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Multiplying Fractions by Whole NumbersFREEWorksheet Generator(Grade 4)

Multiplying Fractions by Whole Numbers worksheets (Grade 4) with step-by-step answer keys. Generate unlimited practice sheets with fresh problems.

Level:
Set:
Count:
Set A โ€ข 10 Qs
PanMaths.comMultiplying Fractions by Whole Numbers Worksheets โ€ข Set A (Medium)
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 10
1.9ร—49
= ย ______
Workspace:
2.78ร—9
= ย ______
Workspace:
3.34ร—3
= ย ______
Workspace:
4.3ร—37
= ย ______
Workspace:
5.8ร—19
= ย ______
Workspace:
6.2ร—39
= ย ______
Workspace:
7.57ร—8
= ย ______
Workspace:
8.3ร—1011
= ย ______
Workspace:
9.2ร—26
= ย ______
Workspace:
10.2ร—24
= ย ______
Workspace:
PanMaths.com โ€ข Free Math Worksheet Generator โ€ข Set A (Medium)Page 1 of 2
PanMaths.comAnswer Key & Worked Solutions โ€ข Set A (Medium)
Answer Key
Total Problems: 10
1.9ร—49
= 4
1. Express Whole Number as Fraction: 9 = 9/1
2. Multiply Numerators & Denominators: (9 ร— 4) / (1 ร— 9) = 36/9
3. Reduce by GCD (9): 4/1
4. Final Product: 4
2.78ร—9
= 7 7/8
1. Express Whole Number as Fraction: 9 = 9/1
2. Multiply Numerators & Denominators: (9 ร— 7) / (1 ร— 8) = 63/8
3. Form Lowest Terms: 63/8
4. Convert to Mixed Number: 7 7/8
3.34ร—3
= 2 1/4
1. Express Whole Number as Fraction: 3 = 3/1
2. Multiply Numerators & Denominators: (3 ร— 3) / (1 ร— 4) = 9/4
3. Form Lowest Terms: 9/4
4. Convert to Mixed Number: 2 1/4
4.3ร—37
= 1 2/7
1. Express Whole Number as Fraction: 3 = 3/1
2. Multiply Numerators & Denominators: (3 ร— 3) / (1 ร— 7) = 9/7
3. Form Lowest Terms: 9/7
4. Convert to Mixed Number: 1 2/7
5.8ร—19
= 8/9
1. Express Whole Number as Fraction: 8 = 8/1
2. Multiply Numerators & Denominators: (8 ร— 1) / (1 ร— 9) = 8/9
3. Form Lowest Terms: 8/9
4. Final Product: 8/9
6.2ร—39
= 2/3
1. Express Whole Number as Fraction: 2 = 2/1
2. Multiply Numerators & Denominators: (2 ร— 3) / (1 ร— 9) = 6/9
3. Reduce by GCD (3): 2/3
4. Final Product: 2/3
7.57ร—8
= 5 5/7
1. Express Whole Number as Fraction: 8 = 8/1
2. Multiply Numerators & Denominators: (8 ร— 5) / (1 ร— 7) = 40/7
3. Form Lowest Terms: 40/7
4. Convert to Mixed Number: 5 5/7
8.3ร—1011
= 2 8/11
1. Express Whole Number as Fraction: 3 = 3/1
2. Multiply Numerators & Denominators: (3 ร— 10) / (1 ร— 11) = 30/11
3. Form Lowest Terms: 30/11
4. Convert to Mixed Number: 2 8/11
9.2ร—26
= 2/3
1. Express Whole Number as Fraction: 2 = 2/1
2. Multiply Numerators & Denominators: (2 ร— 2) / (1 ร— 6) = 4/6
3. Reduce by GCD (2): 2/3
4. Final Product: 2/3
10.2ร—24
= 1
1. Express Whole Number as Fraction: 2 = 2/1
2. Multiply Numerators & Denominators: (2 ร— 2) / (1 ร— 4) = 4/4
3. Reduce by GCD (4): 1/1
4. Final Product: 1
PanMaths.com โ€ข Answer Key & Worked SolutionsPage 2 of 2
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Worksheet Info

Categorygrade-4
Grade LevelGrade 4
DifficultyEasy, Medium, Hard, Sprint
Time5-10 min
CCSS CodeCCSS.MATH.CONTENT.4.NF.B.4

Skills Practiced

  • โœ“ Multiplying Fractions by Whole Numbers

Key Strategies

  • ๐Ÿ” Repeated Addition Model: Think of whole ร— fraction as repeated copies of the fraction: 3 ร— (2/5) = 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5.
  • โœ–๏ธ Multiply Whole by Numerator: Express the whole number as a fraction over 1: w ร— (a/b) = (w/1) ร— (a/b) = (w ร— a)/b. Only the numerator is multiplied by the whole number.
  • ๐Ÿงฑ Unit Fraction Decomposition: Recognize that a/b is a ร— (1/b). Therefore, n ร— (a/b) = n ร— (a ร— 1/b) = (n ร— a) ร— (1/b) (e.g., 5 ร— 3/8 = 15 ร— 1/8 = 15/8).
  • ๐Ÿ”„ Convert Improper Products to Mixed Numbers: When the product (w ร— a)/b has a numerator greater than the denominator, divide to find the whole number and fractional remainder in simplest form.
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Related Worksheets

๐Ÿ“œ Standard: CCSS.MATH.CONTENT.4.NF.B.4๐Ÿ”— CCSS.MATH.CONTENT.4.NF.B.4.A๐Ÿ”— CCSS.MATH.CONTENT.4.NF.B.4.B๐Ÿ”— CCSS.MATH.CONTENT.4.NF.B.4.C

Mastering Multiplying Fractions by Whole Numbers: Core Concepts & Mental Models

Multiplying a fraction by a whole number connects whole number multiplication to fractional amounts. Under CCSS 4.NF.B.4, students learn that a fraction multiple like 4 ร— (2/3) represents 4 groups of 2/3, which is 8 groups of the unit fraction 1/3 (8/3 = 2 2/3).

Worked Example & SolutionTeacher Step-by-Step Method
๐Ÿ“ Problem: Solve: 4 ร— 2/5.
Worked Solution: 1. Express whole number as fraction: 4 = 4/1. 2. Multiply numerators and denominators: (4 ร— 2) / (1 ร— 5) = 8/5. 3. Convert improper fraction to mixed number: 8 รท 5 = 1 with a remainder of 3 โ†’ 1 3/5. Result = 1 3/5.

๐Ÿ’ก Essential Strategies for Multiplying Fractions by Whole Numbers

๐Ÿ” Repeated Addition Model

Think of whole ร— fraction as repeated copies of the fraction: 3 ร— (2/5) = 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5.

โœ–๏ธ Multiply Whole by Numerator

Express the whole number as a fraction over 1: w ร— (a/b) = (w/1) ร— (a/b) = (w ร— a)/b. Only the numerator is multiplied by the whole number.

๐Ÿงฑ Unit Fraction Decomposition

Recognize that a/b is a ร— (1/b). Therefore, n ร— (a/b) = n ร— (a ร— 1/b) = (n ร— a) ร— (1/b) (e.g., 5 ร— 3/8 = 15 ร— 1/8 = 15/8).

๐Ÿ”„ Convert Improper Products to Mixed Numbers

When the product (w ร— a)/b has a numerator greater than the denominator, divide to find the whole number and fractional remainder in simplest form.

โš ๏ธ Common Mistakes & Teacher Fixes

โš ๏ธMultiplying both the numerator and the denominator by the whole number

Why students stumble: Confusing multiplying by a whole with finding an equivalent fraction (e.g., thinking 3 ร— 1/4 = 3/12).

Teacher Fix: Express the whole number as w/1. When you multiply across, the denominator is multiplied by 1, so it remains unchanged.
Example: 3 ร— 1/4 = (3 ร— 1)/(1 ร— 4) = 3/4, not 3/12.
โš ๏ธAdding the whole number to the fraction numerator instead of multiplying

Why students stumble: Confusing mixed number notation (3 1/2) with multiplication (3 ร— 1/2).

Teacher Fix: Multiplication means groups of: 3 ร— 1/2 means three halves (3/2 = 1 1/2), not 3 + 1/2 = 3 1/2.
Example: 3 ร— 1/2 = 3/2 = 1 1/2.
โš ๏ธLeaving improper answers without converting to mixed numbers or simplifying

Why students stumble: Stopping at the raw product (e.g., leaving 8/4 instead of converting to 2).

Teacher Fix: Always divide the numerator by denominator to determine if the product equals an exact integer or a mixed number in lowest terms.
Example: 8/4 = 2; 7/4 = 1 3/4.

๐Ÿ“– Key Mathematical Vocabulary

Whole Number

A positive integer without fractions or decimals (such as 1, 2, 3, 4, ...).

Multiple of a Fraction

The product obtained by multiplying a fraction by a whole number (e.g., 2/5, 4/5, 6/5 are multiples of 2/5).

Unit Fraction Scaling

Representing non-unit fractions and their multiples as repeated groups of 1/d.

Simplest Mixed Number

A mixed number where the proper fraction part has no common factors other than 1 between numerator and denominator.

โ“ Frequently Asked Questions

How do you solve a multiplying fractions by whole numbers problem step by step?

Here is a worked example: "Solve: 4 ร— 2/5.". Solution: 1. Express whole number as fraction: 4 = 4/1. 2. Multiply numerators and denominators: (4 ร— 2) / (1 ร— 5) = 8/5. 3. Convert improper fraction to mixed number: 8 รท 5 = 1 with a remainder of 3 โ†’ 1 3/5. Result = 1 3/5.

What is the core learning objective for multiplying fractions by whole numbers?

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number, expressing n ร— (a/b) as (n ร— a)/b and interpreting the product as repeated addition or scaling of unit fractions. This directly aligns with Common Core Standard CCSS.MATH.CONTENT.4.NF.B.4.

What is the most common mistake students make with multiplying fractions by whole numbers?

A frequent pitfall is: "Multiplying both the numerator and the denominator by the whole number". Why students stumble: Confusing multiplying by a whole with finding an equivalent fraction (e.g., thinking 3 ร— 1/4 = 3/12). How to fix it: Express the whole number as w/1. When you multiply across, the denominator is multiplied by 1, so it remains unchanged. (Example: 3 ร— 1/4 = (3 ร— 1)/(1 ร— 4) = 3/4, not 3/12.)

How does the unlimited multiplying fractions by whole numbers worksheet generator work?

Every click of 'Generate New Worksheet' creates a completely fresh set of multiplying fractions by whole numbers problems with unique numbers. No two worksheets are ever the same โ€” perfect for daily practice, homework variety, and preventing student copying. You can also customize the problem count (6, 8, 10, 12, 15, or 20 problems per sheet).

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Yes! Every single worksheet on PanMaths is 100% free with no sign-up needed. Each sheet includes a dedicated Answer Key on Page 2 with step-by-step intermediate evaluation lines for 1-minute grading.