The third main idea is mixed numbers and adding and subtracting like and unlike denominators. When adding mixed numbered fractions with the same denominator you add the whole numbers like normal and add the fractions like normal remembering to keep the denominator. For example, 2 ⅔ + 1 ⅓ = 2 + 1 = 3 and then 2 +1 for the numerators keeping the denominator a 3 gives you 3 3/3 or 4. In the denominators are not the same you leave the whole number alone and adjust the fractions like you did before. For example, 3 ½ + 5 ⅔ = the LCD is 6 so for ½ 3 /6 2 x 3 =6 and 3 x 1 = 3 keep the new denominator 3/6. For ⅔ 3 x 2 = 6 so 2 x 2 = 4 keep the new denominator 4/6. Then you add like normal 3 + 5 = 8 then the fractions 4 + 3 = 7 over the new denominator 6 so 7/6.
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For subtracting the same rules apply, but you may have to barrow from the whole number. For example, subtracting two mixed numbers would look like this 4 ⅕ - 1 ⅖ ⅕ is smaller than ⅖ so you have two barrow from the whole number 4 so its 5/5 + ⅕ = 6/5. The new problem then reads 3 6/5 - 1 ⅖ you subtract like normal so for the whole numbers 3-1 = 2 and for the fractions 6- 2 = 4 keep the denominator so your answer is 2 3/4 . For unlike mixed numbers the same rules apply for example, 5 ⅙ - 2 ¾. The LDC of 6 and 4 is 12 so kits the new denominator so for ⅙ 6 x 2 =12 so 1 x 2 = 2 you get 2/12. For ¾ 4 x 3 = 12 so 3 x 3 = 9 you get 9/12 then you subtract like normal you leave the whole numbers