Please step by step and discuss rules in multiplying with whole numbers & fractions.

he298c
2021-10-01
Answered

Please step by step and discuss rules in multiplying with whole numbers & fractions.

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Jaylen Fountain

Answered 2021-10-02
Author has **170** answers

Step 1

$2+\frac{1}{7}$ can be written as, $\frac{2\times 7+1}{7}=\frac{14+1}{7}=\frac{15}{7}$

$3+\frac{2}{3}$ can be written as, $\frac{3\times 3+2}{3}=\frac{11}{3}$

Step 2

So, adding them, we get,

$\frac{15}{7}+\frac{11}{3}$

$\frac{15\times 3+11\times 7}{7\times 3}$

$=\frac{45+77}{21}$

$=\frac{122}{21}$

$=5+\frac{17}{21}$

Step 2

So, adding them, we get,

asked 2022-09-11

Struggling to finish an exponential equation

I have this exponential equation I tried solving but I'm stuck at the end.

The problem is this:

$${4}^{x}-{3}^{x-\frac{1}{2}}={3}^{x+\frac{1}{2}}-{2}^{2x-1}$$

And my approach is this:

${2}^{2x}+{2}^{2x-1}={3}^{x+\frac{1}{2}}+{3}^{x-\frac{1}{2}}$

${2}^{2x}(1+{2}^{-1})={3}^{x}({3}^{\frac{1}{2}}+{3}^{-\frac{1}{2}})$

${2}^{2x}\ast \frac{3}{2}={3}^{x}(\sqrt{3}+\frac{1}{\sqrt{3}})$

${2}^{2x}\ast \frac{3}{2}={3}^{x}(\frac{{\sqrt{3}}^{2}+1}{\sqrt{3}})$

${2}^{2x}\ast \frac{3}{2}={3}^{x}\ast \frac{4\sqrt{3}}{3}$--> here I have rationalized the fraction

$\frac{{2}^{2x}}{{3}^{x}}=\frac{4\sqrt{3}}{3}\ast \frac{2}{3}$

${\left(\frac{{2}^{2}}{3}\right)}^{x}=\frac{8\sqrt{3}}{9}$

Now I hope I didn't make an error. How should I proceed from this point? Is there another way around this problem?

I have this exponential equation I tried solving but I'm stuck at the end.

The problem is this:

$${4}^{x}-{3}^{x-\frac{1}{2}}={3}^{x+\frac{1}{2}}-{2}^{2x-1}$$

And my approach is this:

${2}^{2x}+{2}^{2x-1}={3}^{x+\frac{1}{2}}+{3}^{x-\frac{1}{2}}$

${2}^{2x}(1+{2}^{-1})={3}^{x}({3}^{\frac{1}{2}}+{3}^{-\frac{1}{2}})$

${2}^{2x}\ast \frac{3}{2}={3}^{x}(\sqrt{3}+\frac{1}{\sqrt{3}})$

${2}^{2x}\ast \frac{3}{2}={3}^{x}(\frac{{\sqrt{3}}^{2}+1}{\sqrt{3}})$

${2}^{2x}\ast \frac{3}{2}={3}^{x}\ast \frac{4\sqrt{3}}{3}$--> here I have rationalized the fraction

$\frac{{2}^{2x}}{{3}^{x}}=\frac{4\sqrt{3}}{3}\ast \frac{2}{3}$

${\left(\frac{{2}^{2}}{3}\right)}^{x}=\frac{8\sqrt{3}}{9}$

Now I hope I didn't make an error. How should I proceed from this point? Is there another way around this problem?

asked 2022-07-06

Please help me understand this simple fraction

I got started learning about fractions a few days ago, The tutorial I'm using for this, is limited to fractions like this

$g)\frac{7}{12}\times \frac{8}{21}=\frac{2}{9}$

Now as I'm trying to find further exercices, I keep stumbling upon fraction-based problems that are built like this one.

5.Myltiply.

$a)5\frac{1}{4}\times 2\frac{2}{3}=14$

What does the number on the left mean? I mean the huge 5 and huge 2. is it a whole + a fraction? like 5 + (1/4)??

I would like to further my research on this topic, but I don't know what the name of these types of fractions are.

receiving a link to a tutorial would be fine too, I just don't know what search terms to use.

Also why is the solution 14?

I got started learning about fractions a few days ago, The tutorial I'm using for this, is limited to fractions like this

$g)\frac{7}{12}\times \frac{8}{21}=\frac{2}{9}$

Now as I'm trying to find further exercices, I keep stumbling upon fraction-based problems that are built like this one.

5.Myltiply.

$a)5\frac{1}{4}\times 2\frac{2}{3}=14$

What does the number on the left mean? I mean the huge 5 and huge 2. is it a whole + a fraction? like 5 + (1/4)??

I would like to further my research on this topic, but I don't know what the name of these types of fractions are.

receiving a link to a tutorial would be fine too, I just don't know what search terms to use.

Also why is the solution 14?

asked 2022-09-13

Minimum value in 2 variables

Find the Minimum Value of:

$$\frac{18}{a+b}+\frac{12}{ab}+8a+5b.$$

where a and b are positive real numbers

I tried evaluating the expression into 1 denominator, and tried to get squares so i can evaluate to 0 but obviously it was the wrong approach.

Find the Minimum Value of:

$$\frac{18}{a+b}+\frac{12}{ab}+8a+5b.$$

where a and b are positive real numbers

I tried evaluating the expression into 1 denominator, and tried to get squares so i can evaluate to 0 but obviously it was the wrong approach.

asked 2021-09-18

Solve for the indicated variable. Fully reduce fractions.

a.) Solve$2L+2W=P2L+2W=P$ for W

b.)$2xyz=242xyz=24$ for y

a.) Solve

b.)

asked 2022-07-02

Trying to subtract 2 fractional

I'm trying to solve $f(x)=0$ for x, but I can't figure it out as I have to get both the denominators to become for instance 8x, and then only 1 numerator has x in it. How can I solve this?

$f(x)=\frac{1}{4}-\frac{3}{2x}$

I'm trying to solve $f(x)=0$ for x, but I can't figure it out as I have to get both the denominators to become for instance 8x, and then only 1 numerator has x in it. How can I solve this?

$f(x)=\frac{1}{4}-\frac{3}{2x}$

asked 2021-11-13

In the following exercises, solve the equation by clearing the fractions.

$\frac{2}{3}\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\frac{3}{4}$

asked 2022-06-22

inequality with three variables and condition

If $a$, $b$ and $c$ positive real numbers such that $a+b+c=1$, prove

$\frac{{b}^{2}}{a+{b}^{2}}}+{\displaystyle \frac{{c}^{2}}{b+{c}^{2}}}+{\displaystyle \frac{{a}^{2}}{c+{a}^{2}}}\u2a7e{\displaystyle \frac{3}{4}$. I have tried several methods to solve this,but can't get any result. Any idea?

If $a$, $b$ and $c$ positive real numbers such that $a+b+c=1$, prove

$\frac{{b}^{2}}{a+{b}^{2}}}+{\displaystyle \frac{{c}^{2}}{b+{c}^{2}}}+{\displaystyle \frac{{a}^{2}}{c+{a}^{2}}}\u2a7e{\displaystyle \frac{3}{4}$. I have tried several methods to solve this,but can't get any result. Any idea?