Multiplying Fraction by Whole Numbers Worksheet with Solutions

Complete practice worksheet for multiplying fractions by whole numbers with detailed step-by-step solutions for 4th grade math students.

Worksheet Solutions: Problems 1 to 3
1 Basic Multiplication
Problem 1
Multiply 2/5 × 3
Definition:

Fraction by whole number multiplication: Multiply the numerator of the fraction by the whole number, keeping the denominator the same.

Multiplication method:
  1. Write the whole number as a fraction over 1 (3 = 3/1)
  2. Multiply the numerators together
  3. Multiply the denominators together
  4. Simplify the result if possible
Step 1
2/5 × 3/1
Step 2
2 × 3 = 6
Step 3
5 × 1 = 5
Result
6/5
Step 1: Write whole number as fraction

2/5 × 3 = 2/5 × 3/1

Step 2: Multiply numerators

2 × 3 = 6

Step 3: Multiply denominators

5 × 1 = 5

Step 4: Write result

6/5

Step 5: Convert to mixed number if needed

6/5 = 1 1/5

2/5 × 3 = 6/5 = 1 1/5
Final answer:

2/5 × 3 = 6/5 or 1 1/5

Applied rules:

• Whole number conversion: Any whole number n = n/1

• Fraction multiplication: Multiply numerators and denominators separately

• Improper to mixed: Divide numerator by denominator

2 Intermediate Problem
Problem 2
Multiply 3/4 × 8 and simplify the result.
Definition:

Simplification: Reducing a fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor.

Multiply
3/4 × 8/1 = 24/4
Simplify
24/4 = 6
Step 1: Write whole number as fraction

3/4 × 8 = 3/4 × 8/1

Step 2: Multiply numerators and denominators

(3×8)/(4×1) = 24/4

Step 3: Simplify the fraction

24 ÷ 4 = 6, so 24/4 = 6

3/4 × 8 = 6
Final answer:

3/4 × 8 = 6

Applied rules:

• Multiplication rule: Multiply numerators and denominators

• Simplification: Divide both numerator and denominator by their GCD

• Whole number result: Sometimes the result is a whole number

3 Advanced Problem
Problem 3
Multiply 5/6 × 9 and express in simplest form.
Definition:

Simplest form: A fraction where the numerator and denominator have no common factors other than 1.

Multiply
5/6 × 9/1 = 45/6
Simplify
45/6 = 15/2 = 7 1/2
Step 1: Set up the multiplication

5/6 × 9 = 5/6 × 9/1

Step 2: Multiply numerators and denominators

(5×9)/(6×1) = 45/6

Step 3: Simplify the fraction

GCD of 45 and 6 is 3, so 45/6 = 15/2

Step 4: Convert to mixed number

15 ÷ 2 = 7 remainder 1, so 15/2 = 7 1/2

5/6 × 9 = 7 1/2
Final answer:

5/6 × 9 = 7 1/2

Applied rules:

• Greatest common divisor: Find largest number that divides both numerator and denominator

• Simplification: Divide both by GCD to get simplest form

• Mixed number conversion: Divide numerator by denominator

Worksheet Concepts & Rules
\(\frac{a}{b} \times n = \frac{a \times n}{b}\)
Fraction × Whole Number
Rule 1
\(\frac{a}{b} \times n = \frac{an}{b}\)
Multiply numerator by whole number
Rule 2
\(\frac{a}{b} \times \frac{n}{1} = \frac{an}{b}\)
Convert whole to fraction
Rule 3
\(\frac{an}{b} = q + \frac{r}{b}\)
Convert to mixed number
Key definitions:

Fraction multiplication by whole number: The process of scaling a fraction by a whole number, which is equivalent to repeated addition of the fraction.

Numerator: The top number in a fraction, representing the number of parts taken.

Denominator: The bottom number in a fraction, representing the total number of equal parts.

Greatest Common Divisor (GCD): The largest positive integer that divides both the numerator and denominator without remainder.

Complete multiplication process:
  1. Convert: Write the whole number as a fraction over 1
  2. Multiply: Multiply the numerators together
  3. Multiply: Multiply the denominators together
  4. Simplify: Reduce to lowest terms if possible
  5. Convert: Change to mixed number if needed
Tip 1: Always convert the whole number to a fraction first.
Tip 2: Look for common factors before multiplying to simplify calculations.
Tip 3: Check if the result can be simplified by finding the GCD.
Tip 4: Practice converting between improper and mixed numbers regularly.
Common errors: Forgetting to multiply the denominator by 1, not simplifying the final answer, arithmetic mistakes, misplacing decimal points.
Worksheet strategies: Box your final answers, show all work clearly, double-check calculations, verify that answers are in simplest form.
Worksheet Solutions: Problems 4 to 5
4 Complex Problem
Problem 4
Multiply 7/8 × 12 and express in simplest form.
Definition:

Complex multiplication: Problems with larger numbers that require careful arithmetic and simplification.

Multiply
7/8 × 12/1 = 84/8
Simplify
84/8 = 21/2 = 10 1/2
Step 1: Set up the multiplication

7/8 × 12 = 7/8 × 12/1

Step 2: Multiply numerators and denominators

(7×12)/(8×1) = 84/8

Step 3: Simplify the fraction

GCD of 84 and 8 is 4, so 84/8 = 21/2

Step 4: Convert to mixed number

21 ÷ 2 = 10 remainder 1, so 21/2 = 10 1/2

7/8 × 12 = 10 1/2
Final answer:

7/8 × 12 = 10 1/2

Applied rules:

• Large number multiplication: Same rules apply regardless of size

• GCD simplification: Find largest common factor

• Mixed number conversion: Divide to convert

5 Challenge Problem
Problem 5
Multiply 9/10 × 15 and express in simplest form.
Definition:

Challenge problem: More complex problems that require multiple steps and careful attention to detail.

Multiply
9/10 × 15/1 = 135/10
Simplify
135/10 = 27/2 = 13 1/2
Step 1: Set up the multiplication

9/10 × 15 = 9/10 × 15/1

Step 2: Multiply numerators and denominators

(9×15)/(10×1) = 135/10

Step 3: Simplify the fraction

GCD of 135 and 10 is 5, so 135/10 = 27/2

Step 4: Convert to mixed number

27 ÷ 2 = 13 remainder 1, so 27/2 = 13 1/2

9/10 × 15 = 13 1/2
Final answer:

9/10 × 15 = 13 1/2

Applied rules:

• Systematic approach: Same method for all problems

• Verification: Double-check calculations with large numbers

• Final form: Express in required format

Worksheet Summary: Key Concepts & Formulas
\(\text{Fraction} \times \text{Whole Number} \rightarrow \text{Scaled Fraction}\)
Concept Overview
Key definitions:

Fraction multiplication by whole number: The process of scaling a fraction by a whole number, which is equivalent to repeated addition of the fraction.

Improper fraction: A fraction where the numerator is greater than or equal to the denominator.

Mixed number: A number consisting of a whole number and a proper fraction.

Simplification: Reducing a fraction to its lowest terms by dividing both numerator and denominator by their GCD.

Complete worksheet methodology:
  1. Read carefully: Identify the fraction and whole number
  2. Convert: Write the whole number as a fraction over 1
  3. Multiply: Apply the multiplication rule
  4. Simplify: Reduce to lowest terms if possible
  5. Convert: Change to mixed number if required
  6. Verify: Check your work and ensure proper form
Tip 1: Always convert the whole number to a fraction first.
Tip 2: Look for opportunities to simplify before multiplying.
Tip 3: Practice converting between improper and mixed numbers regularly.
Tip 4: Show all work clearly to avoid mistakes and make corrections easier.
Common errors: Forgetting to multiply the denominator by 1, not simplifying the final answer, arithmetic mistakes, misplacing decimal points.
Worksheet success strategies: Box your final answers, check your work, use scratch paper for complex calculations, read instructions carefully.
Key multiplication principles:

• Conversion rule: Any whole number n = n/1

• Multiplication rule: Multiply numerator by whole number, keep denominator

• Simplification rule: Always reduce to lowest terms

• Conversion rule: Convert improper fractions to mixed numbers when appropriate

• Verification: Check that your answer makes sense in context

Worksheet Success Guide

📋
Worksheet Process

1. Read the problem carefully

2. Identify the fraction and whole number

3. Convert whole number to fraction

4. Multiply numerators and denominators

5. Simplify if possible

6. Convert to mixed number if needed

7. Box your final answer

Key Formula

a/b × n = (a × n)/b

Example: 2/3 × 4 = 8/3 = 2 2/3

Worksheet Workflow
1
Identify
2
Convert
3
Multiply
4
Simplify
5
Convert
6
Check
Worksheet Practice Tips

• Show all work

• Box final answers

• Check for simplification

• Verify with estimation

📚 Practice Makes Perfect!

Worksheet Questions & Answers

Question: Why do I need to convert the whole number to a fraction? Can't I just multiply the numerator by the whole number?

Answer: Technically, you can think of it as multiplying the numerator by the whole number, but converting to a fraction helps you understand the concept:

  • It maintains the same rule for all fraction multiplication
  • It helps you remember that you're multiplying both parts of the fraction relationship
  • It prepares you for more complex problems involving fractions

Example: 2/3 × 4 can be thought of as 2/3 × 4/1, which equals (2×4)/(3×1) = 8/3. This is the same as multiplying the numerator by the whole number.

Question: My child sometimes gets very large numbers after multiplying. How do I help them simplify?

Answer: Here are strategies to help with simplification:

  • Look for common factors of 2, 3, 5, or 10 first
  • Use divisibility rules (numbers ending in 0 or 5 are divisible by 5)
  • Break down the numbers into prime factors
  • Practice with smaller numbers first to build confidence

Example: For 24/8, both numbers are divisible by 8, so 24/8 = 3. For 45/6, both are divisible by 3, so 45/6 = 15/2.

Question: What if my answer is a whole number? Do I need to write it as a fraction?

Answer: No, if your answer is a whole number, you can write it as a whole number. For example:

  • If you get 24/4, that simplifies to 6
  • You can write the answer as 6, not 6/1
  • Only write it as a fraction if the problem specifically asks for it

Example: 3/4 × 8 = 24/4 = 6. The final answer is just 6.

However, if the problem asks for the answer as a mixed number and you have a whole number, you can write it as the whole number (like 6) or as a mixed number with 0 fractional part (like 6 0/1, though this is unnecessary).