Yolanda received $$\frac{7}{8}$$ of the 240 votes cast for class president. How many votes did she receive?

Kailey Vargas
2022-09-13
Answered

Yolanda received $$\frac{7}{8}$$ of the 240 votes cast for class president. How many votes did she receive?

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Clarence Mills

Answered 2022-09-14
Author has **18** answers

Yolanda received. $$\frac{7}{8}$$ of the 240 votes.

That means she received $$\frac{7}{8}\cdot 240$$ votes

So she received total votes:

$$\frac{7}{8}\cdot 240\phantom{\rule{0ex}{0ex}}=7\cdot \frac{240}{8}\phantom{\rule{0ex}{0ex}}=7\cdot 30\phantom{\rule{0ex}{0ex}}=210$$

So Yolanda received 210 votes in total

That means she received $$\frac{7}{8}\cdot 240$$ votes

So she received total votes:

$$\frac{7}{8}\cdot 240\phantom{\rule{0ex}{0ex}}=7\cdot \frac{240}{8}\phantom{\rule{0ex}{0ex}}=7\cdot 30\phantom{\rule{0ex}{0ex}}=210$$

So Yolanda received 210 votes in total

asked 2022-08-18

Write 7.001 as a mixed number. Do not reduce your answers

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Simplification imaginary fractions

In an exercise, a partial fraction expansion has to be done. I have no problem with that, but one of the last steps includes a simplification as follows:

$(-\frac{1}{2}-\frac{1}{6}i)\left(\frac{1}{s+1+3i}\right)+(-\frac{1}{2}+\frac{1}{6}i)\left(\frac{1}{s+1-3i}\right)\phantom{\rule{0ex}{0ex}}=-\frac{s+1}{(s+1{)}^{2}+{3}^{2}}-\frac{1}{3}\left(\frac{3}{(s+1{)}^{2}+{3}^{2}}\right).$

My problem is that I do not understand the steps in between these two results. Could anyone explain how this is done? Any help is appreciated!

In an exercise, a partial fraction expansion has to be done. I have no problem with that, but one of the last steps includes a simplification as follows:

$(-\frac{1}{2}-\frac{1}{6}i)\left(\frac{1}{s+1+3i}\right)+(-\frac{1}{2}+\frac{1}{6}i)\left(\frac{1}{s+1-3i}\right)\phantom{\rule{0ex}{0ex}}=-\frac{s+1}{(s+1{)}^{2}+{3}^{2}}-\frac{1}{3}\left(\frac{3}{(s+1{)}^{2}+{3}^{2}}\right).$

My problem is that I do not understand the steps in between these two results. Could anyone explain how this is done? Any help is appreciated!

asked 2022-06-25

Here are two fractions, $\frac{2}{3}$, $\frac{7}{8}$, which of these fractions are closer to $\frac{3}{4}$?

I've been throwing this question around my family. No one has a clue, therefore can someone help?

I'm pretty sure this will be easy to do

I've been throwing this question around my family. No one has a clue, therefore can someone help?

I'm pretty sure this will be easy to do

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Fast way to calculate Fraction

I want to solve this problem not by using common denominator. Is there any innovative and fast way ?.

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I want to solve this problem not by using common denominator. Is there any innovative and fast way ?.

$\frac{1}{6}+\frac{4}{21}+\frac{5}{84}+\frac{7}{228}+\frac{9}{532}=\text{}?$

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$\left(\frac{3{x}^{\frac{3}{2}}{y}^{3}}{{x}^{2}{y}^{-\frac{1}{2}}}\right)}^{-2$

It seems pretty simple at first. I know that a negative exponent means you flip a fraction. So I flip it.

$\left(\frac{{x}^{2}{y}^{-\frac{1}{2}}}{3{x}^{\frac{3}{2}}{y}^{3}}\right)}^{2$

Now I need to square it, which is tricky because there are a lot of weird rules with squaring. This is probably where I went wrong.

$\left(\frac{{x}^{2}{y}^{-\frac{1}{2}}}{9{x}^{\frac{3}{2}}{y}^{3}}\right)$

Now I need to try and simplify things. I know that I can get rid of the x on top since there is a larger one on the bottom.

$\frac{4}{2}-\frac{3}{2}=\frac{1}{2}$

$\left(\frac{{x}^{\frac{1}{2}}{y}^{-\frac{1}{2}}}{9{y}^{3}}\right)$

Now I need to get rid of the y exponent.

I am not sure how that is possible.

I am trying to simplify

It seems pretty simple at first. I know that a negative exponent means you flip a fraction. So I flip it.

Now I need to square it, which is tricky because there are a lot of weird rules with squaring. This is probably where I went wrong.

Now I need to try and simplify things. I know that I can get rid of the x on top since there is a larger one on the bottom.

Now I need to get rid of the y exponent.

I am not sure how that is possible.

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Is this fraction non-terminating?

I recently stumbled upon an observation: the fraction $\frac{x}{y}$ terminates if and only if $y$ only has prime factors $2$ and $5$

For example:

$\frac{1}{20}=\frac{1}{2\cdot 2\cdot 5}=0.05$

$\frac{1}{6}=\frac{1}{2\cdot 3}=0.1\overline{6}$

I think this is true because fractions are in the form:

$\frac{a}{10}+\frac{b}{100}+\frac{c}{1000}+\dots $

$\frac{a}{2\cdot 5}+\frac{b}{2\cdot 2\cdot 5\cdot 5}+\frac{c}{2\cdot 2\cdot 2\cdot 5\cdot 5\cdot 5}+\dots $

How can I rigorously prove this?\

I recently stumbled upon an observation: the fraction $\frac{x}{y}$ terminates if and only if $y$ only has prime factors $2$ and $5$

For example:

$\frac{1}{20}=\frac{1}{2\cdot 2\cdot 5}=0.05$

$\frac{1}{6}=\frac{1}{2\cdot 3}=0.1\overline{6}$

I think this is true because fractions are in the form:

$\frac{a}{10}+\frac{b}{100}+\frac{c}{1000}+\dots $

$\frac{a}{2\cdot 5}+\frac{b}{2\cdot 2\cdot 5\cdot 5}+\frac{c}{2\cdot 2\cdot 2\cdot 5\cdot 5\cdot 5}+\dots $

How can I rigorously prove this?\

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