gibsonj338

Problem \(\frac{1}{2}\)

To convert a fraction into a deimal, think of the fraction as division problem, \(1÷2\), and simplify the division problem.

Answer: \(0.5\)

Type it in Calc like this: \(2-(sec(x))^2/(sec(x))^2\)

\({2x}^{2}-3x-5=0\)

\({2x}^{2}-5x+2x-5=0\)

\(({2x}^{2}-5x)+(2x-5)=0\)

\(x\times(2x-5)+1\times(2x-5)=0\)

\((x+1)(2x-5)=0\)

\(x+1=0\)  \(2x-5=0\)

\(x+1=0\)

\(x=-1\)

\(2x-5=0\)

\(2x=5\)

\(x=\frac{5}{2}\)

\(x=-1\) and \(x=\frac{5}{2}\)

\(2x-4=2\times(x-2)+3\)

\(2x-4≠2\times(x-2)+3\)

\(2x-4≠2x-4+3\)

\(2x-4≠2x-1\)

\(2x≠2x+3\)

\(0≠3\)

\(3y+53=7y-55\)

\(3y=7y-108\)

\(-4y=-108\)

\(y=27\)

Replace \(y\) with 27 in the original problem to check if the answer is correct.

\(3\times27+53=7\times27-55\)

\(81+53=7\times27-55\)

\(134=7\times27-55\)

\(134=189-55\)

\(134=134\)

That checks out.  The answer of \(y=27\) is correct.

To change a decimal number into a fraction, it depends on what kind of decimal number you are talking about: terminating, repeating, or irrational.

To change a terminating decimal into a fraction:

Example:  \(0.125\)

Change the terminating decimal into an integer by multiplying by the place value of the number and then putting the place value under the new number.  

\(0.125\times1000\)

\(125\)

\(125/1000\)

Reduce the fracton to its lowest term if possible.

\(\frac{1}{8}\)

To change a repeating decimal into a fraction:

Example 1:  \(0.66666666...\)

Set the repeating deimal equal to a variable.  I will use \(x.\)

\(x=0.66666666...\)

Multiply the variable and the repeating decimal by the place holder of the first repeating number.

\(10x=6.6666666...\)

Subtract \(x\) from \(10x\).

\(10x=6.6666666...\)

\(-\)\(x=0.66666666...\)

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

\(9x=6\)

Solve for \(x.\)

\(9x=6\)

\(x=\frac{6}{9}\)

Reduce the fraction to its lowest term if possible

\(x=\frac{2}{3}\)

Drop the \(x.\)

\(\frac{2}{3}\)

Example 2:

\(0.1222222...\)

Set the repeating deimal equal to a variable.  I will use \(x.\)

\(x=0.1222222...\)

Multiply the variable and the repeating decimal by the place holder of the first repeating number.

\(10x=1.222222...\)

Subtract \(x\) from \(10x\).

\(10x=1.22222...\)

\(-\)\(x=0.1222222...\)

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

\(9x=1.1\)

Solve for \(x.\)

\(9x=1.1\)

\(x=\frac{1.1}{9}\)

Multiply the numerator by a multiple of \(10\) to get the numerator to be a whole number.  Whatever number you multiply the numerator by you do the same to the demonator.

\(x=\frac{11}{90}\)

Reduce the fraction to its lowest term if possible

\(x=\frac{11}{90}\)

Drop the \(x.\)

\(\frac{11}{90}\)

An irrational number cannot be changed into a fraction because an irrational number is a decimal number that not only acts like a repeating decimal (a decimal number that goes on forever), but none of the digits repeat in a pattern.  Two such examples of an irrational number are \(\pi\) (pi) and \(e\) (Euler's number).  \(\pi= 3.1415926535897932...\) and \(e= 2.7182818284590452...\) 

\(2\times\sqrt{2}\times(-\sqrt{12})\)

Since \(\sqrt{2}\) and \(\sqrt{12}\) are not perfect squares, instead of finding what \(\sqrt{2}\)  and \(\sqrt{12}\) are, expand the terms inside the radicals to find perfect squares:

\(2\times\sqrt{2}\times\sqrt{12}\)

\(2\times\sqrt{2}\times\sqrt{4\times3}\)

\(2\times\sqrt{2}\times\sqrt{2\times\times2\times3}\)

\(2\times\sqrt{2}\times2\times\sqrt{3}\)

\(2\times\sqrt{2}\times2\times\sqrt{3}\)

\(4\times\sqrt{2}\times\sqrt{3}\)

\(4\times\sqrt{6}\)

\(4\sqrt{6}\)

If you want an approximate answer:

\(2\times\sqrt{2}\times\sqrt{12}\)

\(2\times 1.414213562373095\times\sqrt{12}\)

\(2.82842712474619\times\sqrt{12}\)

\(2.82842712474619\times3.4641016151377546\)

\(9.797958971132712091295411504974\)

\({tan}^{-1}(\frac{7}{6})\)

\(0.862170054667\)

\(\sqrt{\pi}\)

1.7724538509055159...

\(0=9\times(3-\frac{2}{3})+33\)

\(0≠9\times(3-\frac{2}{3})+33\)

\(0≠27-\frac{2}{3}+33\)

\(0≠\frac{81}{3}-\frac{2}{3}+33\)

\(0≠\frac{79}{3}+33\)

\(0≠\frac{79}{3}+\frac{99}{3}\)

\(0≠\frac{178}{3}\)

\(0≠ 59.3333333333333333...\)