3 years ago

(REPEATING DECIMALS) do part A and B please

Mathematics

1 answer:

sertanlavr [38]3 years ago

7 0

Answer:

.2121/1000

Step-by-step explanation:

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Solve 2 1/2 divided by 5 1/3 = 8/x

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$2\frac { 1 }{ 2 } \quad divided\quad by\quad 5\frac { 1 }{ 3 } \\ \\ 2\frac { 1 }{ 2 } =2+\frac { 1 }{ 2 } =\frac { 5 }{ 2 } \\ \\ 5\frac { 1 }{ 3 } =5+\frac { 1 }{ 3 } =\frac { 15+1 }{ 3 } =\frac { 16 }{ 3 } \\ \\ \\ \frac { \frac { 5 }{ 2 } }{ \frac { 16 }{ 3 } }$

We're dividing fractions, so we will flip the one in the denominator upside down and we will multiply it with the numerator.

$\frac { \frac { 5 }{ 2 } }{ \frac { 16 }{ 3 } } \quad =\quad \frac { 5 }{ 2 } \cdot \frac { 3 }{ 16 } =\frac { 5\cdot 3 }{ 2\cdot 16 } =\frac { 15 }{ 32 }$

Let's equal this too 8/x

$\frac { 15 }{ 32 } =\frac { 8 }{ x }$

Cross multiply.

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Divide both sides by 15.

$\frac { 256 }{ 15 } =\frac { 15x }{ 15 } \\ \\ \frac { 256 }{ 15 } =x$

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