Question

11,13,15,17 I need help with

Answer 1

Answer:  11) x = 1        13) $\bold{11)\quad x=1\qquad 13)\quad \dfrac{4}{9}\qquad 15)\quad \dfrac{7}{45}\qquad 17)\quad \dfrac{5}{12}}$

Step-by-step explanation:

11) Multiply everything by the LCD to clear the denominator, then distribute the negative sign.

$\dfrac{2(2x+1)}{5}-\dfrac{x+2}{3}=\dfrac{1}{5}\\\\\\(15)\dfrac{2(2x+1)}{5}-(15)\dfrac{x+2}{3}=(15)\dfrac{1}{5}\\\\\\3\cdot2(2x+1)-5(x+2)=3(1)\\\\\\6(2x+1)-5(x+2)=3(1)\\\\12x + 6 - (5x + 10) = 3\\\\12x + 6 - 5x - 10 = 3\\\\7x-4=3\\\\7x=7\\\\\large\boxed{x=1}$

13) Since the repeating digit is in the tenths place, divide the repeating decimal by 9

$0.\overline4\quad =\dfrac{4}{9}$

15) Since the repeating digit is in the hundredths place, divide the repeating decimal by 90 and divide the non-repeating decimal by 10

$0.1\overline5\quad =\dfrac{1}{10}+\dfrac{5}{90}\\\\\\.\quad \quad =\bigg(\dfrac{9}{9}\bigg)\dfrac{1}{10}+\dfrac{5}{90}\\\\\\.\quad \quad =\dfrac{9}{90}+\dfrac{5}{90}\\\\\\.\quad \quad =\dfrac{14}{90}\qquad \text{simplify by dividing by 2}\\\\.\quad \quad =\large\boxed{\dfrac{7}{45}}$

17) Since the repeating digit is in the thousandths place, divide the repeating decimal by 900 and the non-repeating decimal by 100

$0.41\overline6\quad =\dfrac{41}{100}+\dfrac{6}{900}\\\\\\.\quad \quad =\bigg(\dfrac{9}{9}\bigg)\dfrac{41}{100}+\dfrac{6}{900}\\\\\\.\quad \quad =\dfrac{369}{900}+\dfrac{6}{900}\\\\\\.\quad \quad =\dfrac{375}{900}\qquad \text{simplify by dividing by 75}\\\\\\.\quad \quad =\large\boxed{\dfrac{5}{12}}$

Answer 2

Step-by-step explanation:

[ Refer to the attached file ]

( Slide to refer all files )

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• To solve Questions of type 11 we need to simplify the equation by using mathematical operations !!

• To solve Questions of type ( 13 , 15 and 17 ) we try to make the bar numeral to come other side of decimal

° and by subtracting we get the required fraction !!

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