Multiplying and Dividing Fractions Word Problems

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?”

Question 5 divides 20 pounds of flour by 6 bowls, expresses 20/6 as 3 1/3, and places it between 3 and 4.

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 2, 4 and 8a are the multiplication stories, from 8 × 3/4 of a fence board to Jordan's 4 × 2 1/3 = 9 1/3 miles.

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?”

Questions 1, 3, 6 and 7 pair both division directions: whole numbers by unit fractions (raisin bags, doll dresses) and unit fractions by whole numbers (paint, and 1/2 gallon shared by 4).