5.NF.1
“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.)”
Questions 1 to 4 rename fractions over denominators of 12, 24, 10 and 12, with the regrouping subtraction 3 1/4 − 1 2/3 as the hardest case.
5.NF.2
“Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 <1/2.”
Question 13 is the word-problem version: 3/4 cup of oat flour plus 2/3 cup of almond flour makes 1 5/12 cups.
5.NF.3
“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?”
No question here rewrites a whole-number quotient as a fraction; the nearest step is expressing 20/8 as the mixed number 2 1/2 in question 6.
5.NF.4.a
“Interpret the product (a/b) x 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) x 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) x (c/d) = ac/bd.)”
Questions 5 to 8 all use the ac/bd computation, from 3/4 × 2/5 = 6/20 to (3/2) × (2/3) = 6/6.
5.NF.6
“Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.”
Questions 13 and 15 are the real-world multiplication problems, ending at 1 5/12 cups of flour and 5/9 of a mile.
5.NF.7.c
“Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?”
Question 14 divides 6 pounds of cheese by 1/3 pound per pizza to get 18 pizzas.
