order of operations with fractions. simplify.

amanf
2021-10-02
Answered

order of operations with fractions. simplify.

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hesgidiauE

Answered 2021-10-03
Author has **106** answers

Given

$\frac{5}{9}\times \frac{7}{19}+\frac{7}{19}\xf7\frac{18}{19}$

$\Rightarrow \frac{5}{9}\times \frac{1}{2}+\frac{7}{19}\times \frac{19}{18}$

$\Rightarrow \frac{5}{18}+\frac{7}{18}$

$\Rightarrow \frac{5+7}{18}=\frac{12}{18}=\frac{2}{3}$

$\Rightarrow \frac{5}{9}\times \frac{1}{2}+\frac{7}{19}\xf7\frac{18}{19}=\frac{2}{3}$

asked 2021-12-18

How do you write the fraction $\frac{36}{}$ in simplest form ?

asked 2022-05-22

Why does the least common denominator work?

Take for instance the following problem. You have two beakers of the same height. One has tick marks that break it into thirds. The other has tick marks that separate it into fourths. The water levels are 1/3 and 1/4 respectively. If I did not know about the concept of LCDs, how would I figure out how much water there is all together? Please walk me through your reasoning.

Note: I understand the need to find a common scale between the two beakers. I don't know how I would find that 12 is the smallest possible common scale, if I had never been introduced to the concept of LCDs/LCMs.

Take for instance the following problem. You have two beakers of the same height. One has tick marks that break it into thirds. The other has tick marks that separate it into fourths. The water levels are 1/3 and 1/4 respectively. If I did not know about the concept of LCDs, how would I figure out how much water there is all together? Please walk me through your reasoning.

Note: I understand the need to find a common scale between the two beakers. I don't know how I would find that 12 is the smallest possible common scale, if I had never been introduced to the concept of LCDs/LCMs.

asked 2021-10-18

Add.

$-\frac{8}{9}+\frac{1}{3}$

Write your answer in simplest form

Write your answer in simplest form

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How do you write 15% as a fraction?

asked 2022-05-18

Prove that $\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+d}+\frac{d}{d+a}\ge 1+4\sqrt{\frac{abcd}{(a+b)(b+c)(c+d)(d+a)}}$

Let $a$, $b$, $c$ and $d$ be positive numbers. Prove that:

$\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+d}+\frac{d}{d+a}\ge 1+4\sqrt{\frac{abcd}{(a+b)(b+c)(c+d)(d+a)}}$

We can prove this inequality by using $b=a+u$, $c=a+v$ and $d=a+w$ after squaring of the both sides. I am looking for a nice proof. Thank you!

Let $a$, $b$, $c$ and $d$ be positive numbers. Prove that:

$\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+d}+\frac{d}{d+a}\ge 1+4\sqrt{\frac{abcd}{(a+b)(b+c)(c+d)(d+a)}}$

We can prove this inequality by using $b=a+u$, $c=a+v$ and $d=a+w$ after squaring of the both sides. I am looking for a nice proof. Thank you!

asked 2022-05-17

How do I show that $\frac{{\mathrm{cos}}^{2}A}{{\mathrm{cos}}^{2}B}+\frac{{\mathrm{cos}}^{2}B}{{\mathrm{cos}}^{2}C}+\frac{{\mathrm{cos}}^{2}C}{{\mathrm{cos}}^{2}A}\ge 4({\mathrm{cos}}^{2}A+{\mathrm{cos}}^{2}B+{\mathrm{cos}}^{2}C)$?

$A,B,C$ be the angles of an acute triangle.

How should I approach this kind of "geometric inequalities"? I've considered substituting the cosines using the law of the cosines and then use the Ravi transformation to turn it into an algebraic one, but that seems too tedious and unlikely to yield any beautiful solution. Any hints will be appreciated!

$A,B,C$ be the angles of an acute triangle.

How should I approach this kind of "geometric inequalities"? I've considered substituting the cosines using the law of the cosines and then use the Ravi transformation to turn it into an algebraic one, but that seems too tedious and unlikely to yield any beautiful solution. Any hints will be appreciated!

asked 2021-12-13

How do you write 0.4 as a fraction?