# Teaching 4.NF.B.4 .a.b.c – Understand a Fraction a/b as a Multiple of 1/b – Multiply Fraction by a Whole Number

## Number & Operations – Fractions – 4th Grade

**Build fractions from unit fractions.**

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Understand 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)*.

Understand 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.)*

Solve 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?*

**Teacher Notes**

How does repeated addition of fractions relate to multiplication of a fraction by a whole number?

Fractions can be thought of as parts of a whole or as individual units. Multiplying a fraction by a whole number yields the number of unit fractions or individual units.

After teaching how multiplying is the same as repeated addition with fractions, explaining to students how multiplying a whole number by a fraction will always result in a lower whole number by using an example with half. Example: One half of four is two, correct? This is the same as one half times four which equals two.

**Student Knowledge Goals**

I know that adding unit fractions is the same as multiplying a unit fraction by a whole number.

I can explain how a fraction is a multiple of another fraction using models, drawings, or equations.

**Vocabulary**

No new vocabulary

**Lessons**

Engage NY Module 5 G-35 – Represent the multiplication of *n* times *a*/*b *as (*n *× *a)*/*b *using the associative property and visual models.

Engage NY Module 5 G-36 – Represent the multiplication of *n* times *a*/*b *as (*n *×* a*)/*b *using the associative property and visual models.

Engage NY Module 5 G-37 – Find the product of a whole number and a mixed number using the distributive property.

Engage NY Module 5 G-38 – Find the product of a whole number and a mixed number using the distributive property.

Engage NY Module 5 G-39 – Solve multiplicative comparison word problems involving fractions.

Engage NY Module 5 G-40 – Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.

Multiplying Fractions – Various Lessons

**Student Video Lessons**

Learn Zillion – Understand multiplication of fractions by whole numbers

Virtual Nerd – Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

**Online Problems and Assessments**

Khan Academy – Questions and Video Lessons

Multiply unit fractions by whole numbers using number lines

Multiply unit fractions and whole numbers: sorting

Multiply unit fractions by whole numbers

Multiply fractions by whole numbers using number lines

Multiply fractions and whole numbers: sorting

Multiply fractions by whole numbers

Multiply unit fractions by whole numbers: word problems

Multiply fractions by whole numbers: word problems

Multiply fractions and mixed numbers by whole numbers in recipes

** Online Games**

Multiply Fractions

**Printables**

Multiplying Fractions

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