Mastering Simple Algebra with Helpful Tips and Examples

  • Thread starter DB
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In summary, the conversation discusses solving a simple algebra question involving fractions. The solution involves multiplying both sides of the equation by a common factor to eliminate the variables in the denominators. The final answer is confirmed to be correct and the conversation ends with a discussion on how to approach a similar but slightly more complex equation.
  • #1
DB
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(another) simple algebra question

[tex]\frac{300}{5v_w}+\frac{300}{3v_w}=8[/tex]

can some1 give me a hand on the algebra here? thanks
 
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  • #2
Multiply both sides with [itex]v_w[/itex] to get:

[tex]\frac{{300}}
{{5v_w }} + \frac{{300}}
{{3v_w }} = 8 \Leftrightarrow v_w \left( {\frac{{300}}
{{5v_w }} + \frac{{300}}
{{3v_w }}} \right) = 8v_w \Leftrightarrow \frac{{300}}
{5} + \frac{{300}}
{3} = 8v_w [/tex]
 
  • #3
okay but i only multiply the numerators by v_w? otherwise i would get v_w^2 in the denominators...right?
 
  • #4
i get 20 btw
 
  • #5
Yes, that wouldn't help anything. You just multiply both sides with it, and when you multiply a fraction with a factor, it's always in the nominator. c * a/b = ca/b.

You do this to get rid of the v_w in the denominators since you can cancel them out when they're also in the numerators.

DB said:
i get 20 btw
Correct :smile: You can check it by plugging it in the initial equation.
 
  • #6
thanks TD, i see it perfectly now
 
  • #7
No problem, glad I could help :smile:
 
  • #8
just out of curiosity...how would i approach:
[tex]\frac{300}{5v_w+10}+\frac{300}{3v_w}=8[/tex]
?
thanks
 
  • #9
You can try simplify the equation a bit:
[tex]\frac{300}{5v_w + 10} + \frac{300}{3v_w} = 8[/tex]
[tex]\Leftrightarrow \frac{60}{v_w + 2} + \frac{100}{v_w} = 8[/tex]
Then, you can try multiplying both sides with vw(vw + 2) to get rid of the denominator. And you will have:
[tex]60v_w + 100(v_w + 2) = 8v_w(v_w + 2)[/tex]
You can rearrange a bit, and you will have a quadratic equation.
Can you go from here?
Viet Dao,
 

1. What is algebra?

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols to solve equations and understand relationships between quantities.

2. What are variables in algebra?

Variables are symbols used to represent unknown quantities in algebraic equations. They can take on different values, and their values can be determined by solving the equation.

3. How do you solve a simple algebraic equation?

To solve a simple algebraic equation, you need to isolate the variable on one side of the equation by using inverse operations, such as addition, subtraction, multiplication, and division.

4. What are the basic operations in algebra?

The basic operations in algebra are addition, subtraction, multiplication, and division. These operations can be used to manipulate equations and solve for unknown quantities.

5. Can you use algebra in real life?

Yes, algebra is used in many real-life situations, such as calculating distances, solving financial problems, and understanding patterns and relationships in data. It is an essential tool in fields such as science, engineering, and economics.

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