- #1
Spencer23
- 4
- 0
Hello,
Wondering how to simplify this fraction...
3/90 * (36x+54)
Wondering how to simplify this fraction...
3/90 * (36x+54)
Simplifying Algebraic fraction
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- Thread starter Spencer23
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- Fraction Simplifying
In summary, the conversation is about simplifying a fraction with a complex algebraic expression in the denominator. The poster provides a screenshot of the question and the experts help by explaining how to simplify the fraction by factoring and using an example for guidance. The final result is that the fraction can be simplified to a simpler form.
- #2
anemone
Gold Member
MHB
POTW Director
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Hi Spencer23, welcome to MHB!:)
Can you be a little bit more clear about the math expression that you've there, do you mean
1. $\dfrac{3}{90(36x+54)}$ or
2. $\dfrac{3(36x+54)}{90}$?
Can you be a little bit more clear about the math expression that you've there, do you mean
1. $\dfrac{3}{90(36x+54)}$ or
2. $\dfrac{3(36x+54)}{90}$?
- #3
- #4
MarkFL
Gold Member
MHB
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- 12
The form in your attached image is equivalent to the second form given by anemone. This is because the following are equivalent:
\(\displaystyle \frac{a}{b}\cdot c=\frac{ac}{b}\)
For example, consider:
\(\displaystyle \frac{1}{2}\cdot4=\frac{1\cdot4}{2}=\frac{4}{2}=\frac{2\cdot\cancel{2}}{\cancel{2}}=2\)
Can you factor anything from the expression in parentheses?
\(\displaystyle \frac{a}{b}\cdot c=\frac{ac}{b}\)
For example, consider:
\(\displaystyle \frac{1}{2}\cdot4=\frac{1\cdot4}{2}=\frac{4}{2}=\frac{2\cdot\cancel{2}}{\cancel{2}}=2\)
Can you factor anything from the expression in parentheses?
- #5
anemone
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Also, another example that might be helpful to be used as guidance would be the following:
$\dfrac{6+9}{12}$, it could be simplified further down by rewriting it as $\dfrac{2(3)+3(3)}{3(4)}=\dfrac{3(2+3)}{3(4)}=\dfrac{\cancel{3}(5)}{\cancel{3}(4)}=\dfrac{5}{4}$.
$\dfrac{6+9}{12}$, it could be simplified further down by rewriting it as $\dfrac{2(3)+3(3)}{3(4)}=\dfrac{3(2+3)}{3(4)}=\dfrac{\cancel{3}(5)}{\cancel{3}(4)}=\dfrac{5}{4}$.
- #6
Spencer23
- 4
- 0
Thanks guys , didnt realize it was the same as the example you gave... understand how its done now! Thank you both!
- #7
Jason85
- 2
- 0
Attachments
FAQ: Simplifying Algebraic fraction
What is an algebraic fraction?
An algebraic fraction is an expression that contains one or more variables in the numerator and/or denominator. It can be simplified by dividing out any common factors in the numerator and denominator.
Why is it important to simplify algebraic fractions?
Simplifying algebraic fractions makes them easier to work with and understand. It also allows us to find equivalent fractions and solve equations involving fractions more easily.
What are the steps to simplify an algebraic fraction?
The steps to simplify an algebraic fraction are:
- Factor out any common factors in the numerator and denominator.
- If possible, cancel out any common factors.
- If there are still variables in the numerator and denominator, rewrite the fraction with the remaining factors.
Can algebraic fractions be simplified further?
Yes, in some cases, algebraic fractions can be simplified further by using more advanced techniques such as multiplying by the conjugate or using polynomial long division.
What are some common mistakes to avoid when simplifying algebraic fractions?
Some common mistakes to avoid when simplifying algebraic fractions include:
- Forgetting to factor out common factors.
- Incorrectly canceling out common factors.
- Making a mistake when rewriting the fraction with remaining factors.