Simplify.

(1/2)^{2}−6(2−2/3)

Enter your answer, as a simplified fraction

bmichelle9 Aug 15, 2017

#2**+1 **

I'll help you simplfy this expression \(\left(\frac{1}{2}\right)^2-6\left(2-\frac{2}{3}\right)\):

\(\left(\frac{1}{2}\right)^2-6\left(2-\frac{2}{3}\right)\) | To abide to order of operations, I will start with the parentheses 2-(2/3). |

\(\frac{2}{1}-\frac{2}{3}\) | In order to subtract fractions, we must establish a common denominator. Currently, this isn't the case. To do that, we must figure out the LCM (lowest common multiple) of the denominators. In this case, one of the denominators is 1. That means that the LCM is whatever the other number is. The LCM is 3. Let's convert the fraction |

\(\frac{2}{1}*\frac{3}{3}=\frac{6}{3}\) | Note that I am really multiplying the fraction by 1, so I am not changing the value of the fraction. |

\(\frac{6}{3}-\frac{2}{3}=\frac{4}{3}\) | Of course, when subtraction fractions, you only subtract the numerator. |

\(\left(\frac{1}{2}\right)^2-6*\frac{4}{3}\) | Yet again, to abide by the rules of the order of operations, I will now do the exponent. I will apply the rule that \(\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}\) |

\(\left(\frac{1}{2}\right)^2=\frac{1^2}{2^2}=\frac{1}{4}\) | I just applied the rule that I mentioned before. |

\(\frac{1}{4}-6*\frac{4}{3}\) | Now, I will do the multiplication of 6*(4/3) |

\(\frac{6}{1}*\frac{4}{3}=\frac{24}{3}=8\) | This is the multiplication done now. Now, we can move on to the next step. |

\(\frac{1}{4}-8\) | Yet again, manipulate 8 such that there are common denominators. |

\(\frac{8}{1}*\frac{4}{4}=\frac{32}{4}\) | |

\(\frac{1}{4}-\frac{32}{4}\) | Do the subtraction. |

\(-\frac{31}{4}=-7\frac{3}{4}\) | |

Therefore, \(\left(\frac{1}{2}\right)^2-6\left(2-\frac{2}{3}\right)=-\frac{31}{4}=-7\frac{3}{4}\)

.TheXSquaredFactor Aug 15, 2017