4.NF.4: Multiplying Fractions by Whole Numbers

Visual Models for Multiplying Fractions by Whole Numbers

1. Number Line Model

Use a number line to show repeated jumps of the same fraction. For example, to show 3 × 2/5, start at 0 and make 3 jumps of 2/5 each to land at 6/5.

2. Area Model

Use rectangles to represent multiplication of fractions by whole numbers. For example, to show 4 × 1/3, draw 4 rectangles, each divided into thirds with one-third shaded. Count the total number of shaded pieces (4) and the total number of pieces (12) to get 4/12 = 1/3.

3. Fraction Strips

Use fraction strips to show repeated addition of the same fraction. For example, to show 5 × 1/4, line up 5 strips, each with 1/4 shaded, to see that the total shaded area is 5/4.

Strategies for Multiplying Fractions by Whole Numbers

1. Repeated Addition

Show that multiplying a fraction by a whole number is the same as adding that fraction multiple times.

Example: 3 × 2/7

• This means 2/7 + 2/7 + 2/7
• When adding fractions with the same denominator, add the numerators: 2 + 2 + 2 = 6
• Keep the denominator the same: 6/7
• So 3 × 2/7 = 6/7

2. Multiplication Property

Multiply the numerator by the whole number and keep the denominator the same.

Example: 4 × 3/8

• Multiply the numerator by the whole number: 4 × 3 = 12
• Keep the denominator the same: 8
• So 4 × 3/8 = 12/8 = 3/2 or 1 1/2

Everyday Applications

1. Cooking and Recipes

Apply fraction multiplication when adjusting recipes:

• If a recipe calls for 1/3 cup of oil and you're making 4 batches, how much oil do you need? (4 × 1/3 = 4/3 cups = 1 1/3 cups)
• If each serving needs 1/4 teaspoon of salt and you're making 6 servings, how much salt do you need? (6 × 1/4 = 6/4 = 1 1/2 teaspoons)

2. Crafts and Construction

Apply fraction multiplication when working with measurements:

• If each picture frame needs 2/3 yard of trim and you're making 5 frames, how much trim do you need? (5 × 2/3 = 10/3 = 3 1/3 yards)
• If each bookshelf needs 3/4 gallon of paint and you're building 3 bookshelves, how much paint do you need? (3 × 3/4 = 9/4 = 2 1/4 gallons)

3. Time Management

Apply fraction multiplication when planning activities:

• If each math problem takes 1/6 hour to solve and you have 8 problems, how much time do you need? (8 × 1/6 = 8/6 = 1 1/3 hours)
• If each chore takes 1/5 of an hour and you have 7 chores, how much time will all the chores take? (7 × 1/5 = 7/5 = 1 2/5 hours)

When Your Child Struggles

1. Connect to Repeated Addition

If your child is having trouble understanding fraction multiplication, start with the concept of repeated addition. Show them that 3 × 2/5 means 2/5 + 2/5 + 2/5. This builds on their existing understanding of multiplication as repeated addition.

2. Use Visual Models

Draw pictures or use manipulatives to represent the multiplication. For example, to show 4 × 1/3, draw 4 circles, each divided into thirds with one-third shaded. Count the total number of shaded pieces to find the answer.

3. Start with Unit Fractions

Begin with multiplying whole numbers by unit fractions (fractions with numerator 1) before moving on to other fractions. For example, practice 3 × 1/4 before trying 3 × 2/4.

4. Simplify After Multiplying

Remind your child to simplify their answers when possible. For example, 3 × 2/6 = 6/6 = 1.

5. Convert to Mixed Numbers

When the answer is an improper fraction (numerator larger than denominator), help your child convert it to a mixed number. For example, 4 × 3/5 = 12/5 = 2 2/5.

5-Minute Activities

Activity 1: Fraction Multiplication Cards

Create cards with whole numbers (2-6) and cards with fractions (1/2, 1/3, 1/4, 2/3, 3/4). Have your child draw one card from each pile and multiply them. For added challenge, include fractions with larger numerators.

Activity 2: Real-World Multiplication

Give your child real-world scenarios that involve multiplying fractions by whole numbers:

• "If each friend gets 1/4 of a pizza and there are 5 friends, how much pizza do you need?"
• "If each plant needs 1/3 cup of water and you have 6 plants, how much water do you need?"

Activity 3: Draw and Solve

Give your child a multiplication problem like 3 × 2/5 and ask them to draw a picture to solve it. They can use number lines, area models, or any other visual representation that makes sense to them.

Activity 4: Equivalent Expressions

Write a fraction multiplication problem like 4 × 3/8 and ask your child to write it as a repeated addition expression (3/8 + 3/8 + 3/8 + 3/8). Then have them solve it both ways to show that they get the same answer.

Mid-Year Expectations

By the middle of the school year, your child should be able to:

• Understand that multiplying a fraction by a whole number is like repeated addition of that fraction
• Multiply a unit fraction (numerator of 1) by a whole number
• Represent fraction multiplication using visual models
• Solve simple word problems involving multiplication of fractions by whole numbers
• Convert improper fractions to mixed numbers

End-of-Year Expectations

By the end of the school year, your child should be able to:

• Multiply any fraction by a whole number fluently
• Use the rule: multiply the numerator by the whole number, keep the denominator the same
• Simplify fractions after multiplication
• Solve multi-step word problems involving multiplication of fractions by whole numbers
• Explain their reasoning when multiplying fractions by whole numbers

Signs of Mastery

Your child has mastered this standard when they can:

• Consistently and accurately multiply fractions by whole numbers
• Choose appropriate strategies for different types of fraction multiplication problems
• Represent fraction multiplication using multiple models (number lines, area models, etc.)
• Solve complex word problems involving multiplication of fractions by whole numbers
• Explain the relationship between repeated addition and multiplication of fractions
• Apply fraction multiplication concepts to solve real-world problems

Questions to Check Understanding:

• "What is 5 × 2/3? Can you show me using a visual model?"
• "How can you write 4 × 1/5 as a repeated addition problem?"
• "If each serving of cereal needs 2/3 cup of milk and you're making 4 servings, how much milk do you need?"
• "What happens to the numerator when you multiply a fraction by a whole number? What happens to the denominator?"

Below Grade Level

For students who need additional support with basic fraction concepts and simple fraction multiplication.

📥 Download Practice Worksheet

At Grade Level

For students who need practice with grade-level fraction multiplication concepts.

📥 Download Grade Level Worksheet

Above Grade Level

For students ready for more challenging fraction multiplication concepts and applications.

📥 Download Challenge Worksheet