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makvit [3.9K]
4 years ago
11

Converting repeating decimals to a fraction

Mathematics
1 answer:
Goshia [24]4 years ago
3 0

Step-by-step explanation:

Step 1:

Let x equal the repeating decimal you are trying to convert to a fraction.

Step 2:

Examine the repeating decimal to find the repeating digit(s).

Step 3:

Place the repeating digit(s) to the left of the decimal point.

Step 4:

Place the repeating digit(s) to the right of the decimal point.

Step 5:

Using the two equations you found in step 3 and step 4, subtract the left sides of the two equations. Then, subtract the right sides of the two equations

As you subtract, just make sure that the difference is positive for both sides.

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What is the remainder when the polynomial 6x2+11x−3 is divided by 2x−1?
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Answer: 4

There are three different ways to find the remainder.  Since I don't know which lesson you are working on, I will show you all three methods.

<u>Long Division:</u>

           <u>3x  +  7      </u>

2x - 1 ) 6x² + 11x - 3

       -  <u>(6x²  -  3x)</u>   ↓

                    14x  - 3

                -   (<u>14x  - 7)</u>  

                              4    

<u>Synthetic Division:</u>

2x - 1 = 0   ⇒   x = \frac{1}{2}


\frac{1}{2}   | 6      11     -3

    <u>| ↓       3     7</u>

      6      14    4

<u>Remainder Theorem:</u>

2x - 1 = 0   ⇒   x = \frac{1}{2}

f(x) = 6x² + 11x - 3

f(\frac{1}{2}) = 6(\frac{1}{2})² + 11(\frac{1}{2}) - 3

      = 6(\frac{1}{4}) + \frac{11}{2} - 3

      = \frac{3}{2} + \frac{11}{2} - \frac{6}{2}

      = \frac{8}{2}

      = 4

                                     

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