Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
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
Once students can multiply fractions, they apply that skill to everyday situations: scaling a recipe, finding part of a distance, working out the area of a garden with fractional sides or the cost of a fraction of a pound of cheese. The challenge is less the arithmetic than recognizing that the situation calls for multiplication, usually signaled by taking a fraction of an amount or by repeated equal groups of a fractional size.
Mixed numbers are part of this work. To find 2 1/2 batches of a recipe that uses 3/4 cup of oats, students can convert 2 1/2 to 5/2 and multiply (5/2 × 3/4 = 15/8 = 1 7/8 cups), or use the distributive property: 2 × 3/4 plus 1/2 × 3/4, which is 1 1/2 + 3/8. Visual fraction models and equations both help students show what they did, and estimation (about 2 1/2 batches of almost a cup is around 2 cups) keeps answers sensible.
Students may compute 2 1/2 × 3 1/3 as 2 × 3 plus 1/2 × 1/3. This misses the cross terms; converting to fractions or using a full area model avoids the error.
'Three fourths of a 2/3-pound bag' is a multiplication, 3/4 × 2/3. Students who add the fractions misread the relationship.
In an area problem the answer is in square units; in a recipe problem it is in cups. Asking 'what does this number count?' keeps the context clear.
15/8 cups is correct but harder to picture than 1 7/8 cups. Converting helps students check against their estimate.
A granola recipe uses 3/4 cup of oats per batch. How many cups of oats are needed for 2 1/2 batches?
Answer: 1 7/8 cups of oats are needed.
Give students the same problem with three representations side by side: a strip diagram, an area model and an equation. Ask them to point out where each number in the equation appears in each picture.
Assessment problems involve recipes, distances, areas and money, sometimes in two steps, such as finding a fraction of a fraction and then subtracting from the whole.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 4 (also accepted: 4 miles)
2/3 × 6 = 12/3 = 4 miles.
Answer: 1/4 (also accepted: 3/12, 1/4 pound)
1/3 × 3/4 = 3/12 = 1/4 pound.
Answer: D) 1 m²
1 1/2 = 3/2. Area = 3/2 × 2/3 = 6/6 = 1 square meter.
Answer: 1 1/2 (also accepted: 1 4/8, 3/2, 1 1/2 miles)
4 × 3/8 = 12/8 = 1 4/8 = 1 1/2 miles.
Answer: B) $18
2 1/4 = 9/4. 9/4 × 8 = 72/4 = 18, so the cheese costs $18.
Answer: 5 (also accepted: 5 square yards)
3 1/3 = 10/3 and 1 1/2 = 3/2. 10/3 × 3/2 = 30/6 = 5 square yards.
A full lesson with slides, activities and an exit ticket on real-world fraction multiplication, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.NF.B.6 with an answer key, ready in about a minute.
Make a worksheet →Turn real-world fraction multiplication into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Real-world problems that multiply fractions and mixed numbers, such as recipes, distances, areas and costs, represented with visual models or equations.
Converting to fractions is reliable. Using the distributive property with a whole part and a fraction part also works and is good for mental math.