Fraction Addition

Combining mixed numbers or fractions involves adding their values to find their sum. A mixed number combines a whole number and a proper fraction. You add their whole number parts separately and then their fractional parts for mixed numbers. Ensure fractions have the same denominator, then add their numerators while keeping the denominator constant. Finally, simplify the result if possible.

Example Additions

Add the following mixed numbers and fractions:
2 1/3 + 1 2/5

Convert mixed numbers to improper fractions:
2 1/3 = (2 * 3 +1)/3 = 7/3
1 2/5 = (1 * 5+2)/5 = 7/5
Find a common denominator and add the fractions:
The common denominator of 3 and 5 is 15.
Convert fractions to the common denominator of 15:
7/3 = (7 * 5) / (3 * 5) = 35/15
7/5 = (7 * 3)/(5 * 3) = 21/15
Add the fractions:
35/15 + 21/15 = (35 + 21)/15 = 56/15
Convert the improper fraction back to a mixed number:
56/15 can be written as 3 11 /15? because 56 ÷ 15 =3 with a remainder of 11.

The sum of 2 1/3 and 1 2/5 is 3 11/15.

Add the fractions 1/4 and 10/32:

To add 1/4 and 10/32, we need to find a common denominator and then add the numerators:
First, let's find the least common multiple (LCM) of the denominators, which are 4 and 32. The LCM of 4 and 32 is 32.
Now, rewrite both fractions with the common denominator of 32:
multiply both the numerator and denominator by 8:
1 * 8 = 8   
4 * 8 = 32
1/4 can be expressed as 8/32
10/32 remains unchanged.
Add the numerators of the fractions together:
8/32 + 10/32 = 18/32
Since both the numerator and the denominator have a common factor of 2, we can simplify the fraction:
Divide both the numerator and the denominator by 2:
18 ÷ 2 = 9
32 ÷ 2 = 16
You can simplify 18/32 to 9/16.

The sum of 1/4 + 10/32 is 9/16.

Add the mixed fractions 2 1/4 and 3 5/16 together:

To add the mixed fractions 2 1/4? and 3 5/16 together, we first convert them into improper fractions:
2 1/4 ? can be expressed as 2 * 4/4 + 1/4, which equals 9/4
Similarly, 3 5/16 can be expressed as 3 *1 6/16 + 5/16, which equals 53/16
Now, we add the two improper fractions:
9/4 +53/16
To add fractions with different denominators, we find a common denominator. In this case, the least common multiple (LCM) of 4 and 16 is 16.
multiply the numerator and the denominator by 4:
9 * 4 = 36
4 * 4 = 16
9/4 can be expressed as 36/16
53/16 remains unchanged.
Add the numerators of the fractions together:
36/16 + 53/16 = 36 + 53/16 = 89/16
Now, 2 1/4 + 3 5/16 = 89/16
We can also express this as a mixed fraction:
89/16 = 5 9/16

So, 2 1/4 + 3 5/16 = 5 9/16

Whether you're a student, teacher, or anyone needing to perform fraction addition, our tool provides a quick and reliable solution. It is perfect for solving math problems, checking homework, or performing quick calculations in your day-to-day tasks.

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