-3/7 + (-6/11) + (-8/21) + 5/22?
Explanation:
Adding and subtracting fractions with different denominators can be a bit tricky, but it's manageable if we follow the correct steps. Here, we will break down the given fractions and then find their common denominator to simplify the expression.
1. Finding a Common Denominator:
To add or subtract fractions, we need a common denominator. In this case, the denominators are 7, 11, 21, and 22. To find the least common multiple (LCM) of these numbers, we can start by listing their multiples:
7: 7, 14, 21, 28, ...
11: 11, 22, 33, ...
21: 21, 42, ...
22: 22, 44, ...
The least common multiple of 7, 11, 21, and 22 is 462. Therefore, we will convert each fraction to have a denominator of 462.
2. Converting Fractions:
-3/7 = -3 * 66 / 7 * 66 = -198/462
-6/11 = -6 * 42 / 11 * 42 = -252/462
-8/21 = -8 * 22 / 21 * 22 = -176/462
5/22 = 5 * 21 / 22 * 21 = 105/462
3. Adding the Fractions:
Now that all fractions have the same denominator, we can add them together:
-198/462 + (-252/462) + (-176/462) + 105/462 = -521/462
Therefore, the sum of -3/7 + (-6/11) + (-8/21) + 5/22 is -521/462.