Multiplying a fraction by a whole number worksheets
Aligned with Common Core 4.NF.B.4
Printable fourth-grade worksheets and how-to teaching pages for multiplying a fraction by a whole number: unit fractions, repeated addition, fraction strips, number line jumps, multiplying on graph paper, and word problems.
The worksheets
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How to Write a Fraction as Unit Fractions
5/4 and 3/8 shown with fraction strips and written as sums of unit fractions and as 5 × 1/4 and 3 × 1/8.
Fractions as Unit Fractions
Fractions like 7/8 to write as 7 × 1/8, with strips on Fewer and Standard. Standard includes fractions more than 1, and More also goes the other way, like 4 × 1/5 = 4/5.
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How to Multiply a Fraction by a Whole Number
3 × 2/5 shown as three groups of 2/5 with strips, as 2/5 + 2/5 + 2/5, with the multiply-the-top shortcut, and as jumps on a number line.
Repeated Addition to Multiplication
Sums like 2/5 + 2/5 + 2/5 to write as 3 × 2/5 and solve on graph paper. More adds up to five of the same fraction.
Multiply with Fraction Strips
One strip for each group to shade, like three strips of 2/3, then the product. More has up to four groups.
Multiply a Fraction by a Whole Number
Problems like 4 × 3/8 on graph paper with the × in a yellow square. Standard uses whole numbers to 9, and More also asks for each answer as a mixed number.
Jumps on a Number Line
Number lines cut into fourths, fifths, sixths and more to draw jumps like 3 jumps of 2/5. Fewer shows the jumps already drawn.
Fraction Times Whole Number Word Problems
Stories about running, pizza, flour, ribbon and water. More also asks which two whole numbers the answer is between.
Print the whole packet
One copy of every sheet above, in order. Tap + for more copies (up to 10).
For the parent or teacher
What it is
Fourth graders learn that a fraction like 5/4 is five copies of the unit fraction 1/4, so 5/4 = 5 × 1/4. Then they multiply a fraction by a whole number, like 3 × 2/5. Three groups of 2/5 is 2/5 + 2/5 + 2/5, which is 6/5. The shortcut is to multiply the top number and keep the bottom number, then change the answer to a mixed number when it is more than 1.
What comes next
Decimals to hundredths, where tenths and hundredths are written as decimals.
How to teach it
- Start with unit fractions. Build 5/4 from five 1/4 pieces of a fraction strip.
- Connect multiplication to repeated addition, the same way 3 × 4 means 4 + 4 + 4.
- Show the groups with strips or jumps on a number line before using the shortcut.
- Say the bottom number as a word, like "fifths," so it stays the size of the pieces.
- In word problems, ask which number is the number of groups and which is the size of each group.
Common mistakes
- Multiplying both the top and the bottom number, like 3 × 2/5 = 6/15.
- Forgetting to change an answer like 6/5 to the mixed number 1 1/5 when asked.
- Mixing up which number in a story is the whole number and which is the fraction.
- Drawing the wrong number of groups on a picture or number line.