Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the fraction equivalent of each of the following numbers in simplest form.

Answer 1

Answer: they would be

2/3

9/11

8/15

                 

Answer 2

Answer with Step-by-step explanation:

1.Let x=$0.\bar 6=0.6666...$ ..(1)

Multiply by 10 on both side then we get

$10x=6.666...$  ...(2)

Subtract equation(1) from equation (2)

$9x=6$

$x=\frac{6}{9}=\frac{2}{3}$

$x=\frac{2}{3}$

2.Let $x=0.\bar{81}$

$x=0.818181...$   ..(1)

Multiply by 100 on both sides then we get

$100x=81.8181...$      ..(2)

Subtract equation (1) from equation(2)

$99x=81$

$x=\frac{81}{99}=\frac{9}{11}$

$x=\frac{9}{11}$

3.Let $x=0.5\bar{3}$

$x=0.5333...$.   ..(1)

Multiply by 10 on both sides

$10x=5.333...$    ...(2)

Subtract equation (1) from equation(2)

$9x=4.8$

$x=\frac{4.8}{9}$

$x=\frac{1.6}{3}=\frac{8}{15}$

$x=\frac{8}{15}$