer)= 3

Remainder = 19

So, $3\frac{19}{105}$ is the final answer,

If my answer was helpful please mark me as brainliest:)

Answer 2

Answer:

hiiii mate

-3/2×-6/5+2/3+5/6÷7/6

-3/2×-6/5 +2/3+5/7

9/5+2/3+5/7

189+70+75/105

334/105