Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
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
Multiplication of whole numbers is repeated groups, and fourth graders discover that the same idea works with fractions. Since 5/4 is five copies of 1/4, it can be written as 5 × (1/4). Taking that further, 3 × (2/5) means three copies of 2/5, which is six copies of 1/5, or 6/5. In general, n × (a/b) = (n × a)/b: multiply the numerator by the whole number and keep the denominator.
The standard is built in three steps. First, students see any fraction a/b as a multiple of the unit fraction 1/b. Next, they use that to multiply a fraction by a whole number, showing the product with a fraction model or number line. Finally, they solve word problems, such as finding how many pounds of fruit are needed if each of 5 people eats 3/8 of a pound. Students also judge between which two whole numbers an answer such as 15/8 lies, which keeps the answer connected to real quantities.
Students often write 3 × 2/5 = 6/15. A number line with three jumps of 2/5 lands at 6/5, showing the pieces stay fifths.
Some students are surprised that 4 × 1/8 is only 1/2. Multiplying by a whole number does make the fraction larger, but the result can still be less than one.
An answer of 15/8 pounds may be left without meaning. Asking which two whole numbers it falls between (1 and 2) connects the fraction to the context.
Each of 5 friends eats 3/8 of a pound of grapes. How many pounds of grapes do they eat in all? Between which two whole numbers is the answer?
Answer: They eat 15/8 = 1 7/8 pounds of grapes, which is between 1 and 2 pounds.
Number lines are especially helpful here: show 4 × (2/3) as four jumps of 2/3 and count the thirds. Then connect the jumps to the equation (4 × 2)/3 = 8/3. Students who see the jumps rarely multiply the denominator.
Assessment items often ask for an equivalent expression (3 × 2/5 = 6 × 1/5) or a word problem answer between two whole numbers. Practice both the computation and the interpretation.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 6/5 (also accepted: 1 1/5)
Three copies of 2/5 is six copies of 1/5, so the product is 6/5, which is 1 1/5.
Answer: B) 7 × (1/4)
7/4 is seven copies of the unit fraction 1/4, so 7/4 = 7 × (1/4).
Answer: 12/10 (also accepted: 1 2/10, 6/5, 1 1/5)
Multiply the numerator by 4: (4 × 3)/10 = 12/10, which is 1 2/10.
Answer: D) 8/3 cups
4 × (2/3) = 8/3 cups, which is 2 2/3 cups. The denominator stays thirds.
Answer: C) 2 and 3
6 × 3/8 = 18/8. Since 16/8 = 2 and 24/8 = 3, 18/8 lies between 2 and 3.
Answer: 10
Each 2/3 is two thirds, so five of them make 10 thirds: 5 × (2/3) = 10 × (1/3).
A full lesson with slides, activities and an exit ticket on multiplying a fraction by a whole number, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.NF.B.4 with an answer key, ready in about a minute.
Make a worksheet →Turn multiplying a fraction by a whole number into a quiz students answer online that marks itself, with a class summary for you.
Build a test →The denominator tells the size of each piece. Multiplying by a whole number makes more pieces of the same size, so only the numerator changes.
In fifth grade, 5.NF.B.4 extends multiplication to a fraction times a fraction, and 5.NF.B.5 treats multiplication as scaling.