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3 years ago

How to add fractions containing pi

1 answer:

3 0

"pi" is just another number. Fractions that contain the number pi can be dealt with like all other fractions.

Examples:

Example 1...

$\frac { 1 }{ \pi } +\frac { 1 }{ \pi } =\frac { 1+1 }{ \pi } =\frac { 2 }{ \pi }$

Example 2...

$\\ \\ \frac { \pi }{ 3 } +\frac { 2\pi }{ 3 } =\frac { \pi +2\pi }{ 3 } =\frac { 3\pi }{ 3 } =\pi$

Example 3...

$\\ \\ \frac { 2 }{ 3\pi } +\frac { 5 }{ 4\pi } \\ \\ =\frac { 2 }{ 3\pi } \cdot \frac { 4 }{ 4 } +\frac { 5 }{ 4\pi } \cdot \frac { 3 }{ 3 } \\ \\ =\frac { 8 }{ 12\pi } +\frac { 15 }{ 12\pi } \\ \\ =\frac { 8+15 }{ 12\pi } \\ \\ =\frac { 23 }{ 12\pi }$

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The missing coordinates of the parallelogram is (m + h, n).

Solution:

Diagonals of the parallelogram bisect each other.

Solve using mid-point formula:

$$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right )$

Here $x_1=m, y_1=n, x_2=h, y_2=0$

$$=\left( \frac{m+h}{2}, \frac{n+0}{2}\right )$

$$\text{Midpoint} =\left( \frac{m+h}{2}, \frac{n}{2}\right )$

<u>To find the missing coordinate:</u>

Let the missing coordinates by x and y.

Here $x_1=0, y_1=0, x_2=x, y_2=y$

$$\text{Midpoint}=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{x}{2}, \frac{y}{2}\right )$

Now equate the x-coordinate.

$$ \frac{m+h}{2}=\frac{x}{2}$

Multiply by 2 on both sides of the equation, we get

m + h = x

x = m + h

Now equate the y-coordinate.

$$\frac{n}{2} = \frac{y}{2}$

Multiply by 2 on both sides of the equation, we get

n = y

y = n

Hence the missing coordinates of the parallelogram is (m + h, n).

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Step-by-step explanation:

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<h3>Deformation of an object</h3>

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Answer:

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Explicación paso a paso:

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