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?
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
The fraction bar is also a division sign. Fifth graders learn that 3/4 can be read as 3 ÷ 4: if 3 pizzas are shared equally among 4 people, each person gets 3/4 of a pizza. One way to see it is to cut each of the 3 pizzas into fourths, giving 12 fourths, and hand out 3 fourths to each person.
This idea turns division problems with remainders into problems with exact fraction answers. If 9 people share a 50-pound sack of rice equally, each gets 50 ÷ 9 = 50/9 pounds, which is 5 5/9 pounds, a value between 5 and 6. Students solve such word problems with visual fraction models or equations and should be able to explain both views: a/b as a parts of size 1/b, and a/b as the size of one share when a wholes are split among b people. Checking with multiplication (3/4 × 4 = 3) ties the two together.
When 3 cookies are shared by 4 children, students sometimes compute 4 ÷ 3. The amount being shared is divided by the number of people: 3 ÷ 4 = 3/4.
50 ÷ 9 = 5 remainder 5 becomes 5 5/9, not 5.5 or 5 5/10. The remainder is shared among 9, so it is 5 ninths.
Students used to remainders may say 2 ÷ 5 'can't be done'. Sharing 2 sandwiches among 5 people clearly gives each person 2/5 of a sandwich.
Some students accept 3/4 as 'three of four parts' but not as 3 ÷ 4. Showing both with the same drawing links them.
9 people share a 50-pound sack of rice equally by weight. How many pounds does each person get? Between which two whole numbers is the answer?
Answer: Each person gets 50/9 = 5 5/9 pounds of rice, between 5 and 6 pounds.
Act out sharing with paper circles: 2 'pizzas' shared by 3 students. Students cut, distribute and name the share. Recording 2 ÷ 3 = 2/3 beside the drawing makes the equivalence memorable.
Expect word problems about sharing money, food or lengths, items asking which expression equals a fraction, and questions asking between which two whole numbers an answer falls.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 7/8
a ÷ b = a/b, so 7 ÷ 8 = 7/8.
Answer: B) 3/4 of a bar
The amount shared, 3 bars, is divided by the number of friends, 4: 3 ÷ 4 = 3/4 of a bar each.
Answer: 4 2/5 (also accepted: 4 2/5 feet, 22/5)
22 ÷ 5 = 22/5. 5 × 4 = 20, leaving 2, so each piece is 4 2/5 feet.
Answer: D) 6 and 7
6 × 6 = 36 and 6 × 7 = 42. 41 is between 36 and 42, so 41 ÷ 6 = 6 5/6, between 6 and 7.
Answer: 8
8/3 means 8 ÷ 3, so the whole number is 8.
Answer: B) Because 2/5 is the share when 2 is divided into 5 equal parts, and 5 of those shares make 2
2/5 = 2 ÷ 5. Five equal shares of size 2/5 put back together give the original 2.
A full lesson with slides, activities and an exit ticket on fractions as division, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.NF.B.3 with an answer key, ready in about a minute.
Make a worksheet →Turn fractions as division into a quiz students answer online that marks itself, with a class summary for you.
Build a test →It connects fractions and division, so remainders can be expressed exactly as fractions. This underpins fraction division in sixth grade and ratios such as unit rates.
Both are correct. Word problems often read better as mixed numbers, such as 5 5/9 pounds, and asking where the answer lies between two whole numbers encourages that form.