Adding mixed numbers with different denominators involves several key steps to ensure accurate calculation. The fundamental principle is to find a common denominator for the fractional parts before performing the addition.
Here's a detailed explanation with examples:
-
Identify the Mixed Numbers: Recognize the mixed numbers you need to add. For example, let's consider adding ( 5 \frac{1}{4} ) and ( \frac{3}{5} ).
-
Find the Least Common Denominator (LCD): Determine the LCD for the fractional parts of the mixed numbers.
- In the example ( \frac{1}{4} ) and ( \frac{3}{5} ), the denominators are 4 and 5.
- The LCD of 4 and 5 is 20.
-
Convert Fractions to Equivalent Fractions with the LCD: Convert each fraction to an equivalent fraction using the LCD.
-
To convert ( \frac{1}{4} ) to a fraction with a denominator of 20, multiply both the numerator and the denominator by 5:
[
\frac{1}{4} \times \frac{5}{5} = \frac{5}{20}
] -
To convert ( \frac{3}{5} ) to a fraction with a denominator of 20, multiply both the numerator and the denominator by 4:
[
\frac{3}{5} \times \frac{4}{4} = \frac{12}{20}
]
-
-
Add the Whole Numbers and Fractions Separately:
-
Add the whole numbers: In our example, we only have the whole number 5 from the mixed number ( 5 \frac{1}{4} ), so it remains 5.
-
Add the fractions:
[
\frac{5}{20} + \frac{12}{20} = \frac{17}{20}
]
-
-
Combine the Results: Combine the sum of the whole numbers and the sum of the fractions.
-
In our example:
[
5 + \frac{17}{20} = 5 \frac{17}{20}
]
-
Therefore, ( 5 \frac{1}{4} + \frac{3}{5} = 5 \frac{17}{20} ).
