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In the Common Core, adding and subtracting fractions with the same denominator is grade 4 work, with halves, thirds, fourths, fifths, sixths, eighths, tenths and twelfths. Mixed numbers with the same denominator are grade 4 as well; unlike denominators, mixed numbers included, are grade 5. Start with like denominators, then adding with unlike denominators, then subtracting, then both on one sheet. The mixed numbers sheet with unlike denominators is the hardest.

Same denominator

Add or subtract the top numbers and keep the bottom number: 3/8 + 2/8 = 5/8, because three eighths and two eighths make five eighths. Adding the bottom numbers too, 3/8 + 2/8 = 5/16, is the most common mistake: the parts are still eighths. When the answer is more than 1, write it as a mixed number: 7/8 + 5/8 = 12/8 = 1 4/8 = 1 1/2.

Unlike denominators

Write both fractions with the same denominator first, then add or subtract. The easiest is the least common multiple of the two denominators: for 1/6 + 3/4 it is 12, so 1/6 = 2/12 and 3/4 = 9/12, and 2/12 + 9/12 = 11/12. Multiplying the two denominators, 6 × 4 = 24, also works, but leaves a bigger fraction to simplify. When one denominator divides the other, as in 1/2 + 3/8, only one fraction changes: 4/8 + 3/8 = 7/8.

Mixed numbers

Give the fractions the same denominator, then add the whole numbers and the fractions apart: 2 1/2 + 1 2/3 = 2 3/6 + 1 4/6 = 3 7/6, and 7/6 is 1 1/6, so the answer is 4 1/6. To take away when the first fraction is the smaller, take one whole from the whole number: 3 1/4 − 1 2/3 = 3 3/12 − 1 8/12, and 3 3/12 is 2 15/12, so the answer is 1 7/12. With the same denominator there is no first step: 2 3/8 + 1 7/8 = 3 10/8, and 10/8 is 1 2/8, so the answer is 4 2/8, which is 4 1/4.

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