Add. Simplify if possible.
7/9z^3 + 1/21z^3
I came up with 49+3z/63z^3
Is this correct?
We have this:
7/9z^3 + 1/21z^3
Our LCD is 63z^3.
We now divide the LCD by each denominator and then multiply the quotient by each numerator.
63z^3/9z^3 = 7
Then, 7 times 7 = 49
=====================
Next fraction:
63z^3 divided by 21z^3 = 3
Then, 3 x 1 = 3
We now add the numerators and keep the LCD.
(49 + 3)/63z^2
Final answer: 52/63z^3
Done!
Thanks Guido.
To add the fractions (7/9z^3) and (1/21z^3), you need a common denominator. In this case, the least common denominator is 63z^3 (since 9z^3 and 21z^3 both divide evenly into 63z^3).
To convert the fractions to have a denominator of 63z^3, multiply the numerator and denominator of the first fraction by 7z^3, and multiply the numerator and denominator of the second fraction by 3z^3:
(7/9z^3) * (7z^3/7z^3) = 49z^3/63z^3
(1/21z^3) * (3z^3/3z^3) = 3z^3/63z^3
Now, the fractions have a common denominator of 63z^3. Combining the fractions, you get:
49z^3/63z^3 + 3z^3/63z^3
To add fractions, you add the numerators together:
(49z^3 + 3z^3)/63z^3
Simplifying the numerator:
(52z^3)/63z^3
Finally, since the numerator and denominator share a common factor of z^3, you can cancel them out:
52/63
Therefore, the simplified sum is 52/63.