Math News - Operations with 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.)

Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret the product (𝘢/𝘣) × 𝘲 as a parts of a partition of 𝘲 into 𝘣 equal parts; equivalently, as the result of a sequence of operations 𝘢 × 𝘲 ÷ 𝘣. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (𝘢/𝘣) × (𝘤/𝘥) = 𝘢𝘤/𝘣𝘥.)

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.