Solve Two Thirds Plus One Ninth: Quick Math Guide
Table of Contents :
To solve the expression "Two thirds plus one ninth," it's essential to understand how to add fractions. In this guide, we’ll break down the steps needed to perform the addition accurately, ensuring clarity for everyone, regardless of their math expertise.
Understanding the Fractions
Definitions of the Fractions
Two thirds (2/3): This fraction means you have two parts out of three equal parts.
One ninth (1/9): This represents one part out of nine equal parts.
To add these fractions, we need a common denominator.
Finding the Common Denominator
The first step in adding fractions is to identify the least common denominator (LCD).
Finding the LCD of 3 and 9:
The denominators of our fractions are 3 and 9. The least common denominator is the smallest number that both denominators can divide into evenly. In this case, the LCD is 9.
Why Choose the Least Common Denominator?
Using the least common denominator simplifies calculations and avoids unnecessary complications. It’s also efficient, especially when dealing with larger fractions.
Converting the Fractions
Now, we need to convert the fractions so that they have the same denominator.
-
Convert Two Thirds (2/3) to a Fraction with Denominator 9:
- Multiply both the numerator and denominator of 2/3 by 3:
[ \frac{2 \times 3}{3 \times 3} = \frac{6}{9} ]
-
One Ninth (1/9) is Already in the Correct Form:
- The fraction remains 1/9.
The Updated Fractions
After conversion, we now have:
- Two thirds = 6/9
- One ninth = 1/9
Adding the Fractions
Now that both fractions have the same denominator, we can easily add them together:
[ \frac{6}{9} + \frac{1}{9} = \frac{6 + 1}{9} = \frac{7}{9} ]
So, the sum of two thirds plus one ninth is seven ninths (7/9).
Visual Representation
To enhance understanding, let’s visualize the addition of these fractions:
<table> <tr> <th>Fraction</th> <th>Representation</th> </tr> <tr> <td>Two Thirds (2/3)</td> <td>⬜⬜⬛</td> </tr> <tr> <td>One Ninth (1/9)</td> <td>⬜</td> </tr> <tr> <td>Total (7/9)</td> <td>⬜⬜⬜⬜⬜⬜⬜⬛</td> </tr> </table>
In the table above, each box represents a fraction. The shaded boxes indicate the portions represented by each fraction, leading up to the total.
Important Notes
Tip: Always ensure that your fractions are simplified as much as possible. In this case, ( \frac{7}{9} ) is already in its simplest form.
Conclusion
In summary, solving "Two thirds plus one ninth" involves:
- Finding a common denominator.
- Converting the fractions accordingly.
- Adding the numerators together while keeping the denominator the same.
The answer to the problem is ( \frac{7}{9} ) 🎉. This method can be applied to other fraction addition problems as well!