Mixed numbers have a whole-number part and a fraction part. You only need a common denominator for the fraction parts so you can add or subtract them.

The LCD of 5 and 3 is 15, so rewrite as 3615 + 1515. Add the whole numbers (3 + 1 = 4) and the fractions (615 + 515 = 1115) to get 41115.

When the fraction being subtracted is larger, take 1 from the whole number and add it to the fraction part as an equivalent amount, just like borrowing in whole-number subtraction.

First convert 14 to 28. Since 28 is less than 58, borrow 1 whole (which equals 88) from the 6, making it 5 and adding 88 + 28 = 108.

Using the LCD of 12, add 912 + 812 = 1712 = 1512. Add the whole numbers 2 + 4 = 6, then add the extra 1, giving 7512.

Since 5 and 9 share no common factors, multiply them together: 5 times 9 = 45, which is the smallest denominator both 5 and 9 divide into.

With the LCD of 12, rewrite as 8212 − 3912. Since 212 < 912, borrow 1 from 8 to get 71412 − 3912 = 4512.

When the fraction parts sum to an improper fraction (like 1312), take out 1 whole (1212) and carry it over to the whole-number column, just like carrying in addition.

Using the LCD of 30, convert to 12530 + 22130. Add the whole numbers (1 + 2 = 3) and the fractions (2530 + 2130 = 4630 = 11630), then combine to get 41630, which simplifies to 4815.

Correct matches: 513 + 214 → 7712; 712 − 325 → 4110; 438 + 116 → 51324; 914 − 523 → 3712.