5.NF.A.1 — Add & Subtract Fractions

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Students first identify whether fractions can be added or subtracted directly or whether they need to be rewritten. This builds the understanding that denominators must name the same-sized parts before combining quantities.

Students rewrite fractions as equivalent fractions so both fractions use the same denominator. This step connects multiplication of numerators and denominators to preserving the value of a fraction.

Once denominators match, students combine or separate the numerators while keeping the common denominator. This helps students see that the count of parts changes, but the size of each part stays the same.

Students apply the same process to mixed numbers by rewriting them as needed and finding equivalent fractions with common denominators. This extends fraction addition and subtraction into more complex real and abstract problems.

Students describe why equivalent fractions make unlike-denominator problems solvable and connect examples to the general rule. This supports mathematical reasoning beyond following a memorized procedure.