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KonstantinChe [14]
3 years ago
15

35/23 improper fraction

Mathematics
1 answer:
charle [14.2K]3 years ago
5 0

35/23 is an improper fraction because the numerator is larger than the denominator.

To convert to a mixed number, use long division to find 35 into 23 goes in exactly one whole time (quotient) and there is 12 leftover (remainder)

You can see it through doing it like this

35/23 = (23+12)/23 = 23/23 + 12/23 = 1 + 12/23 = 1 & 12/23

So in short, 35/23 = 1 & 12/23

1 & 12/23 is a mixed number with 1 as the whole part and 12/23 as the fractional part.

---------------------

Real life example: if you had 35 cookies and 23 friends, then each friend would get 1 whole cookie. There would be 12 cookies left over.

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Solve the equation uding the most direct method: 3x(x+6)=-10?​
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To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

<h3>Distribute</h3>

Use the distributive property to distribute 3x into the term (x + 6):

3x(x+6)=-10

3x^2+18x=-10

<h3>Rearrange</h3>

To create a quadratic equation, add 10 to both sides of the equation:

3x^2+18x+10=-10+10

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<h3>Use the Quadratic Formula</h3>

The quadratic formula is defined as:

\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

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Set up the quadratic formula:

\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}

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Brackets

Parentheses

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Division

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Use BPEMDAS:

\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}

Simplify the radicand:

\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}

Create a factor tree for 204:

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The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

\sqrt{4\times51}

Then, using the Product Property of Square Roots, break this into two radicands:

\sqrt{4} \times \sqrt{51}

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2 \times \sqrt{51}

To simplify further for easier reading, remove the multiplication symbol:

2\sqrt{51}

Then, substitute for the quadratic formula:

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This gives us a combined root, which we should separate to make things easier on ourselves.

<h3>Separate the Roots</h3>

Separate the roots at the plus-minus symbol:

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Then, simplify the numerator of the roots by factoring 2 out:

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Then, simplify the fraction by reducing 2/6 to 1/3:

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The final answer to this problem is:

\displaystyle x=\frac{-9 + \sqrt{51}}{3}

\displaystyle x=\frac{-9 - \sqrt{51}}{3}

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