View largerMultiply fractions by whole numbers
How to multiply a fraction by a whole number with groups, a number line and n × (a/b) = (n × a)/b
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Multiplying Fractions by Whole Numbers
Multiply a fraction by a whole number: a chart, unit fractions, fraction bar groups, number line jumps, practice and word problems. With keys.
Download the multiplying fractions by whole numbers worksheets
Multiply a fraction by a whole number with models
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View all 2 pagesFractions as multiples of unit fractions
Writing a fraction a/b as a × (1/b), for example 5/4 = 5 × (1/4), with fraction bars
Answer key on page 2
2 pages43 KB
View all 2 pagesMultiply fractions with models
Showing n × (a/b) as n groups of a/b, then as (n × a) unit fractions, with fraction bars
Answer key on page 2
2 pages40 KB
View all 2 pagesMultiply fractions on a number line
Showing a whole number times a fraction as equal jumps on a number line
Answer key on page 2
2 pages48 KB
Multiply and solve
View all 2 pagesMultiply fractions by whole Numbers, sheet A
Multiplying a fraction by a whole number: multiply the numerator, keep the denominator
Answer key on page 2
2 pages41 KB
View all 2 pagesMultiply fractions by whole Numbers, sheet B
Multiplying a fraction by a whole number and writing the product as a mixed number
Answer key on page 2
2 pages45 KB
View all 2 pagesMultiplying fractions word problems
Solving word problems that multiply a fraction by a whole number, and saying between which whole numbers the answer lies
Answer key on page 2
2 pages44 KB
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About these multiplying fractions by whole numbers worksheets
Multiplying a fraction by a whole number means adding equal groups of that fraction. 3 × 2/5 is 2/5 + 2/5 + 2/5, which is 6 fifths, or 6/5. In general, multiply the whole number by the numerator and keep the denominator: n × a/b = (n × a)/b.
It starts with seeing any fraction as a whole number times a unit fraction: 5/4 = 5 × 1/4. The model pages show groups of fraction bars and jumps on a number line, so the rule makes sense before children use it.
Practice pages ask for the product as a fraction and, on Sheet B, as a mixed number. The word problems ask which two whole numbers the answer lies between. Every practice page has an answer key.
Standards
CCSS.MATH.CONTENT.4.NF.B.4.AUnderstand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).CCSS.MATH.CONTENT.4.NF.B.4.BUnderstand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)CCSS.MATH.CONTENT.4.NF.B.4.CSolve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
How to use them
- Teach from the chart, then use Fractions as Multiples of Unit Fractions.
- Use the fraction bar and number line pages to build the idea of equal groups.
- Practice with Sheet A, then Sheet B with mixed numbers.
- Finish with the word problems.
Teaching tips
- Read 4 × 3/4 as 4 groups of 3 fourths.
- The denominator does not change because the parts stay the same size.
- Ask children to estimate first: 5 × 3/8 is a bit less than 2.
Questions teachers and parents ask
How do you multiply a fraction by a whole number?
Multiply the whole number by the numerator and keep the denominator. 4 × 2/3 = 8/3, which is 2 2/3.
Do 4th graders multiply two fractions?
No. In 4th grade one factor is a whole number. Multiplying a fraction by a fraction comes in 5th grade.