Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
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
In fourth grade students multiplied a fraction by a whole number. Now they multiply by a fraction, and the meaning shifts from 'groups of' to 'part of'. The product (2/3) × 4 can be read as 2 parts of a partition of 4 into 3 equal parts, or as 2 × 4 ÷ 3. Either way the answer is 8/3. With two fractions, (2/3) × (4/5) means two thirds of four fifths, and the area model shows 8 of 15 equal pieces shaded, so the product is 8/15.
The second part of the standard is about area. A rectangle that is 3/4 unit by 2/3 unit can be tiled with small rectangles that each measure 1/4 by 1/3. Twelve of these fit in a unit square, so each is 1/12 of a square unit, and the rectangle holds 6 of them, an area of 6/12 or 1/2. That matches 3/4 × 2/3 = 6/12, showing why multiplying the numerators and multiplying the denominators gives the right result.
Students who have seen cross-multiplication for comparing fractions sometimes use it here, getting 2/3 × 4/5 = 10/12. Multiplication uses numerator times numerator and denominator times denominator.
Common denominators are needed for adding, not multiplying. Converting first is not wrong, but it adds work and often causes errors.
Multiplying 4/5 by 2/3 gives 8/15, which is smaller than both factors. Taking a part of an amount makes it smaller.
When tiling a rectangle with fractional sides, students may count tiles inside the rectangle but forget to find the size of each tile relative to the unit square.
A garden bed is 3/4 yard long and 2/3 yard wide. Find its area by tiling and by multiplying.
Answer: The area is 6/12 = 1/2 square yard.
Use paper folding: fold a sheet into thirds one way and shade two, then fold into fifths the other way and double-shade four of the fifths of the shaded part. The double-shaded region is 8 of 15 pieces. This physically shows 4/5 of 2/3.
Assessment items include direct products, area problems with fractional sides, and choosing the area model or story that matches an equation.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 4
Split 6 into 3 equal parts of 2, then take 2 of those parts: 2 × 2 = 4. Or 2 × 6 ÷ 3 = 12 ÷ 3 = 4.
Answer: 6/35
Multiply numerators and denominators: (3 × 2)/(5 × 7) = 6/35.
Answer: B) 15/4
(3/4) × 5 = (3 × 5)/4 = 15/4, which is 3 3/4.
Answer: 5/12 (also accepted: 5/12 m²)
Area = 1/2 × 5/6 = (1 × 5)/(2 × 6) = 5/12 square meters.
Answer: D) 15 pieces, 8 double-shaded
Thirds one way and fifths the other make 3 × 5 = 15 pieces. The overlap is 2 × 4 = 8 pieces, so the product is 8/15.
Answer: A) A quarter of 8 apples are green
(1/4) × 8 means one fourth of 8, so a quarter of 8 apples are green, which is 2 apples.
A full lesson with slides, activities and an exit ticket on multiplying fractions, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.NF.B.4 with an answer key, ready in about a minute.
Make a worksheet →Turn multiplying fractions into a quiz students answer online that marks itself, with a class summary for you.
Build a test →That is the efficient method, but 5.NF.B.4 asks students to understand why it works, using partitions and area models, before relying on the rule.
This standard focuses on fractions and whole numbers. Real-world problems with mixed numbers are the focus of 5.NF.B.6.