Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
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
Fifth grade fraction division is limited to two kinds of problems, both with unit fractions (fractions with a numerator of 1). The first divides a unit fraction by a whole number, such as (1/3) ÷ 4. A story might be: 1/3 of a pan of brownies is shared equally by 4 friends. Cutting the third into 4 pieces makes each piece 1/12 of the pan, so (1/3) ÷ 4 = 1/12. Checking with multiplication confirms it, since (1/12) × 4 = 1/3.
The second divides a whole number by a unit fraction, such as 4 ÷ (1/5): how many fifths are in 4 wholes? Each whole holds 5 fifths, so 4 wholes hold 20, and 4 ÷ (1/5) = 20, because 20 × (1/5) = 4. Students should create story contexts, draw models and use the link between multiplication and division to justify answers. The general invert-and-multiply rule is saved for sixth grade, when students divide any fraction by any fraction.
4 ÷ (1/5) = 20 surprises students. Asking how many fifths fit into 4 wholes makes the large answer sensible.
(1/3) ÷ 4 and 4 ÷ (1/3) have very different answers (1/12 and 12). Students should say each problem aloud as a question before solving.
Some students compute (1/4) ÷ 2 as 1/2 by dividing 4 by 2. Splitting a fourth into 2 pieces makes eighths, so the answer is 1/8.
A quick multiplication check, such as 1/8 × 2 = 1/4, shows immediately whether the quotient is right.
How many 1/3-cup servings are in 2 cups of raisins? Then share 1/2 pound of chocolate equally among 3 people.
Answer: There are 6 servings of raisins, and each person gets 1/6 pound of chocolate.
Use fraction strips: to show 3 ÷ (1/4), lay 3 whole strips and count the fourth-pieces that fit. To show (1/4) ÷ 3, take one fourth-strip and split it into 3 equal parts, then compare a part with a whole strip.
Assessment items ask for quotients, ask which story matches an expression, or ask students to explain a quotient with a model or multiplication check.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 1/8
Splitting one fourth into 2 equal parts gives eighths. (1/4) ÷ 2 = 1/8, and 1/8 × 2 = 1/4 checks it.
Answer: 15
Each whole holds 3 thirds, so 5 wholes hold 15 thirds. Check: 15 × 1/3 = 5.
Answer: A) 1/6
(1/2) ÷ 3 = 1/6. Check: 1/6 × 3 = 3/6 = 1/2.
Answer: D) How many 1/4-mile laps make 6 miles?
6 ÷ (1/4) asks how many fourths fit into 6, which matches counting 1/4-mile laps in 6 miles. The answer is 24 laps.
Answer: 15 (also accepted: 15 pieces)
Each foot holds 5 fifths, so 3 feet hold 3 × 5 = 15 pieces.
Answer: 1/6
(1/3) ÷ 2 = 1/6 of a gallon in each cup. Check: 1/6 × 2 = 1/3.
A full lesson with slides, activities and an exit ticket on dividing unit fractions and whole numbers, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.NF.B.7 with an answer key, ready in about a minute.
Make a worksheet →Turn dividing unit fractions and whole numbers into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Not as part of 5.NF.B.7. Fifth grade is limited to unit fractions with whole numbers, solved with models and the multiplication link. Dividing any fraction by any fraction, often with the invert-and-multiply method, is 6.NS.A.1.
A fraction with a numerator of 1, such as 1/2, 1/5 or 1/12.